TSTP Solution File: SWW654_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW654_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:34 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW654_2 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 20:46:55 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(lt_tree1_type, type, (
% 0.20/0.49 lt_tree1: ( $int * tree1 ) > $o)).
% 0.20/0.49 tff(node1_type, type, (
% 0.20/0.49 node1: ( color1 * tree1 * $int * $int * tree1 ) > tree1)).
% 0.20/0.49 tff(tptp_fun_X14_26_type, type, (
% 0.20/0.49 tptp_fun_X14_26: tree1)).
% 0.20/0.49 tff(node_proj_41_type, type, (
% 0.20/0.49 node_proj_41: tree1 > $int)).
% 0.20/0.49 tff(tptp_fun_X13_27_type, type, (
% 0.20/0.49 tptp_fun_X13_27: $int)).
% 0.20/0.49 tff(tptp_fun_X12_28_type, type, (
% 0.20/0.49 tptp_fun_X12_28: $int)).
% 0.20/0.49 tff(tptp_fun_X11_29_type, type, (
% 0.20/0.49 tptp_fun_X11_29: tree1)).
% 0.20/0.49 tff(tptp_fun_X10_30_type, type, (
% 0.20/0.49 tptp_fun_X10_30: color1)).
% 0.20/0.49 tff(node_proj_31_type, type, (
% 0.20/0.49 node_proj_31: tree1 > $int)).
% 0.20/0.49 tff(red1_type, type, (
% 0.20/0.49 red1: color1)).
% 0.20/0.49 tff(tptp_fun_X4_11_type, type, (
% 0.20/0.49 tptp_fun_X4_11: tree1)).
% 0.20/0.49 tff(tptp_fun_X3_12_type, type, (
% 0.20/0.49 tptp_fun_X3_12: $int)).
% 0.20/0.49 tff(tptp_fun_X2_13_type, type, (
% 0.20/0.49 tptp_fun_X2_13: $int)).
% 0.20/0.49 tff(tptp_fun_X1_14_type, type, (
% 0.20/0.49 tptp_fun_X1_14: tree1)).
% 0.20/0.49 tff(tptp_fun_X_15_type, type, (
% 0.20/0.49 tptp_fun_X_15: color1)).
% 0.20/0.49 tff(node_proj_51_type, type, (
% 0.20/0.49 node_proj_51: tree1 > tree1)).
% 0.20/0.49 tff(node_proj_21_type, type, (
% 0.20/0.49 node_proj_21: tree1 > tree1)).
% 0.20/0.49 tff(node_proj_11_type, type, (
% 0.20/0.49 node_proj_11: tree1 > color1)).
% 0.20/0.49 tff(leaf1_type, type, (
% 0.20/0.49 leaf1: tree1)).
% 0.20/0.49 tff(black1_type, type, (
% 0.20/0.49 black1: color1)).
% 0.20/0.49 tff(bst1_type, type, (
% 0.20/0.49 bst1: tree1 > $o)).
% 0.20/0.49 tff(tptp_fun_R_7_type, type, (
% 0.20/0.49 tptp_fun_R_7: tree1)).
% 0.20/0.49 tff(tptp_fun_V_8_type, type, (
% 0.20/0.49 tptp_fun_V_8: $int)).
% 0.20/0.49 tff(tptp_fun_K_9_type, type, (
% 0.20/0.49 tptp_fun_K_9: $int)).
% 0.20/0.49 tff(tptp_fun_X9_21_type, type, (
% 0.20/0.49 tptp_fun_X9_21: tree1)).
% 0.20/0.49 tff(tptp_fun_X8_22_type, type, (
% 0.20/0.49 tptp_fun_X8_22: $int)).
% 0.20/0.49 tff(tptp_fun_X7_23_type, type, (
% 0.20/0.49 tptp_fun_X7_23: $int)).
% 0.20/0.49 tff(tptp_fun_X6_24_type, type, (
% 0.20/0.49 tptp_fun_X6_24: tree1)).
% 0.20/0.49 tff(gt_tree1_type, type, (
% 0.20/0.49 gt_tree1: ( $int * tree1 ) > $o)).
% 0.20/0.49 tff(tptp_fun_X5_25_type, type, (
% 0.20/0.49 tptp_fun_X5_25: color1)).
% 0.20/0.49 tff(tptp_fun_X14_31_type, type, (
% 0.20/0.49 tptp_fun_X14_31: tree1)).
% 0.20/0.49 tff(tptp_fun_X13_32_type, type, (
% 0.20/0.49 tptp_fun_X13_32: $int)).
% 0.20/0.49 tff(tptp_fun_X12_33_type, type, (
% 0.20/0.49 tptp_fun_X12_33: $int)).
% 0.20/0.49 tff(tptp_fun_X11_34_type, type, (
% 0.20/0.49 tptp_fun_X11_34: tree1)).
% 0.20/0.49 tff(tptp_fun_X10_35_type, type, (
% 0.20/0.49 tptp_fun_X10_35: color1)).
% 0.20/0.49 tff(tptp_fun_X9_16_type, type, (
% 0.20/0.49 tptp_fun_X9_16: tree1)).
% 0.20/0.49 tff(tptp_fun_X8_17_type, type, (
% 0.20/0.49 tptp_fun_X8_17: $int)).
% 0.20/0.49 tff(tptp_fun_X7_18_type, type, (
% 0.20/0.49 tptp_fun_X7_18: $int)).
% 0.20/0.49 tff(tptp_fun_X6_19_type, type, (
% 0.20/0.49 tptp_fun_X6_19: tree1)).
% 0.20/0.49 tff(tptp_fun_X5_20_type, type, (
% 0.20/0.49 tptp_fun_X5_20: color1)).
% 0.20/0.49 tff(tptp_fun_L_10_type, type, (
% 0.20/0.49 tptp_fun_L_10: tree1)).
% 0.20/0.49 tff(1,plain,
% 0.20/0.49 ((leaf1 = X1!14) <=> (X1!14 = leaf1)),
% 0.20/0.49 inference(commutativity,[status(thm)],[])).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (^[X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : refl((bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1))))) <=> (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1))))) <=> ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (^[X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : rewrite((bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4))) <=> (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4))) <=> ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.49 tff(6,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4))) <=> ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (^[X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : rewrite((bst1(node1(X, X1, X2, X3, X4)) <=> (((bst1(X1) & bst1(X4)) & lt_tree1(X2, X1)) & gt_tree1(X2, X4))) <=> (bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (((bst1(X1) & bst1(X4)) & lt_tree1(X2, X1)) & gt_tree1(X2, X4))) <=> ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.49 tff(9,axiom,(bst1(leaf1) & ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (((bst1(X1) & bst1(X4)) & lt_tree1(X2, X1)) & gt_tree1(X2, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bst_def')).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (((bst1(X1) & bst1(X4)) & lt_tree1(X2, X1)) & gt_tree1(X2, X4)))),
% 0.20/0.49 inference(and_elim,[status(thm)],[9])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[10, 8])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.20/0.49 tff(13,plain,(
% 0.20/0.49 ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (bst1(X1) & bst1(X4) & lt_tree1(X2, X1) & gt_tree1(X2, X4)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[12])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[14, 3])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 ((bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24)))))) <=> (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(18,plain,
% 0.20/0.50 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[21, 15])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : refl(($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0) <=> ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : trans(monotonicity(rewrite($sum(node_proj_41(node1(U, U1, U2, U3, U4)), $product(-1, U3)) = $sum($product(-1, U3), node_proj_41(node1(U, U1, U2, U3, U4)))), (($sum(node_proj_41(node1(U, U1, U2, U3, U4)), $product(-1, U3)) = 0) <=> ($sum($product(-1, U3), node_proj_41(node1(U, U1, U2, U3, U4))) = 0))), rewrite(($sum($product(-1, U3), node_proj_41(node1(U, U1, U2, U3, U4))) = 0) <=> ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)), (($sum(node_proj_41(node1(U, U1, U2, U3, U4)), $product(-1, U3)) = 0) <=> ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(node_proj_41(node1(U, U1, U2, U3, U4)), $product(-1, U3)) = 0) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : rewrite((node_proj_41(node1(U, U1, U2, U3, U4)) = U3) <=> ($sum(node_proj_41(node1(U, U1, U2, U3, U4)), $product(-1, U3)) = 0))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_41(node1(U, U1, U2, U3, U4)) = U3) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(node_proj_41(node1(U, U1, U2, U3, U4)), $product(-1, U3)) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_41(node1(U, U1, U2, U3, U4)) = U3) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_41(node1(U, U1, U2, U3, U4)) = U3)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(30,axiom,(![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_41(node1(U, U1, U2, U3, U4)) = U3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','node_proj_4_def')).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_41(node1(U, U1, U2, U3, U4)) = U3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(node_proj_41(node1(U, U1, U2, U3, U4)), $product(-1, U3)) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.20/0.50 tff(34,plain,(
% 0.20/0.50 ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(skolemize,[status(sab)],[33])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X8!22, $product(-1, node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)))) = 0)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 ($sum(X8!22, $product(-1, node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 ((~($sum(X8!22, $product(-1, node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)))) = 0)) | $lesseq($sum(X8!22, $product(-1, node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 ($lesseq($sum(X8!22, $product(-1, node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 ((~($sum(X8!22, $product(-1, node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)))) = 0)) | $greatereq($sum(X8!22, $product(-1, node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 ($greatereq($sum(X8!22, $product(-1, node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (X8!22 = node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[41, 39])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)) = X8!22),
% 0.20/0.50 inference(symmetry,[status(thm)],[42])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : refl((node_proj_51(node1(U, U1, U2, U3, U4)) = U4) <=> (node_proj_51(node1(U, U1, U2, U3, U4)) = U4))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(47,axiom,(![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','node_proj_5_def')).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.50 tff(49,plain,(
% 0.20/0.50 ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)),
% 0.20/0.50 inference(skolemize,[status(sab)],[48])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)) | (node_proj_51(node1(black1, X6!19, X7!18, X8!17, X9!16)) = X9!16)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 (node_proj_51(node1(black1, X6!19, X7!18, X8!17, X9!16)) = X9!16),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X8!17, $product(-1, node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)))) = 0)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 ($sum(X8!17, $product(-1, node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[53, 35])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 ((~($sum(X8!17, $product(-1, node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)))) = 0)) | $lesseq($sum(X8!17, $product(-1, node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 ($lesseq($sum(X8!17, $product(-1, node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 ((~($sum(X8!17, $product(-1, node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)))) = 0)) | $greatereq($sum(X8!17, $product(-1, node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 ($greatereq($sum(X8!17, $product(-1, node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 (X8!17 = node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[58, 56])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 (node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)) = X8!17),
% 0.20/0.50 inference(symmetry,[status(thm)],[59])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : refl(($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0) <=> ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : trans(monotonicity(rewrite($sum(node_proj_31(node1(U, U1, U2, U3, U4)), $product(-1, U2)) = $sum($product(-1, U2), node_proj_31(node1(U, U1, U2, U3, U4)))), (($sum(node_proj_31(node1(U, U1, U2, U3, U4)), $product(-1, U2)) = 0) <=> ($sum($product(-1, U2), node_proj_31(node1(U, U1, U2, U3, U4))) = 0))), rewrite(($sum($product(-1, U2), node_proj_31(node1(U, U1, U2, U3, U4))) = 0) <=> ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)), (($sum(node_proj_31(node1(U, U1, U2, U3, U4)), $product(-1, U2)) = 0) <=> ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(node_proj_31(node1(U, U1, U2, U3, U4)), $product(-1, U2)) = 0) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : rewrite((node_proj_31(node1(U, U1, U2, U3, U4)) = U2) <=> ($sum(node_proj_31(node1(U, U1, U2, U3, U4)), $product(-1, U2)) = 0))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_31(node1(U, U1, U2, U3, U4)) = U2) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(node_proj_31(node1(U, U1, U2, U3, U4)), $product(-1, U2)) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_31(node1(U, U1, U2, U3, U4)) = U2) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_31(node1(U, U1, U2, U3, U4)) = U2)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(68,axiom,(![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_31(node1(U, U1, U2, U3, U4)) = U2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','node_proj_3_def')).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_31(node1(U, U1, U2, U3, U4)) = U2)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(node_proj_31(node1(U, U1, U2, U3, U4)), $product(-1, U2)) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[70, 64])).
% 0.20/0.50 tff(72,plain,(
% 0.20/0.50 ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(skolemize,[status(sab)],[71])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))) = 0)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 ($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 ((~($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))) = 0)) | $lesseq($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 ($lesseq($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 ((~($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))) = 0)) | $greatereq($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 ($greatereq($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 (X7!18 = node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[79, 77])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)) = X7!18),
% 0.20/0.50 inference(symmetry,[status(thm)],[80])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : refl((node_proj_21(node1(U, U1, U2, U3, U4)) = U1) <=> (node_proj_21(node1(U, U1, U2, U3, U4)) = U1))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(85,axiom,(![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','node_proj_2_def')).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.50 tff(87,plain,(
% 0.20/0.50 ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)),
% 0.20/0.50 inference(skolemize,[status(sab)],[86])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)) | (node_proj_21(node1(black1, X6!19, X7!18, X8!17, X9!16)) = X6!19)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 (node_proj_21(node1(black1, X6!19, X7!18, X8!17, X9!16)) = X6!19),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 (^[U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : refl((node_proj_11(node1(U, U1, U2, U3, U4)) = U) <=> (node_proj_11(node1(U, U1, U2, U3, U4)) = U))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U) <=> ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(94,axiom,(![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','node_proj_1_def')).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.51 tff(96,plain,(
% 0.20/0.51 ![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)),
% 0.20/0.51 inference(skolemize,[status(sab)],[95])).
% 0.20/0.51 tff(97,plain,
% 0.20/0.51 (![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)) | (node_proj_11(node1(black1, X6!19, X7!18, X8!17, X9!16)) = black1)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 (node_proj_11(node1(black1, X6!19, X7!18, X8!17, X9!16)) = black1),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 (node1(node_proj_11(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_21(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_51(node1(black1, X6!19, X7!18, X8!17, X9!16))) = node1(black1, X6!19, X7!18, X8!17, X9!16)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[99, 90, 81, 60, 52])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 (X9!16 = node_proj_51(node1(black1, X6!19, X7!18, X8!17, X9!16))),
% 0.20/0.51 inference(symmetry,[status(thm)],[52])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 (X6!19 = node_proj_21(node1(black1, X6!19, X7!18, X8!17, X9!16))),
% 0.20/0.51 inference(symmetry,[status(thm)],[90])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 (black1 = node_proj_11(node1(black1, X6!19, X7!18, X8!17, X9!16))),
% 0.20/0.51 inference(symmetry,[status(thm)],[99])).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 (node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16) = node1(node_proj_11(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_21(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_51(node1(black1, X6!19, X7!18, X8!17, X9!16)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[103, 102, 101])).
% 0.20/0.51 tff(105,plain,
% 0.20/0.51 (node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16) = node1(black1, X6!19, X7!18, X8!17, X9!16)),
% 0.20/0.51 inference(transitivity,[status(thm)],[104, 100])).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16)) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16))),
% 0.20/0.51 inference(symmetry,[status(thm)],[106])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) <=> (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 ((bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16)))))) <=> (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.52 tff(112,plain,
% 0.20/0.52 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[111, 109])).
% 0.20/0.52 tff(113,plain,
% 0.20/0.52 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(114,plain,
% 0.20/0.52 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.52 tff(115,plain,
% 0.20/0.52 (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[114, 15])).
% 0.20/0.52 tff(116,plain,
% 0.20/0.52 ((node1(black1, X4!11, K!9, V!8, R!7) = leaf1) <=> (leaf1 = node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.52 inference(commutativity,[status(thm)],[])).
% 0.20/0.52 tff(117,plain,
% 0.20/0.52 ((leaf1 = node1(black1, X4!11, K!9, V!8, R!7)) <=> (node1(black1, X4!11, K!9, V!8, R!7) = leaf1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[116])).
% 0.20/0.52 tff(118,plain,
% 0.20/0.52 ((~(leaf1 = node1(black1, X4!11, K!9, V!8, R!7))) <=> (~(node1(black1, X4!11, K!9, V!8, R!7) = leaf1))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.52 tff(119,plain,
% 0.20/0.52 (^[V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : refl((~(leaf1 = node1(V, V1, V2, V3, V4))) <=> (~(leaf1 = node1(V, V1, V2, V3, V4))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(120,plain,
% 0.20/0.52 (![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4))) <=> ![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.52 tff(121,plain,
% 0.20/0.52 (![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4))) <=> ![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(122,axiom,(![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','leaf_Node')).
% 0.20/0.52 tff(123,plain,
% 0.20/0.52 (![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.52 tff(124,plain,(
% 0.20/0.52 ![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[123])).
% 0.20/0.52 tff(125,plain,
% 0.20/0.52 (![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 ((~![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4)))) | (~(leaf1 = node1(black1, X4!11, K!9, V!8, R!7)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 (~(leaf1 = node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.52 tff(128,plain,
% 0.20/0.52 (~(node1(black1, X4!11, K!9, V!8, R!7) = leaf1)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[127, 118])).
% 0.20/0.52 tff(129,plain,
% 0.20/0.52 (^[U: tree1] : refl(((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U)))) <=> ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(130,plain,
% 0.20/0.52 (![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U)))) <=> ![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.52 tff(131,plain,
% 0.20/0.52 (![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U)))) <=> ![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(132,axiom,(![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','tree_inversion')).
% 0.20/0.52 tff(133,plain,
% 0.20/0.52 (![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.52 tff(134,plain,(
% 0.20/0.52 ![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[133])).
% 0.20/0.52 tff(135,plain,
% 0.20/0.52 (![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.20/0.52 tff(136,plain,
% 0.20/0.52 (((~![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))) | ((node1(black1, X4!11, K!9, V!8, R!7) = leaf1) | (node1(black1, X4!11, K!9, V!8, R!7) = node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))) <=> ((~![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))) | (node1(black1, X4!11, K!9, V!8, R!7) = leaf1) | (node1(black1, X4!11, K!9, V!8, R!7) = node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 ((~![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))) | ((node1(black1, X4!11, K!9, V!8, R!7) = leaf1) | (node1(black1, X4!11, K!9, V!8, R!7) = node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 ((~![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))) | (node1(black1, X4!11, K!9, V!8, R!7) = leaf1) | (node1(black1, X4!11, K!9, V!8, R!7) = node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.52 tff(139,plain,
% 0.20/0.52 ((node1(black1, X4!11, K!9, V!8, R!7) = leaf1) | (node1(black1, X4!11, K!9, V!8, R!7) = node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (node1(black1, X4!11, K!9, V!8, R!7) = node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[139, 128])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 (node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))) = node1(black1, X4!11, K!9, V!8, R!7)),
% 0.20/0.52 inference(symmetry,[status(thm)],[140])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X3!12, $product(-1, node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)))) = 0)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 ($sum(X3!12, $product(-1, node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)))) = 0),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[142, 35])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 ((~($sum(X3!12, $product(-1, node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)))) = 0)) | $lesseq($sum(X3!12, $product(-1, node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.20/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 ($lesseq($sum(X3!12, $product(-1, node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 ((~($sum(X3!12, $product(-1, node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)))) = 0)) | $greatereq($sum(X3!12, $product(-1, node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.20/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.52 tff(147,plain,
% 0.20/0.52 ($greatereq($sum(X3!12, $product(-1, node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[146, 143])).
% 0.20/0.53 tff(148,plain,
% 0.20/0.53 (X3!12 = node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[147, 145])).
% 0.20/0.53 tff(149,plain,
% 0.20/0.53 (node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)) = X3!12),
% 0.20/0.53 inference(symmetry,[status(thm)],[148])).
% 0.20/0.53 tff(150,plain,
% 0.20/0.53 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X2!13, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))) = 0)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(151,plain,
% 0.20/0.53 ($sum(X2!13, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))) = 0),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[150, 73])).
% 0.20/0.53 tff(152,plain,
% 0.20/0.53 ((~($sum(X2!13, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))) = 0)) | $lesseq($sum(X2!13, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(153,plain,
% 0.20/0.53 ($lesseq($sum(X2!13, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.53 tff(154,plain,
% 0.20/0.53 ((~($sum(X2!13, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))) = 0)) | $greatereq($sum(X2!13, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(155,plain,
% 0.20/0.53 ($greatereq($sum(X2!13, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[154, 151])).
% 0.20/0.53 tff(156,plain,
% 0.20/0.53 (X2!13 = node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[155, 153])).
% 0.20/0.53 tff(157,plain,
% 0.20/0.53 (node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)) = X2!13),
% 0.20/0.53 inference(symmetry,[status(thm)],[156])).
% 0.20/0.53 tff(158,plain,
% 0.20/0.53 (node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))) = node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[157, 149, 141])).
% 0.20/0.53 tff(159,plain,
% 0.20/0.53 (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.53 tff(160,plain,
% 0.20/0.53 (bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) <=> bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.20/0.53 inference(symmetry,[status(thm)],[159])).
% 0.20/0.53 tff(161,plain,
% 0.20/0.53 ((~bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))) <=> (~bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.53 tff(162,assumption,(~((~(X4!11 = leaf1)) | (~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16))))), introduced(assumption)).
% 0.20/0.53 tff(163,plain,
% 0.20/0.53 (((~(X4!11 = leaf1)) | (~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))) | (~bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(164,plain,
% 0.20/0.53 (~bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.20/0.53 tff(165,plain,
% 0.20/0.53 (~bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[164, 161])).
% 0.20/0.53 tff(166,plain,
% 0.20/0.53 ((~(bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))))) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | ((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(167,plain,
% 0.20/0.53 ((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[166, 165, 115])).
% 0.20/0.53 tff(168,plain,
% 0.20/0.53 (bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))) <=> bst1(node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.53 tff(169,plain,
% 0.20/0.53 (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.20/0.53 inference(symmetry,[status(thm)],[168])).
% 0.20/0.53 tff(170,plain,
% 0.20/0.53 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(171,plain,
% 0.20/0.53 ((bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X4!11)) | (~bst1(R!7)) | (~lt_tree1(K!9, X4!11))))) <=> (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(172,plain,
% 0.20/0.53 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X4!11)) | (~bst1(R!7)) | (~lt_tree1(K!9, X4!11)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.53 tff(173,plain,
% 0.20/0.53 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X4!11)) | (~bst1(R!7)) | (~lt_tree1(K!9, X4!11)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[172, 170])).
% 0.20/0.54 tff(174,plain,
% 0.20/0.54 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X4!11)) | (~bst1(R!7)) | (~lt_tree1(K!9, X4!11)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(175,plain,
% 0.20/0.54 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.54 tff(176,plain,
% 0.20/0.54 (bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[175, 15])).
% 0.20/0.54 tff(177,plain,
% 0.20/0.54 (((lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7)) & ((L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)) & (((X4!11 = leaf1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)) & (((X5!25 = red1) & ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) & ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))) | ((X5!25 = black1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))))) <=> (lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7) & (L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)) & (((X4!11 = leaf1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)) & (((X5!25 = red1) & ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) & ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))) | ((X5!25 = black1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(178,plain,
% 0.20/0.54 (((~(~(L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)))) & (((~(~(X4!11 = leaf1))) & (~(bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X!15 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((~(~(X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)))) & (((~(~(X5!25 = red1))) & ((~(bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X!15 = red1)) | (~(X1!14 = leaf1)))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | ((bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)) | (~(X!15 = red1))) & (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)) | (~(X!15 = red1)))))))) | ((~(~(X5!25 = black1))) & (~(bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X!15 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))))))))) <=> ((L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)) & (((X4!11 = leaf1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)) & (((X5!25 = red1) & ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) & ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))) | ((X5!25 = black1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(179,plain,
% 0.20/0.54 ((~(~(lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7)))) <=> (lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(180,plain,
% 0.20/0.54 (((~(~(lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7)))) & ((~(~(L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)))) & (((~(~(X4!11 = leaf1))) & (~(bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X!15 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((~(~(X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)))) & (((~(~(X5!25 = red1))) & ((~(bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X!15 = red1)) | (~(X1!14 = leaf1)))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | ((bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)) | (~(X!15 = red1))) & (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)) | (~(X!15 = red1)))))))) | ((~(~(X5!25 = black1))) & (~(bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X!15 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))))) <=> ((lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7)) & ((L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)) & (((X4!11 = leaf1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)) & (((X5!25 = red1) & ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) & ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))) | ((X5!25 = black1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))))))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[179, 178])).
% 0.20/0.54 tff(181,plain,
% 0.20/0.54 (((~(~(lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7)))) & ((~(~(L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)))) & (((~(~(X4!11 = leaf1))) & (~(bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X!15 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((~(~(X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)))) & (((~(~(X5!25 = red1))) & ((~(bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X!15 = red1)) | (~(X1!14 = leaf1)))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | ((bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)) | (~(X!15 = red1))) & (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)) | (~(X!15 = red1)))))))) | ((~(~(X5!25 = black1))) & (~(bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X!15 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))))) <=> (lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7) & (L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)) & (((X4!11 = leaf1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)) & (((X5!25 = red1) & ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) & ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))) | ((X5!25 = black1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[180, 177])).
% 0.20/0.54 tff(182,plain,
% 0.20/0.54 ((~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14))))))))))) <=> (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14)))))))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(183,plain,
% 0.20/0.55 ((~![L: tree1, K: $int, V: $int, R: tree1] : ((((lt_tree1(K, L) & gt_tree1(K, R)) & bst1(L)) & bst1(R)) => ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((L = node1(X, X1, X2, X3, X4)) => (((X4 = leaf1) => ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((X1 = node1(X5, X6, X7, X8, X9)) => ((X5 = red1) => ((X = red1) => bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((X4 = node1(X5, X6, X7, X8, X9)) => (((X5 = red1) => (((X1 = leaf1) => ((X = red1) => bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((X1 = node1(X10, X11, X12, X13, X14)) => (((X10 = red1) => ((X = red1) => bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))))) & ((X10 = black1) => ((X = red1) => bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))))))))) & ((X5 = black1) => ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((X1 = node1(X10, X11, X12, X13, X14)) => ((X10 = red1) => ((X = red1) => bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))))))))))))) <=> (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14)))))))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(184,axiom,(~![L: tree1, K: $int, V: $int, R: tree1] : ((((lt_tree1(K, L) & gt_tree1(K, R)) & bst1(L)) & bst1(R)) => ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((L = node1(X, X1, X2, X3, X4)) => (((X4 = leaf1) => ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((X1 = node1(X5, X6, X7, X8, X9)) => ((X5 = red1) => ((X = red1) => bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((X4 = node1(X5, X6, X7, X8, X9)) => (((X5 = red1) => (((X1 = leaf1) => ((X = red1) => bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((X1 = node1(X10, X11, X12, X13, X14)) => (((X10 = red1) => ((X = red1) => bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))))) & ((X10 = black1) => ((X = red1) => bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))))))))) & ((X5 = black1) => ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((X1 = node1(X10, X11, X12, X13, X14)) => ((X10 = red1) => ((X = red1) => bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_lbalance')).
% 0.20/0.55 tff(185,plain,
% 0.20/0.55 (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.55 tff(186,plain,
% 0.20/0.55 (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[185, 182])).
% 0.20/0.55 tff(187,plain,
% 0.20/0.55 (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.20/0.55 tff(188,plain,
% 0.20/0.55 (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[187, 182])).
% 0.20/0.55 tff(189,plain,
% 0.20/0.55 (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[188, 182])).
% 0.20/0.55 tff(190,plain,
% 0.20/0.55 (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.20/0.55 tff(191,plain,
% 0.20/0.55 (~![L: tree1, K: $int, V: $int, R: tree1] : ((~(lt_tree1(K, L) & gt_tree1(K, R) & bst1(L) & bst1(R))) | ![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : ((~(L = node1(X, X1, X2, X3, X4))) | (((~(X4 = leaf1)) | ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : (bst1(node1(red1, node1(black1, X6, X7, X8, X9), X2, X3, node1(black1, X4, K, V, R))) | (~(X5 = red1)) | (~(X = red1)) | (~(X1 = node1(X5, X6, X7, X8, X9))))) & ![X5: color1, X6: tree1, X7: $int, X8: $int, X9: tree1] : ((~(X4 = node1(X5, X6, X7, X8, X9))) | (((~(X5 = red1)) | ((bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X = red1)) | (~(X1 = leaf1))) & ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : ((~(X1 = node1(X10, X11, X12, X13, X14))) | ((bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1))) & (bst1(node1(red1, node1(black1, X1, X2, X3, X6), X7, X8, node1(black1, X9, K, V, R))) | (~(X10 = black1)) | (~(X = red1))))))) & ((~(X5 = black1)) | ![X10: color1, X11: tree1, X12: $int, X13: $int, X14: tree1] : (bst1(node1(red1, node1(black1, X11, X12, X13, X14), X2, X3, node1(black1, X4, K, V, R))) | (~(X10 = red1)) | (~(X = red1)) | (~(X1 = node1(X10, X11, X12, X13, X14))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[190, 182])).
% 0.20/0.55 tff(192,plain,
% 0.20/0.55 (lt_tree1(K!9, L!10) & gt_tree1(K!9, R!7) & bst1(L!10) & bst1(R!7) & (L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)) & (((X4!11 = leaf1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)) & (((X5!25 = red1) & ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) & ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))) | ((X5!25 = black1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[191, 181])).
% 0.20/0.55 tff(193,plain,
% 0.20/0.55 (L!10 = node1(X!15, X1!14, X2!13, X3!12, X4!11)),
% 0.20/0.55 inference(and_elim,[status(thm)],[192])).
% 0.20/0.55 tff(194,plain,
% 0.20/0.55 (node1(X!15, X1!14, X2!13, X3!12, X4!11) = L!10),
% 0.20/0.55 inference(symmetry,[status(thm)],[193])).
% 0.20/0.55 tff(195,plain,
% 0.20/0.55 (bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11)) <=> bst1(L!10)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.55 tff(196,plain,
% 0.20/0.55 (bst1(L!10) <=> bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.55 inference(symmetry,[status(thm)],[195])).
% 0.20/0.55 tff(197,plain,
% 0.20/0.55 (bst1(L!10)),
% 0.20/0.55 inference(and_elim,[status(thm)],[192])).
% 0.20/0.55 tff(198,plain,
% 0.20/0.55 (bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.55 tff(199,plain,
% 0.20/0.55 (^[K: $int, V: $int, L: tree1, R: tree1, C: color1] : refl((bst1(R) | (~bst1(node1(C, L, K, V, R)))) <=> (bst1(R) | (~bst1(node1(C, L, K, V, R)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(200,plain,
% 0.20/0.55 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R)))) <=> ![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[199])).
% 0.20/0.55 tff(201,plain,
% 0.20/0.55 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R)))) <=> ![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(202,plain,
% 0.20/0.55 (^[K: $int, V: $int, L: tree1, R: tree1, C: color1] : rewrite((bst1(node1(C, L, K, V, R)) => bst1(R)) <=> (bst1(R) | (~bst1(node1(C, L, K, V, R)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(203,plain,
% 0.20/0.55 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(node1(C, L, K, V, R)) => bst1(R)) <=> ![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[202])).
% 0.20/0.55 tff(204,axiom,(![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(node1(C, L, K, V, R)) => bst1(R))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bst_right')).
% 0.20/0.55 tff(205,plain,
% 0.20/0.55 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.55 tff(206,plain,
% 0.20/0.55 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.20/0.55 tff(207,plain,(
% 0.20/0.55 ![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))),
% 0.20/0.55 inference(skolemize,[status(sab)],[206])).
% 0.20/0.55 tff(208,plain,
% 0.20/0.55 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.20/0.55 tff(209,plain,
% 0.20/0.55 (((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))) | (bst1(X4!11) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))))) <=> ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))) | bst1(X4!11) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(210,plain,
% 0.20/0.55 ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))) | (bst1(X4!11) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(211,plain,
% 0.20/0.55 ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))) | bst1(X4!11) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.55 tff(212,plain,
% 0.20/0.55 (bst1(X4!11) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[211, 208])).
% 0.20/0.55 tff(213,plain,
% 0.20/0.55 (bst1(X4!11)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[212, 198])).
% 0.20/0.55 tff(214,plain,
% 0.20/0.56 (lt_tree1(K!9, node1(X!15, X1!14, X2!13, X3!12, X4!11)) <=> lt_tree1(K!9, L!10)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.56 tff(215,plain,
% 0.20/0.56 (lt_tree1(K!9, L!10) <=> lt_tree1(K!9, node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.56 inference(symmetry,[status(thm)],[214])).
% 0.20/0.56 tff(216,plain,
% 0.20/0.56 (lt_tree1(K!9, L!10)),
% 0.20/0.56 inference(and_elim,[status(thm)],[192])).
% 0.20/0.56 tff(217,plain,
% 0.20/0.56 (lt_tree1(K!9, node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.56 tff(218,plain,
% 0.20/0.56 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : refl(((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R)) <=> ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R)))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(219,plain,
% 0.20/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[218])).
% 0.20/0.56 tff(220,plain,
% 0.20/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(221,plain,
% 0.20/0.56 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : rewrite((lt_tree1(X, node1(C, L, Y, V, R)) => lt_tree1(X, R)) <=> ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R)))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(222,plain,
% 0.20/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) => lt_tree1(X, R)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.56 tff(223,axiom,(![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) => lt_tree1(X, R))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lt_right')).
% 0.20/0.56 tff(224,plain,
% 0.20/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.56 tff(225,plain,
% 0.20/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.20/0.56 tff(226,plain,(
% 0.20/0.56 ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))),
% 0.20/0.56 inference(skolemize,[status(sab)],[225])).
% 0.20/0.56 tff(227,plain,
% 0.20/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.20/0.56 tff(228,plain,
% 0.20/0.56 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(K!9, node1(X!15, X1!14, X2!13, X3!12, X4!11))) | lt_tree1(K!9, X4!11))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(K!9, node1(X!15, X1!14, X2!13, X3!12, X4!11))) | lt_tree1(K!9, X4!11))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(229,plain,
% 0.20/0.56 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(K!9, node1(X!15, X1!14, X2!13, X3!12, X4!11))) | lt_tree1(K!9, X4!11))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(230,plain,
% 0.20/0.56 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(K!9, node1(X!15, X1!14, X2!13, X3!12, X4!11))) | lt_tree1(K!9, X4!11)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.56 tff(231,plain,
% 0.20/0.56 ((~lt_tree1(K!9, node1(X!15, X1!14, X2!13, X3!12, X4!11))) | lt_tree1(K!9, X4!11)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.20/0.56 tff(232,plain,
% 0.20/0.56 (lt_tree1(K!9, X4!11)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[231, 217])).
% 0.20/0.56 tff(233,plain,
% 0.20/0.56 (bst1(R!7)),
% 0.20/0.56 inference(and_elim,[status(thm)],[192])).
% 0.20/0.56 tff(234,plain,
% 0.20/0.56 (gt_tree1(K!9, R!7)),
% 0.20/0.56 inference(and_elim,[status(thm)],[192])).
% 0.20/0.56 tff(235,plain,
% 0.20/0.56 ((~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7)))) | (~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(236,plain,
% 0.20/0.56 (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[235, 234, 233, 232, 213])).
% 0.20/0.56 tff(237,plain,
% 0.20/0.56 ((~(bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7)))))) | bst1(node1(black1, X4!11, K!9, V!8, R!7)) | ((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7)))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(238,plain,
% 0.20/0.56 ((~(bst1(node1(black1, X4!11, K!9, V!8, R!7)) <=> (~((~bst1(X4!11)) | (~gt_tree1(K!9, R!7)) | (~lt_tree1(K!9, X4!11)) | (~bst1(R!7)))))) | bst1(node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.20/0.56 tff(239,plain,
% 0.20/0.56 (bst1(node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[238, 176])).
% 0.20/0.56 tff(240,plain,
% 0.20/0.56 (bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[239, 169])).
% 0.20/0.56 tff(241,plain,
% 0.20/0.56 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))) <=> gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.56 tff(242,plain,
% 0.20/0.56 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, V!8, R!7)) <=> gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.20/0.56 inference(symmetry,[status(thm)],[241])).
% 0.20/0.56 tff(243,plain,
% 0.20/0.56 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(V!8, $product(-1, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)))) = 0)),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(244,plain,
% 0.20/0.56 ($sum(V!8, $product(-1, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)))) = 0),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[243, 35])).
% 0.20/0.56 tff(245,plain,
% 0.20/0.56 ((~($sum(V!8, $product(-1, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)))) = 0)) | $lesseq($sum(V!8, $product(-1, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)))), 0)),
% 0.20/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.56 tff(246,plain,
% 0.20/0.56 ($lesseq($sum(V!8, $product(-1, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)))), 0)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.20/0.56 tff(247,plain,
% 0.20/0.56 ((~($sum(V!8, $product(-1, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)))) = 0)) | $greatereq($sum(V!8, $product(-1, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)))), 0)),
% 0.20/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.56 tff(248,plain,
% 0.20/0.56 ($greatereq($sum(V!8, $product(-1, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)))), 0)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[247, 244])).
% 0.20/0.56 tff(249,plain,
% 0.20/0.56 (V!8 = node_proj_41(node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.56 inference(theory_lemma,[status(thm)],[248, 246])).
% 0.20/0.56 tff(250,plain,
% 0.20/0.56 (node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)) = V!8),
% 0.20/0.56 inference(symmetry,[status(thm)],[249])).
% 0.20/0.56 tff(251,plain,
% 0.20/0.56 (node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7) = node1(black1, X4!11, K!9, V!8, R!7)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[250])).
% 0.20/0.56 tff(252,plain,
% 0.20/0.56 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, V!8, R!7))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[251])).
% 0.20/0.56 tff(253,plain,
% 0.20/0.56 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, V!8, R!7)) <=> gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.20/0.56 inference(symmetry,[status(thm)],[252])).
% 0.20/0.56 tff(254,plain,
% 0.20/0.56 ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, V!8, R!7))) <=> (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[253])).
% 0.20/0.56 tff(255,assumption,(~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, V!8, R!7))), introduced(assumption)).
% 0.20/0.56 tff(256,plain,
% 0.20/0.56 (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.20/0.56 tff(257,assumption,(~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)), introduced(assumption)).
% 0.20/0.56 tff(258,plain,
% 0.20/0.56 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)) | (node_proj_51(node1(X!15, X1!14, X2!13, X3!12, X4!11)) = X4!11)),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(259,plain,
% 0.20/0.56 (node_proj_51(node1(X!15, X1!14, X2!13, X3!12, X4!11)) = X4!11),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[258, 50])).
% 0.20/0.56 tff(260,plain,
% 0.20/0.56 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)) | (node_proj_21(node1(X!15, X1!14, X2!13, X3!12, X4!11)) = X1!14)),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(261,plain,
% 0.20/0.56 (node_proj_21(node1(X!15, X1!14, X2!13, X3!12, X4!11)) = X1!14),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[260, 88])).
% 0.20/0.56 tff(262,plain,
% 0.20/0.56 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)) | (node_proj_11(node1(X!15, X1!14, X2!13, X3!12, X4!11)) = X!15)),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(263,plain,
% 0.20/0.56 (node_proj_11(node1(X!15, X1!14, X2!13, X3!12, X4!11)) = X!15),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[262, 97])).
% 0.20/0.56 tff(264,plain,
% 0.20/0.56 (node1(node_proj_11(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_21(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_51(node1(X!15, X1!14, X2!13, X3!12, X4!11))) = node1(X!15, X1!14, X2!13, X3!12, X4!11)),
% 0.20/0.56 inference(monotonicity,[status(thm)],[263, 261, 157, 149, 259])).
% 0.20/0.56 tff(265,plain,
% 0.20/0.56 (X4!11 = node_proj_51(node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.56 inference(symmetry,[status(thm)],[259])).
% 0.20/0.56 tff(266,plain,
% 0.20/0.56 (X1!14 = node_proj_21(node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.56 inference(symmetry,[status(thm)],[261])).
% 0.20/0.56 tff(267,plain,
% 0.20/0.56 (X!15 = node_proj_11(node1(X!15, X1!14, X2!13, X3!12, X4!11))),
% 0.20/0.56 inference(symmetry,[status(thm)],[263])).
% 0.20/0.56 tff(268,plain,
% 0.20/0.56 (node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11) = node1(node_proj_11(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_21(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_51(node1(X!15, X1!14, X2!13, X3!12, X4!11)))),
% 0.48/0.56 inference(monotonicity,[status(thm)],[267, 266, 265])).
% 0.48/0.56 tff(269,plain,
% 0.48/0.56 (node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11) = L!10),
% 0.48/0.56 inference(transitivity,[status(thm)],[268, 264, 194])).
% 0.48/0.56 tff(270,plain,
% 0.48/0.56 (lt_tree1(K!9, node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)) <=> lt_tree1(K!9, L!10)),
% 0.48/0.56 inference(monotonicity,[status(thm)],[269])).
% 0.48/0.56 tff(271,plain,
% 0.48/0.56 (lt_tree1(K!9, L!10) <=> lt_tree1(K!9, node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11))),
% 0.48/0.56 inference(symmetry,[status(thm)],[270])).
% 0.48/0.56 tff(272,plain,
% 0.48/0.56 (lt_tree1(K!9, node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[216, 271])).
% 0.48/0.56 tff(273,plain,
% 0.48/0.56 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : refl(((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R)))) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R)))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(274,plain,
% 0.48/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R)))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[273])).
% 0.48/0.56 tff(275,plain,
% 0.48/0.56 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(rewrite((~$lesseq(X, Y)) <=> (~$lesseq($sum(X, $product(-1, Y)), 0))), (((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R)))) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R)))))), rewrite(((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R)))) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))), (((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R)))) <=> ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(276,plain,
% 0.48/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R)))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[275])).
% 0.48/0.56 tff(277,plain,
% 0.48/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R)))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(278,plain,
% 0.48/0.56 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(rewrite($less(Y, X) <=> (~$lesseq(X, Y))), ((lt_tree1(X, node1(C, L, Y, V, R)) => $less(Y, X)) <=> (lt_tree1(X, node1(C, L, Y, V, R)) => (~$lesseq(X, Y))))), rewrite((lt_tree1(X, node1(C, L, Y, V, R)) => (~$lesseq(X, Y))) <=> ((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R))))), ((lt_tree1(X, node1(C, L, Y, V, R)) => $less(Y, X)) <=> ((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R))))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(279,plain,
% 0.48/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) => $less(Y, X)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[278])).
% 0.48/0.56 tff(280,axiom,(![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) => $less(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lt_node_lt')).
% 0.48/0.56 tff(281,plain,
% 0.48/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.48/0.56 tff(282,plain,
% 0.48/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(X, Y)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[281, 277])).
% 0.48/0.56 tff(283,plain,
% 0.48/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[282, 276])).
% 0.48/0.56 tff(284,plain,(
% 0.48/0.56 ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(skolemize,[status(sab)],[283])).
% 0.48/0.56 tff(285,plain,
% 0.48/0.56 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[284, 274])).
% 0.48/0.56 tff(286,plain,
% 0.48/0.56 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(K!9, node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11))))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~$lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(K!9, node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(287,plain,
% 0.48/0.56 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(K!9, node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11))))),
% 0.48/0.56 inference(quant_inst,[status(thm)],[])).
% 0.48/0.56 tff(288,plain,
% 0.48/0.56 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~$lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(K!9, node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.48/0.56 tff(289,plain,
% 0.48/0.56 ((~$lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(K!9, node1(X!15, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[288, 285])).
% 0.48/0.56 tff(290,plain,
% 0.48/0.56 (~$lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[289, 272])).
% 0.48/0.56 tff(291,plain,
% 0.48/0.56 (^[X: $int, Y: $int, T: tree1] : rewrite(($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(292,plain,
% 0.48/0.56 (![X: $int, Y: $int, T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[291])).
% 0.48/0.56 tff(293,plain,
% 0.48/0.56 (^[X: $int, Y: $int, T: tree1] : refl(($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(294,plain,
% 0.48/0.56 (![X: $int, Y: $int, T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[293])).
% 0.48/0.56 tff(295,plain,
% 0.48/0.56 (![X: $int, Y: $int] : ![T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(pull_quant,[status(thm)],[])).
% 0.48/0.56 tff(296,plain,
% 0.48/0.56 (^[X: $int, Y: $int] : pull_quant(($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(297,plain,
% 0.48/0.56 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ![T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[296])).
% 0.48/0.56 tff(298,plain,
% 0.48/0.56 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(transitivity,[status(thm)],[297, 295])).
% 0.48/0.56 tff(299,plain,
% 0.48/0.56 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(transitivity,[status(thm)],[298, 294])).
% 0.48/0.56 tff(300,plain,
% 0.48/0.56 (^[X: $int, Y: $int] : rewrite(($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(301,plain,
% 0.48/0.56 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[300])).
% 0.48/0.56 tff(302,plain,
% 0.48/0.56 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(transitivity,[status(thm)],[301, 299])).
% 0.48/0.56 tff(303,plain,
% 0.48/0.56 (^[X: $int, Y: $int] : rewrite(($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(304,plain,
% 0.48/0.56 (![X: $int, Y: $int] : ($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[303])).
% 0.48/0.56 tff(305,plain,
% 0.48/0.56 (![X: $int, Y: $int] : ($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(306,plain,
% 0.48/0.56 (^[X: $int, Y: $int] : trans(monotonicity(rewrite($less(Y, X) <=> (~$lesseq(X, Y))), quant_intro(proof_bind(^[T: tree1] : rewrite((gt_tree1(X, T) => gt_tree1(Y, T)) <=> ((~gt_tree1(X, T)) | gt_tree1(Y, T)))), (![T: tree1] : (gt_tree1(X, T) => gt_tree1(Y, T)) <=> ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))), (($less(Y, X) => ![T: tree1] : (gt_tree1(X, T) => gt_tree1(Y, T))) <=> ((~$lesseq(X, Y)) => ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))))), rewrite(((~$lesseq(X, Y)) => ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T))) <=> ($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))), (($less(Y, X) => ![T: tree1] : (gt_tree1(X, T) => gt_tree1(Y, T))) <=> ($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(307,plain,
% 0.48/0.57 (![X: $int, Y: $int] : ($less(Y, X) => ![T: tree1] : (gt_tree1(X, T) => gt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[306])).
% 0.48/0.57 tff(308,axiom,(![X: $int, Y: $int] : ($less(Y, X) => ![T: tree1] : (gt_tree1(X, T) => gt_tree1(Y, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_tree_trans')).
% 0.48/0.57 tff(309,plain,
% 0.48/0.57 (![X: $int, Y: $int] : ($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.48/0.57 tff(310,plain,
% 0.48/0.57 (![X: $int, Y: $int] : ($lesseq(X, Y) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[309, 305])).
% 0.48/0.57 tff(311,plain,
% 0.48/0.57 (![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[310, 304])).
% 0.48/0.57 tff(312,plain,(
% 0.48/0.57 ![X: $int, Y: $int] : ($lesseq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.57 inference(skolemize,[status(sab)],[311])).
% 0.48/0.57 tff(313,plain,
% 0.48/0.57 (![X: $int, Y: $int, T: tree1] : ($lesseq($sum(X, $product(-1, Y)), 0) | ((~gt_tree1(X, T)) | gt_tree1(Y, T)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[312, 302])).
% 0.48/0.57 tff(314,plain,
% 0.48/0.57 (![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[313, 292])).
% 0.48/0.57 tff(315,plain,
% 0.48/0.57 (((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | ((~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7))) <=> ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(316,plain,
% 0.48/0.57 ((gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(K!9, R!7))) <=> ((~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(317,plain,
% 0.48/0.57 (((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(K!9, R!7)))) <=> ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | ((~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[316])).
% 0.48/0.57 tff(318,plain,
% 0.48/0.57 (((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(K!9, R!7)))) <=> ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7))),
% 0.48/0.57 inference(transitivity,[status(thm)],[317, 315])).
% 0.48/0.57 tff(319,plain,
% 0.48/0.57 ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(K!9, R!7)))),
% 0.48/0.57 inference(quant_inst,[status(thm)],[])).
% 0.48/0.57 tff(320,plain,
% 0.48/0.57 ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.48/0.57 tff(321,plain,
% 0.48/0.57 ($false),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[320, 314, 234, 290, 257])).
% 0.48/0.57 tff(322,plain,(gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.57 tff(323,plain,
% 0.48/0.57 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11) <=> gt_tree1(X2!13, X4!11)),
% 0.48/0.57 inference(monotonicity,[status(thm)],[157])).
% 0.48/0.57 tff(324,plain,
% 0.48/0.57 (gt_tree1(X2!13, X4!11) <=> gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)),
% 0.48/0.57 inference(symmetry,[status(thm)],[323])).
% 0.48/0.57 tff(325,plain,
% 0.48/0.57 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11)) <=> (~((~gt_tree1(X2!13, X4!11)) | (~bst1(X1!14)) | (~bst1(X4!11)) | (~lt_tree1(X2!13, X1!14)))))),
% 0.48/0.57 inference(quant_inst,[status(thm)],[])).
% 0.48/0.57 tff(326,plain,
% 0.48/0.57 (bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11)) <=> (~((~gt_tree1(X2!13, X4!11)) | (~bst1(X1!14)) | (~bst1(X4!11)) | (~lt_tree1(X2!13, X1!14))))),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[325, 15])).
% 0.48/0.57 tff(327,plain,
% 0.48/0.57 ((~(bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11)) <=> (~((~gt_tree1(X2!13, X4!11)) | (~bst1(X1!14)) | (~bst1(X4!11)) | (~lt_tree1(X2!13, X1!14)))))) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))) | (~((~gt_tree1(X2!13, X4!11)) | (~bst1(X1!14)) | (~bst1(X4!11)) | (~lt_tree1(X2!13, X1!14))))),
% 0.48/0.57 inference(tautology,[status(thm)],[])).
% 0.48/0.57 tff(328,plain,
% 0.48/0.57 (~((~gt_tree1(X2!13, X4!11)) | (~bst1(X1!14)) | (~bst1(X4!11)) | (~lt_tree1(X2!13, X1!14)))),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[327, 198, 326])).
% 0.48/0.57 tff(329,plain,
% 0.48/0.57 (((~gt_tree1(X2!13, X4!11)) | (~bst1(X1!14)) | (~bst1(X4!11)) | (~lt_tree1(X2!13, X1!14))) | gt_tree1(X2!13, X4!11)),
% 0.48/0.57 inference(tautology,[status(thm)],[])).
% 0.48/0.57 tff(330,plain,
% 0.48/0.57 (gt_tree1(X2!13, X4!11)),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[329, 328])).
% 0.48/0.57 tff(331,plain,
% 0.48/0.57 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[330, 324])).
% 0.48/0.57 tff(332,plain,
% 0.48/0.57 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : refl((gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(333,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[332])).
% 0.48/0.57 tff(334,plain,
% 0.48/0.57 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(trans(monotonicity(rewrite($sum(Y, $product(-1, X)) = $sum($product(-1, X), Y)), ($lesseq($sum(Y, $product(-1, X)), 0) <=> $lesseq($sum($product(-1, X), Y), 0))), rewrite($lesseq($sum($product(-1, X), Y), 0) <=> $greatereq($sum(X, $product(-1, Y)), 0)), ($lesseq($sum(Y, $product(-1, X)), 0) <=> $greatereq($sum(X, $product(-1, Y)), 0))), ((gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $lesseq($sum(Y, $product(-1, X)), 0)) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $greatereq($sum(X, $product(-1, Y)), 0)))), rewrite((gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $greatereq($sum(X, $product(-1, Y)), 0)) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))), ((gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $lesseq($sum(Y, $product(-1, X)), 0)) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(335,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $lesseq($sum(Y, $product(-1, X)), 0)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[334])).
% 0.48/0.57 tff(336,plain,
% 0.48/0.57 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(rewrite($lesseq(Y, X) <=> $lesseq($sum(Y, $product(-1, X)), 0)), ((gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(Y, $product(-1, X)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))))), rewrite((gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(Y, $product(-1, X)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $lesseq($sum(Y, $product(-1, X)), 0))), ((gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $lesseq($sum(Y, $product(-1, X)), 0))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(337,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $lesseq($sum(Y, $product(-1, X)), 0))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[336])).
% 0.48/0.57 tff(338,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(339,plain,
% 0.48/0.57 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite($less(X, Y) <=> (~$lesseq(Y, X))), (($less(X, Y) => gt_tree1(X, node1(C, L, Y, V, R))) <=> ((~$lesseq(Y, X)) => gt_tree1(X, node1(C, L, Y, V, R))))), rewrite(((~$lesseq(Y, X)) => gt_tree1(X, node1(C, L, Y, V, R))) <=> ($lesseq(Y, X) | gt_tree1(X, node1(C, L, Y, V, R)))), (($less(X, Y) => gt_tree1(X, node1(C, L, Y, V, R))) <=> ($lesseq(Y, X) | gt_tree1(X, node1(C, L, Y, V, R))))), ((gt_tree1(X, R) => ($less(X, Y) => gt_tree1(X, node1(C, L, Y, V, R)))) <=> (gt_tree1(X, R) => ($lesseq(Y, X) | gt_tree1(X, node1(C, L, Y, V, R)))))), rewrite((gt_tree1(X, R) => ($lesseq(Y, X) | gt_tree1(X, node1(C, L, Y, V, R)))) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)))), ((gt_tree1(X, R) => ($less(X, Y) => gt_tree1(X, node1(C, L, Y, V, R)))) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R))))), ((gt_tree1(X, L) => (gt_tree1(X, R) => ($less(X, Y) => gt_tree1(X, node1(C, L, Y, V, R))))) <=> (gt_tree1(X, L) => (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)))))), rewrite((gt_tree1(X, L) => (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)))) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))), ((gt_tree1(X, L) => (gt_tree1(X, R) => ($less(X, Y) => gt_tree1(X, node1(C, L, Y, V, R))))) <=> (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(340,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, L) => (gt_tree1(X, R) => ($less(X, Y) => gt_tree1(X, node1(C, L, Y, V, R))))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[339])).
% 0.48/0.57 tff(341,axiom,(![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, L) => (gt_tree1(X, R) => ($less(X, Y) => gt_tree1(X, node1(C, L, Y, V, R)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_tree_node')).
% 0.48/0.57 tff(342,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.48/0.57 tff(343,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(Y, X) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[342, 338])).
% 0.48/0.57 tff(344,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)) | $lesseq($sum(Y, $product(-1, X)), 0))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[343, 337])).
% 0.48/0.57 tff(345,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[344, 335])).
% 0.48/0.57 tff(346,plain,(
% 0.48/0.57 ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(skolemize,[status(sab)],[345])).
% 0.48/0.57 tff(347,plain,
% 0.48/0.57 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[346, 333])).
% 0.48/0.57 tff(348,plain,
% 0.48/0.57 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(349,plain,
% 0.48/0.57 ((gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11))) <=> ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(350,plain,
% 0.48/0.57 ($greatereq($sum($product(-1, K!9), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11))), 0) <=> $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(351,plain,
% 0.48/0.57 ($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, K!9)) = $sum($product(-1, K!9), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(352,plain,
% 0.48/0.57 ($greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, K!9)), 0) <=> $greatereq($sum($product(-1, K!9), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11))), 0)),
% 0.48/0.57 inference(monotonicity,[status(thm)],[351])).
% 0.48/0.57 tff(353,plain,
% 0.48/0.57 ($greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, K!9)), 0) <=> $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.48/0.57 inference(transitivity,[status(thm)],[352, 350])).
% 0.48/0.57 tff(354,plain,
% 0.48/0.57 ((gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, K!9)), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11))) <=> (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[353])).
% 0.48/0.57 tff(355,plain,
% 0.48/0.57 ((gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, K!9)), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11))) <=> ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)))),
% 0.48/0.57 inference(transitivity,[status(thm)],[354, 349])).
% 0.48/0.57 tff(356,plain,
% 0.48/0.57 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, K!9)), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[355])).
% 0.48/0.58 tff(357,plain,
% 0.48/0.58 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, K!9)), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)))),
% 0.48/0.58 inference(transitivity,[status(thm)],[356, 348])).
% 0.48/0.58 tff(358,plain,
% 0.48/0.58 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, K!9)), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(359,plain,
% 0.48/0.58 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X4!11)) | $lesseq($sum(K!9, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), R!7)) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.48/0.58 tff(360,plain,
% 0.48/0.58 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[359, 347, 331, 290, 322])).
% 0.48/0.58 tff(361,plain,
% 0.48/0.58 ($false),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[360, 256])).
% 0.48/0.58 tff(362,plain,(gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X4!11, K!9, V!8, R!7))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.58 tff(363,plain,
% 0.48/0.58 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[362, 242])).
% 0.48/0.58 tff(364,plain,
% 0.48/0.58 (((~(X4!11 = leaf1)) | (~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))) | (X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16))),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(365,plain,
% 0.48/0.58 (X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[364, 162])).
% 0.48/0.58 tff(366,plain,
% 0.48/0.58 (node1(X5!20, X6!19, X7!18, X8!17, X9!16) = X1!14),
% 0.48/0.58 inference(symmetry,[status(thm)],[365])).
% 0.48/0.58 tff(367,plain,
% 0.48/0.58 (((~(X4!11 = leaf1)) | (~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))) | (X5!20 = red1)),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(368,plain,
% 0.48/0.58 (X5!20 = red1),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[367, 162])).
% 0.48/0.58 tff(369,plain,
% 0.48/0.58 (red1 = X5!20),
% 0.48/0.58 inference(symmetry,[status(thm)],[368])).
% 0.48/0.58 tff(370,plain,
% 0.48/0.58 (node1(red1, X6!19, X7!18, X8!17, X9!16) = node1(X5!20, X6!19, X7!18, X8!17, X9!16)),
% 0.50/0.58 inference(monotonicity,[status(thm)],[369])).
% 0.50/0.58 tff(371,plain,
% 0.50/0.58 (node1(red1, X6!19, X7!18, X8!17, X9!16) = X1!14),
% 0.50/0.58 inference(transitivity,[status(thm)],[370, 366])).
% 0.50/0.58 tff(372,plain,
% 0.50/0.58 (bst1(node1(red1, X6!19, X7!18, X8!17, X9!16)) <=> bst1(X1!14)),
% 0.50/0.58 inference(monotonicity,[status(thm)],[371])).
% 0.50/0.58 tff(373,plain,
% 0.50/0.58 (bst1(X1!14) <=> bst1(node1(red1, X6!19, X7!18, X8!17, X9!16))),
% 0.50/0.58 inference(symmetry,[status(thm)],[372])).
% 0.50/0.58 tff(374,plain,
% 0.50/0.58 (^[K: $int, V: $int, L: tree1, R: tree1, C: color1] : refl((bst1(L) | (~bst1(node1(C, L, K, V, R)))) <=> (bst1(L) | (~bst1(node1(C, L, K, V, R)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(375,plain,
% 0.50/0.58 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R)))) <=> ![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[374])).
% 0.50/0.58 tff(376,plain,
% 0.50/0.58 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R)))) <=> ![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(377,plain,
% 0.50/0.58 (^[K: $int, V: $int, L: tree1, R: tree1, C: color1] : rewrite((bst1(node1(C, L, K, V, R)) => bst1(L)) <=> (bst1(L) | (~bst1(node1(C, L, K, V, R)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(378,plain,
% 0.50/0.58 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(node1(C, L, K, V, R)) => bst1(L)) <=> ![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[377])).
% 0.50/0.58 tff(379,axiom,(![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(node1(C, L, K, V, R)) => bst1(L))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bst_left')).
% 0.50/0.58 tff(380,plain,
% 0.50/0.58 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.50/0.58 tff(381,plain,
% 0.50/0.58 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.50/0.58 tff(382,plain,(
% 0.50/0.58 ![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(skolemize,[status(sab)],[381])).
% 0.50/0.58 tff(383,plain,
% 0.50/0.58 (![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[382, 375])).
% 0.50/0.58 tff(384,plain,
% 0.50/0.58 (((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))) | (bst1(X1!14) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))))) <=> ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))) | bst1(X1!14) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(385,plain,
% 0.50/0.58 ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))) | (bst1(X1!14) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(386,plain,
% 0.50/0.58 ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))) | bst1(X1!14) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.50/0.58 tff(387,plain,
% 0.50/0.58 (bst1(X1!14) | (~bst1(node1(X!15, X1!14, X2!13, X3!12, X4!11)))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[386, 383])).
% 0.50/0.58 tff(388,plain,
% 0.50/0.58 (bst1(X1!14)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[387, 198])).
% 0.50/0.58 tff(389,plain,
% 0.50/0.58 (bst1(node1(red1, X6!19, X7!18, X8!17, X9!16))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[388, 373])).
% 0.50/0.58 tff(390,plain,
% 0.50/0.58 (^[C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : refl((bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R)))) <=> (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(391,plain,
% 0.50/0.58 (![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R)))) <=> ![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[390])).
% 0.50/0.58 tff(392,plain,
% 0.50/0.58 (![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R)))) <=> ![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(393,plain,
% 0.50/0.58 (^[C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : rewrite((bst1(node1(C, L, K, V, R)) => bst1(node1(Cqt, L, K, V, R))) <=> (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(394,plain,
% 0.50/0.58 (![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(C, L, K, V, R)) => bst1(node1(Cqt, L, K, V, R))) <=> ![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[393])).
% 0.50/0.58 tff(395,axiom,(![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(C, L, K, V, R)) => bst1(node1(Cqt, L, K, V, R)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bst_color')).
% 0.50/0.58 tff(396,plain,
% 0.50/0.58 (![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.50/0.58 tff(397,plain,
% 0.50/0.58 (![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[396, 392])).
% 0.50/0.58 tff(398,plain,(
% 0.50/0.58 ![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(skolemize,[status(sab)],[397])).
% 0.50/0.58 tff(399,plain,
% 0.50/0.58 (![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[398, 391])).
% 0.50/0.58 tff(400,plain,
% 0.50/0.58 (((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | (bst1(node1(black1, X6!19, X7!18, X8!17, X9!16)) | (~bst1(node1(red1, X6!19, X7!18, X8!17, X9!16))))) <=> ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | bst1(node1(black1, X6!19, X7!18, X8!17, X9!16)) | (~bst1(node1(red1, X6!19, X7!18, X8!17, X9!16))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(401,plain,
% 0.50/0.58 ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | (bst1(node1(black1, X6!19, X7!18, X8!17, X9!16)) | (~bst1(node1(red1, X6!19, X7!18, X8!17, X9!16))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(402,plain,
% 0.50/0.58 ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | bst1(node1(black1, X6!19, X7!18, X8!17, X9!16)) | (~bst1(node1(red1, X6!19, X7!18, X8!17, X9!16)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.50/0.58 tff(403,plain,
% 0.50/0.58 (bst1(node1(black1, X6!19, X7!18, X8!17, X9!16)) | (~bst1(node1(red1, X6!19, X7!18, X8!17, X9!16)))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[402, 399])).
% 0.50/0.58 tff(404,plain,
% 0.50/0.58 (bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[403, 389])).
% 0.50/0.58 tff(405,plain,
% 0.50/0.58 ((~((~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))) | (~bst1(node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(406,plain,
% 0.50/0.58 (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, X7!18, X8!17, X9!16))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[405, 404, 363, 240, 167])).
% 0.50/0.58 tff(407,plain,
% 0.50/0.58 (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[406, 108])).
% 0.50/0.58 tff(408,plain,
% 0.50/0.58 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16)) <=> lt_tree1(X2!13, X1!14)),
% 0.50/0.58 inference(monotonicity,[status(thm)],[157, 371])).
% 0.50/0.58 tff(409,plain,
% 0.50/0.58 (lt_tree1(X2!13, X1!14) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))),
% 0.50/0.58 inference(symmetry,[status(thm)],[408])).
% 0.50/0.58 tff(410,plain,
% 0.50/0.58 (((~gt_tree1(X2!13, X4!11)) | (~bst1(X1!14)) | (~bst1(X4!11)) | (~lt_tree1(X2!13, X1!14))) | lt_tree1(X2!13, X1!14)),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(411,plain,
% 0.50/0.58 (lt_tree1(X2!13, X1!14)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[410, 328])).
% 0.50/0.58 tff(412,plain,
% 0.50/0.58 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[411, 409])).
% 0.50/0.58 tff(413,plain,
% 0.50/0.58 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(414,plain,
% 0.50/0.58 (((~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16)))) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(415,plain,
% 0.50/0.58 ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!18)), 0)) <=> (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(416,plain,
% 0.50/0.58 (((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!18)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16)))) <=> ((~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[415])).
% 0.50/0.58 tff(417,plain,
% 0.50/0.58 (((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!18)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16)))) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.50/0.58 inference(transitivity,[status(thm)],[416, 414])).
% 0.50/0.58 tff(418,plain,
% 0.50/0.58 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!18)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[417])).
% 0.50/0.58 tff(419,plain,
% 0.50/0.58 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!18)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.50/0.58 inference(transitivity,[status(thm)],[418, 413])).
% 0.50/0.58 tff(420,plain,
% 0.50/0.58 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!18)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(421,plain,
% 0.50/0.58 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.50/0.59 tff(422,plain,
% 0.50/0.59 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[421, 285])).
% 0.50/0.59 tff(423,plain,
% 0.50/0.59 (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[422, 412])).
% 0.50/0.59 tff(424,plain,
% 0.50/0.59 ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)) | (~$greatereq($sum(X7!18, $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)) | $greatereq($sum(X7!18, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.50/0.59 inference(theory_lemma,[status(thm)],[])).
% 0.50/0.59 tff(425,plain,
% 0.50/0.59 (~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[424, 79, 423])).
% 0.50/0.59 tff(426,plain,
% 0.50/0.59 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : refl(((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L)) <=> ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L)))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(427,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[426])).
% 0.50/0.59 tff(428,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(429,plain,
% 0.50/0.59 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : rewrite((lt_tree1(X, node1(C, L, Y, V, R)) => lt_tree1(X, L)) <=> ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L)))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(430,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) => lt_tree1(X, L)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[429])).
% 0.50/0.59 tff(431,axiom,(![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) => lt_tree1(X, L))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lt_left')).
% 0.50/0.59 tff(432,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.50/0.59 tff(433,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[432, 428])).
% 0.50/0.59 tff(434,plain,(
% 0.50/0.59 ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))),
% 0.50/0.59 inference(skolemize,[status(sab)],[433])).
% 0.50/0.59 tff(435,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[434, 427])).
% 0.50/0.59 tff(436,plain,
% 0.50/0.59 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(437,plain,
% 0.50/0.59 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(438,plain,
% 0.50/0.59 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.50/0.59 tff(439,plain,
% 0.50/0.59 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[438, 435])).
% 0.50/0.59 tff(440,plain,
% 0.50/0.59 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[439, 412])).
% 0.50/0.59 tff(441,plain,
% 0.50/0.59 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(442,plain,
% 0.50/0.59 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(443,plain,
% 0.50/0.59 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.50/0.59 tff(444,plain,
% 0.50/0.59 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!19, X7!18, X8!17, X9!16))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[443, 227])).
% 0.50/0.59 tff(445,plain,
% 0.50/0.59 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[444, 412])).
% 0.50/0.59 tff(446,plain,
% 0.50/0.59 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : refl((lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))) <=> (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(447,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[446])).
% 0.50/0.59 tff(448,plain,
% 0.50/0.59 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(rewrite($lesseq(X, Y) <=> $lesseq($sum(X, $product(-1, Y)), 0)), ((lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))) <=> (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))))), rewrite((lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))) <=> (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))), ((lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))) <=> (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(449,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[448])).
% 0.50/0.59 tff(450,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(451,plain,
% 0.50/0.59 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite($less(Y, X) <=> (~$lesseq(X, Y))), (($less(Y, X) => lt_tree1(X, node1(C, L, Y, V, R))) <=> ((~$lesseq(X, Y)) => lt_tree1(X, node1(C, L, Y, V, R))))), rewrite(((~$lesseq(X, Y)) => lt_tree1(X, node1(C, L, Y, V, R))) <=> ($lesseq(X, Y) | lt_tree1(X, node1(C, L, Y, V, R)))), (($less(Y, X) => lt_tree1(X, node1(C, L, Y, V, R))) <=> ($lesseq(X, Y) | lt_tree1(X, node1(C, L, Y, V, R))))), ((lt_tree1(X, R) => ($less(Y, X) => lt_tree1(X, node1(C, L, Y, V, R)))) <=> (lt_tree1(X, R) => ($lesseq(X, Y) | lt_tree1(X, node1(C, L, Y, V, R)))))), rewrite((lt_tree1(X, R) => ($lesseq(X, Y) | lt_tree1(X, node1(C, L, Y, V, R)))) <=> (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)))), ((lt_tree1(X, R) => ($less(Y, X) => lt_tree1(X, node1(C, L, Y, V, R)))) <=> (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R))))), ((lt_tree1(X, L) => (lt_tree1(X, R) => ($less(Y, X) => lt_tree1(X, node1(C, L, Y, V, R))))) <=> (lt_tree1(X, L) => (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)))))), rewrite((lt_tree1(X, L) => (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)))) <=> (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))), ((lt_tree1(X, L) => (lt_tree1(X, R) => ($less(Y, X) => lt_tree1(X, node1(C, L, Y, V, R))))) <=> (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(452,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, L) => (lt_tree1(X, R) => ($less(Y, X) => lt_tree1(X, node1(C, L, Y, V, R))))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[451])).
% 0.50/0.59 tff(453,axiom,(![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, L) => (lt_tree1(X, R) => ($less(Y, X) => lt_tree1(X, node1(C, L, Y, V, R)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lt_tree_node')).
% 0.50/0.59 tff(454,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.50/0.59 tff(455,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq(X, Y) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[454, 450])).
% 0.50/0.59 tff(456,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[455, 449])).
% 0.50/0.59 tff(457,plain,(
% 0.50/0.59 ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(skolemize,[status(sab)],[456])).
% 0.50/0.59 tff(458,plain,
% 0.50/0.59 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[457, 447])).
% 0.50/0.59 tff(459,plain,
% 0.50/0.59 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(460,plain,
% 0.50/0.59 ((lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19))) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(461,plain,
% 0.50/0.59 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[460])).
% 0.50/0.59 tff(462,plain,
% 0.50/0.59 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0))),
% 0.50/0.59 inference(transitivity,[status(thm)],[461, 459])).
% 0.50/0.59 tff(463,plain,
% 0.50/0.59 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(464,plain,
% 0.50/0.59 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X9!16)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!19)) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.50/0.59 tff(465,plain,
% 0.50/0.59 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X6!19, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)), node_proj_41(node1(black1, X6!19, X7!18, X8!17, X9!16)), X9!16)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(black1, X6!19, X7!18, X8!17, X9!16)))), 0)),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[464, 458, 445, 440])).
% 0.50/0.60 tff(466,plain,
% 0.50/0.60 ($false),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[465, 425, 407])).
% 0.50/0.60 tff(467,plain,((~(X4!11 = leaf1)) | (~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.60 tff(468,plain,
% 0.50/0.60 ((((X4!11 = leaf1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)) & (((X5!25 = red1) & ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) & ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))) | ((X5!25 = black1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))) <=> ((~((~(X4!11 = leaf1)) | (~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16))))) | (~((~(X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21))) | (~((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(469,plain,
% 0.50/0.60 (((X4!11 = leaf1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16)))))) | ((X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)) & (((X5!25 = red1) & ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) & ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))) | ((X5!25 = black1) & (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))),
% 0.50/0.60 inference(and_elim,[status(thm)],[192])).
% 0.50/0.60 tff(470,plain,
% 0.50/0.60 ((~((~(X4!11 = leaf1)) | (~(X!15 = red1)) | bst1(node1(red1, node1(black1, X6!19, X7!18, X8!17, X9!16), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X5!20 = red1)) | (~(X1!14 = node1(X5!20, X6!19, X7!18, X8!17, X9!16))))) | (~((~(X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21))) | (~((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.50/0.60 tff(471,plain,
% 0.50/0.60 (~((~(X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21))) | (~((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[470, 467])).
% 0.50/0.60 tff(472,plain,
% 0.50/0.60 (((~(X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21))) | (~((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))))))) | ((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(473,plain,
% 0.50/0.60 ((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[472, 471])).
% 0.50/0.60 tff(474,assumption,(~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))), introduced(assumption)).
% 0.50/0.60 tff(475,plain,
% 0.50/0.60 (((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))) | (X5!25 = black1)),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(476,plain,
% 0.50/0.60 (X5!25 = black1),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[475, 474])).
% 0.50/0.60 tff(477,plain,
% 0.50/0.60 (node1(X5!25, X11!34, X12!33, X13!32, X14!31) = node1(black1, X11!34, X12!33, X13!32, X14!31)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[476])).
% 0.50/0.60 tff(478,plain,
% 0.50/0.60 (bst1(node1(X5!25, X11!34, X12!33, X13!32, X14!31)) <=> bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[477])).
% 0.50/0.60 tff(479,plain,
% 0.50/0.60 (((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))) | (X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(480,plain,
% 0.50/0.60 (X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[479, 474])).
% 0.50/0.60 tff(481,plain,
% 0.50/0.60 (node1(X10!35, X11!34, X12!33, X13!32, X14!31) = X1!14),
% 0.50/0.60 inference(symmetry,[status(thm)],[480])).
% 0.50/0.60 tff(482,plain,
% 0.50/0.60 (((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))) | (X10!35 = red1)),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(483,plain,
% 0.50/0.60 (X10!35 = red1),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[482, 474])).
% 0.50/0.60 tff(484,plain,
% 0.50/0.60 (red1 = X10!35),
% 0.50/0.60 inference(symmetry,[status(thm)],[483])).
% 0.50/0.60 tff(485,plain,
% 0.50/0.60 (node1(red1, X11!34, X12!33, X13!32, X14!31) = node1(X10!35, X11!34, X12!33, X13!32, X14!31)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[484])).
% 0.50/0.60 tff(486,plain,
% 0.50/0.60 (node1(red1, X11!34, X12!33, X13!32, X14!31) = X1!14),
% 0.50/0.60 inference(transitivity,[status(thm)],[485, 481])).
% 0.50/0.60 tff(487,plain,
% 0.50/0.60 (bst1(node1(red1, X11!34, X12!33, X13!32, X14!31)) <=> bst1(X1!14)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[486])).
% 0.50/0.60 tff(488,plain,
% 0.50/0.60 (bst1(X1!14) <=> bst1(node1(red1, X11!34, X12!33, X13!32, X14!31))),
% 0.50/0.60 inference(symmetry,[status(thm)],[487])).
% 0.50/0.60 tff(489,plain,
% 0.50/0.60 (bst1(node1(red1, X11!34, X12!33, X13!32, X14!31))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[388, 488])).
% 0.50/0.60 tff(490,plain,
% 0.50/0.60 (((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | (bst1(node1(X5!25, X11!34, X12!33, X13!32, X14!31)) | (~bst1(node1(red1, X11!34, X12!33, X13!32, X14!31))))) <=> ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | bst1(node1(X5!25, X11!34, X12!33, X13!32, X14!31)) | (~bst1(node1(red1, X11!34, X12!33, X13!32, X14!31))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(491,plain,
% 0.50/0.61 ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | (bst1(node1(X5!25, X11!34, X12!33, X13!32, X14!31)) | (~bst1(node1(red1, X11!34, X12!33, X13!32, X14!31))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(492,plain,
% 0.50/0.61 ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | bst1(node1(X5!25, X11!34, X12!33, X13!32, X14!31)) | (~bst1(node1(red1, X11!34, X12!33, X13!32, X14!31)))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.50/0.61 tff(493,plain,
% 0.50/0.61 (bst1(node1(X5!25, X11!34, X12!33, X13!32, X14!31)) | (~bst1(node1(red1, X11!34, X12!33, X13!32, X14!31)))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[492, 399])).
% 0.50/0.61 tff(494,plain,
% 0.50/0.61 (bst1(node1(X5!25, X11!34, X12!33, X13!32, X14!31))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[493, 489])).
% 0.50/0.61 tff(495,plain,
% 0.50/0.61 (bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[494, 478])).
% 0.50/0.61 tff(496,plain,
% 0.50/0.61 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(497,plain,
% 0.50/0.61 ((bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31)))))) <=> (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(498,plain,
% 0.50/0.61 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[497])).
% 0.50/0.61 tff(499,plain,
% 0.50/0.61 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))))))),
% 0.50/0.62 inference(transitivity,[status(thm)],[498, 496])).
% 0.50/0.62 tff(500,plain,
% 0.50/0.62 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))))))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(501,plain,
% 0.50/0.62 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.50/0.62 tff(502,plain,
% 0.50/0.62 (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[501, 15])).
% 0.50/0.62 tff(503,plain,
% 0.50/0.62 (node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))) = node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))),
% 0.50/0.62 inference(monotonicity,[status(thm)],[157, 149, 141])).
% 0.50/0.62 tff(504,plain,
% 0.50/0.62 (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))),
% 0.50/0.62 inference(monotonicity,[status(thm)],[503])).
% 0.50/0.62 tff(505,plain,
% 0.50/0.62 (bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) <=> bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.50/0.62 inference(symmetry,[status(thm)],[504])).
% 0.50/0.62 tff(506,plain,
% 0.50/0.62 ((~bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))) <=> (~bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))),
% 0.50/0.62 inference(monotonicity,[status(thm)],[505])).
% 0.50/0.62 tff(507,plain,
% 0.50/0.62 (((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))) | (~bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(508,plain,
% 0.50/0.62 (~bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[507, 474])).
% 0.50/0.62 tff(509,plain,
% 0.50/0.62 (~bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[508, 506])).
% 0.50/0.62 tff(510,plain,
% 0.50/0.62 ((~(bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))))) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | ((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(511,plain,
% 0.50/0.62 ((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[510, 509, 502])).
% 0.50/0.62 tff(512,plain,
% 0.50/0.62 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31)) <=> lt_tree1(X2!13, X1!14)),
% 0.50/0.62 inference(monotonicity,[status(thm)],[157, 486])).
% 0.50/0.62 tff(513,plain,
% 0.50/0.62 (lt_tree1(X2!13, X1!14) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))),
% 0.50/0.62 inference(symmetry,[status(thm)],[512])).
% 0.50/0.62 tff(514,plain,
% 0.50/0.62 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[411, 513])).
% 0.50/0.62 tff(515,plain,
% 0.50/0.62 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34))),
% 0.55/0.63 inference(rewrite,[status(thm)],[])).
% 0.55/0.63 tff(516,plain,
% 0.55/0.63 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34))),
% 0.55/0.63 inference(quant_inst,[status(thm)],[])).
% 0.55/0.63 tff(517,plain,
% 0.55/0.63 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.55/0.63 tff(518,plain,
% 0.55/0.63 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[517, 435])).
% 0.55/0.63 tff(519,plain,
% 0.55/0.63 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[518, 514])).
% 0.55/0.63 tff(520,plain,
% 0.55/0.63 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31))),
% 0.55/0.63 inference(rewrite,[status(thm)],[])).
% 0.55/0.63 tff(521,plain,
% 0.55/0.63 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31))),
% 0.55/0.63 inference(quant_inst,[status(thm)],[])).
% 0.55/0.63 tff(522,plain,
% 0.55/0.63 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.55/0.63 tff(523,plain,
% 0.55/0.63 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[522, 227])).
% 0.55/0.63 tff(524,plain,
% 0.55/0.63 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[523, 514])).
% 0.55/0.63 tff(525,plain,
% 0.55/0.63 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))) = 0)),
% 0.55/0.63 inference(quant_inst,[status(thm)],[])).
% 0.55/0.63 tff(526,plain,
% 0.55/0.63 ($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))) = 0),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[525, 73])).
% 0.55/0.63 tff(527,plain,
% 0.55/0.63 ((~($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))) = 0)) | $greatereq($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.63 tff(528,plain,
% 0.55/0.63 ($greatereq($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[527, 526])).
% 0.55/0.63 tff(529,plain,
% 0.55/0.63 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.55/0.63 inference(rewrite,[status(thm)],[])).
% 0.55/0.63 tff(530,plain,
% 0.55/0.63 (((~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31)))) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.55/0.63 inference(rewrite,[status(thm)],[])).
% 0.55/0.63 tff(531,plain,
% 0.55/0.63 ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X12!33)), 0)) <=> (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.55/0.63 inference(rewrite,[status(thm)],[])).
% 0.55/0.63 tff(532,plain,
% 0.55/0.63 (((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X12!33)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31)))) <=> ((~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))))),
% 0.55/0.63 inference(monotonicity,[status(thm)],[531])).
% 0.55/0.63 tff(533,plain,
% 0.55/0.63 (((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X12!33)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31)))) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.55/0.63 inference(transitivity,[status(thm)],[532, 530])).
% 0.55/0.63 tff(534,plain,
% 0.55/0.63 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X12!33)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))))),
% 0.55/0.63 inference(monotonicity,[status(thm)],[533])).
% 0.55/0.63 tff(535,plain,
% 0.55/0.63 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X12!33)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.55/0.63 inference(transitivity,[status(thm)],[534, 529])).
% 0.55/0.63 tff(536,plain,
% 0.55/0.63 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X12!33)), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))))),
% 0.55/0.63 inference(quant_inst,[status(thm)],[])).
% 0.55/0.63 tff(537,plain,
% 0.55/0.63 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.55/0.63 tff(538,plain,
% 0.55/0.63 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!34, X12!33, X13!32, X14!31))) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[537, 285])).
% 0.55/0.63 tff(539,plain,
% 0.55/0.63 (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[538, 514])).
% 0.55/0.63 tff(540,plain,
% 0.55/0.63 ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)) | (~$greatereq($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)) | $greatereq($sum(X12!33, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.63 tff(541,plain,
% 0.55/0.63 (~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[540, 539, 528])).
% 0.55/0.63 tff(542,plain,
% 0.55/0.63 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X13!32, $product(-1, node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)))) = 0)),
% 0.55/0.63 inference(quant_inst,[status(thm)],[])).
% 0.55/0.63 tff(543,plain,
% 0.55/0.63 ($sum(X13!32, $product(-1, node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)))) = 0),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[542, 35])).
% 0.55/0.63 tff(544,plain,
% 0.55/0.63 ((~($sum(X13!32, $product(-1, node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)))) = 0)) | $lesseq($sum(X13!32, $product(-1, node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.63 tff(545,plain,
% 0.55/0.63 ($lesseq($sum(X13!32, $product(-1, node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[544, 543])).
% 0.55/0.63 tff(546,plain,
% 0.55/0.63 ((~($sum(X13!32, $product(-1, node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)))) = 0)) | $greatereq($sum(X13!32, $product(-1, node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.63 tff(547,plain,
% 0.55/0.63 ($greatereq($sum(X13!32, $product(-1, node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[546, 543])).
% 0.55/0.63 tff(548,plain,
% 0.55/0.63 (X13!32 = node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31))),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[547, 545])).
% 0.55/0.63 tff(549,plain,
% 0.55/0.63 (node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)) = X13!32),
% 0.55/0.63 inference(symmetry,[status(thm)],[548])).
% 0.55/0.63 tff(550,plain,
% 0.55/0.63 ((~($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))) = 0)) | $lesseq($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.63 tff(551,plain,
% 0.55/0.63 ($lesseq($sum(X12!33, $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[550, 526])).
% 0.55/0.63 tff(552,plain,
% 0.55/0.63 (X12!33 = node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31))),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[528, 551])).
% 0.55/0.63 tff(553,plain,
% 0.55/0.63 (node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)) = X12!33),
% 0.55/0.63 inference(symmetry,[status(thm)],[552])).
% 0.55/0.63 tff(554,assumption,(X5!25 = black1), introduced(assumption)).
% 0.55/0.63 tff(555,plain,
% 0.55/0.63 (node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31) = node1(black1, X11!34, X12!33, X13!32, X14!31)),
% 0.55/0.63 inference(monotonicity,[status(thm)],[554, 553, 549])).
% 0.55/0.63 tff(556,plain,
% 0.55/0.63 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))),
% 0.55/0.63 inference(monotonicity,[status(thm)],[555])).
% 0.55/0.63 tff(557,plain,
% 0.55/0.63 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31)) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31))),
% 0.55/0.63 inference(symmetry,[status(thm)],[556])).
% 0.55/0.63 tff(558,plain,
% 0.55/0.63 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) <=> (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)))),
% 0.55/0.63 inference(monotonicity,[status(thm)],[557])).
% 0.55/0.63 tff(559,assumption,(~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))), introduced(assumption)).
% 0.55/0.63 tff(560,plain,
% 0.55/0.63 (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.55/0.63 tff(561,assumption,(~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)), introduced(assumption)).
% 0.55/0.63 tff(562,assumption,(lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)), introduced(assumption)).
% 0.55/0.63 tff(563,assumption,(lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)), introduced(assumption)).
% 0.55/0.63 tff(564,plain,
% 0.55/0.63 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(565,plain,
% 0.55/0.64 ((lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34))) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(566,plain,
% 0.55/0.64 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31))))),
% 0.55/0.64 inference(monotonicity,[status(thm)],[565])).
% 0.55/0.64 tff(567,plain,
% 0.55/0.64 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)))),
% 0.55/0.64 inference(transitivity,[status(thm)],[566, 564])).
% 0.55/0.64 tff(568,plain,
% 0.55/0.64 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)))),
% 0.55/0.64 inference(quant_inst,[status(thm)],[])).
% 0.55/0.64 tff(569,plain,
% 0.55/0.64 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.55/0.64 tff(570,plain,
% 0.55/0.64 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(X5!25, X11!34, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)), node_proj_41(node1(red1, X11!34, X12!33, X13!32, X14!31)), X14!31))),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[569, 458, 563, 562, 561])).
% 0.55/0.64 tff(571,plain,
% 0.55/0.64 ($false),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[570, 560])).
% 0.55/0.64 tff(572,plain,(lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31)) | (~(X5!25 = black1)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!31)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!34)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(red1, X11!34, X12!33, X13!32, X14!31)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.64 tff(573,plain,
% 0.55/0.64 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[572, 541, 524, 519, 476])).
% 0.55/0.64 tff(574,plain,
% 0.55/0.64 ((~((~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))) | (~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!34, X12!33, X13!32, X14!31))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.55/0.64 inference(tautology,[status(thm)],[])).
% 0.55/0.64 tff(575,plain,
% 0.55/0.64 (~bst1(node1(black1, X11!34, X12!33, X13!32, X14!31))),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[574, 573, 363, 240, 511])).
% 0.55/0.64 tff(576,plain,
% 0.55/0.64 ($false),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[575, 495])).
% 0.55/0.64 tff(577,plain,((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.64 tff(578,plain,
% 0.55/0.64 ((~((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))) | (~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))))),
% 0.55/0.64 inference(tautology,[status(thm)],[])).
% 0.55/0.64 tff(579,plain,
% 0.55/0.64 ((~((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31))))))) | (~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))))))))))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[578, 577])).
% 0.57/0.65 tff(580,plain,
% 0.57/0.65 (~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[579, 473])).
% 0.57/0.65 tff(581,plain,
% 0.57/0.65 (((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))))))))) | (X5!25 = red1)),
% 0.57/0.65 inference(tautology,[status(thm)],[])).
% 0.57/0.65 tff(582,plain,
% 0.57/0.65 (X5!25 = red1),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[581, 580])).
% 0.57/0.65 tff(583,plain,
% 0.57/0.65 (red1 = X5!25),
% 0.57/0.65 inference(symmetry,[status(thm)],[582])).
% 0.57/0.65 tff(584,plain,
% 0.57/0.65 (node1(red1, X6!24, X7!23, X8!22, X9!21) = node1(X5!25, X6!24, X7!23, X8!22, X9!21)),
% 0.57/0.65 inference(monotonicity,[status(thm)],[583])).
% 0.57/0.65 tff(585,plain,
% 0.57/0.65 (node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21)) = node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[584])).
% 0.57/0.65 tff(586,plain,
% 0.57/0.65 (node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)) = node_proj_41(node1(red1, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.65 inference(symmetry,[status(thm)],[585])).
% 0.57/0.65 tff(587,plain,
% 0.57/0.65 (node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)) = X8!22),
% 0.57/0.65 inference(transitivity,[status(thm)],[586, 43])).
% 0.57/0.65 tff(588,plain,
% 0.57/0.65 (node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7)) = node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[587])).
% 0.57/0.65 tff(589,plain,
% 0.57/0.65 (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7)))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[588])).
% 0.57/0.65 tff(590,plain,
% 0.57/0.65 (bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) <=> bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7)))),
% 0.57/0.65 inference(symmetry,[status(thm)],[589])).
% 0.57/0.65 tff(591,plain,
% 0.57/0.65 ((~bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7)))) <=> (~bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[590])).
% 0.57/0.65 tff(592,assumption,(~bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7)))), introduced(assumption)).
% 0.57/0.65 tff(593,plain,
% 0.57/0.65 (~bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7)))),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.57/0.65 tff(594,plain,
% 0.57/0.65 (node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24) = node1(black1, X1!14, X2!13, X3!12, X6!24)),
% 0.57/0.65 inference(monotonicity,[status(thm)],[157, 149])).
% 0.57/0.65 tff(595,plain,
% 0.57/0.65 (node1(black1, X1!14, X2!13, X3!12, X6!24) = node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)),
% 0.57/0.65 inference(symmetry,[status(thm)],[594])).
% 0.57/0.65 tff(596,plain,
% 0.57/0.65 (bst1(node1(black1, X1!14, X2!13, X3!12, X6!24)) <=> bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[595])).
% 0.57/0.65 tff(597,plain,
% 0.57/0.65 (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))),
% 0.57/0.65 inference(symmetry,[status(thm)],[596])).
% 0.57/0.65 tff(598,plain,
% 0.57/0.65 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))))))),
% 0.57/0.65 inference(rewrite,[status(thm)],[])).
% 0.57/0.65 tff(599,plain,
% 0.57/0.65 ((bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~bst1(X1!14)) | (~bst1(X6!24)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14))))) <=> (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))))),
% 0.57/0.65 inference(rewrite,[status(thm)],[])).
% 0.57/0.65 tff(600,plain,
% 0.57/0.65 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~bst1(X1!14)) | (~bst1(X6!24)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))))))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[599])).
% 0.57/0.65 tff(601,plain,
% 0.57/0.65 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~bst1(X1!14)) | (~bst1(X6!24)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))))))),
% 0.57/0.65 inference(transitivity,[status(thm)],[600, 598])).
% 0.57/0.65 tff(602,plain,
% 0.57/0.65 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~bst1(X1!14)) | (~bst1(X6!24)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)))))),
% 0.57/0.65 inference(quant_inst,[status(thm)],[])).
% 0.57/0.65 tff(603,plain,
% 0.57/0.65 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))))),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.57/0.65 tff(604,plain,
% 0.57/0.65 (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[603, 15])).
% 0.57/0.65 tff(605,plain,
% 0.57/0.65 (((~(X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21))) | (~((~((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))))) | (~((~(X!15 = red1)) | (~(X5!25 = black1)) | bst1(node1(red1, node1(black1, X11!34, X12!33, X13!32, X14!31), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!35 = red1)) | (~(X1!14 = node1(X10!35, X11!34, X12!33, X13!32, X14!31)))))))) | (X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.65 inference(tautology,[status(thm)],[])).
% 0.57/0.65 tff(606,plain,
% 0.57/0.65 (X4!11 = node1(X5!25, X6!24, X7!23, X8!22, X9!21)),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[605, 471])).
% 0.57/0.65 tff(607,plain,
% 0.57/0.65 (node1(X5!25, X6!24, X7!23, X8!22, X9!21) = X4!11),
% 0.57/0.65 inference(symmetry,[status(thm)],[606])).
% 0.57/0.65 tff(608,plain,
% 0.57/0.65 (node1(red1, X6!24, X7!23, X8!22, X9!21) = X4!11),
% 0.57/0.65 inference(transitivity,[status(thm)],[584, 607])).
% 0.57/0.65 tff(609,plain,
% 0.57/0.65 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21)) <=> gt_tree1(X2!13, X4!11)),
% 0.57/0.65 inference(monotonicity,[status(thm)],[157, 608])).
% 0.57/0.65 tff(610,plain,
% 0.57/0.65 (gt_tree1(X2!13, X4!11) <=> gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.65 inference(symmetry,[status(thm)],[609])).
% 0.57/0.65 tff(611,plain,
% 0.57/0.65 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[330, 610])).
% 0.57/0.65 tff(612,plain,
% 0.57/0.65 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : refl(((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L)) <=> ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L)))),
% 0.57/0.65 inference(bind,[status(th)],[])).
% 0.57/0.65 tff(613,plain,
% 0.57/0.65 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))),
% 0.57/0.65 inference(quant_intro,[status(thm)],[612])).
% 0.57/0.65 tff(614,plain,
% 0.57/0.65 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))),
% 0.57/0.65 inference(rewrite,[status(thm)],[])).
% 0.57/0.65 tff(615,plain,
% 0.57/0.65 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : rewrite((gt_tree1(X, node1(C, L, Y, V, R)) => gt_tree1(X, L)) <=> ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L)))),
% 0.57/0.65 inference(bind,[status(th)],[])).
% 0.57/0.65 tff(616,plain,
% 0.57/0.65 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) => gt_tree1(X, L)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))),
% 0.57/0.65 inference(quant_intro,[status(thm)],[615])).
% 0.57/0.65 tff(617,axiom,(![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) => gt_tree1(X, L))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_left')).
% 0.57/0.65 tff(618,plain,
% 0.57/0.65 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.57/0.65 tff(619,plain,
% 0.57/0.65 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[618, 614])).
% 0.57/0.65 tff(620,plain,(
% 0.57/0.65 ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))),
% 0.57/0.65 inference(skolemize,[status(sab)],[619])).
% 0.57/0.65 tff(621,plain,
% 0.57/0.65 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[620, 613])).
% 0.57/0.65 tff(622,plain,
% 0.57/0.65 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.65 inference(rewrite,[status(thm)],[])).
% 0.57/0.65 tff(623,plain,
% 0.57/0.65 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.65 inference(quant_inst,[status(thm)],[])).
% 0.57/0.65 tff(624,plain,
% 0.57/0.65 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | gt_tree1(X, L))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.57/0.66 tff(625,plain,
% 0.57/0.66 ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[624, 621])).
% 0.57/0.66 tff(626,plain,
% 0.57/0.66 (gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[625, 611])).
% 0.57/0.66 tff(627,plain,
% 0.57/0.66 (bst1(node1(red1, X6!24, X7!23, X8!22, X9!21)) <=> bst1(X4!11)),
% 0.57/0.66 inference(monotonicity,[status(thm)],[608])).
% 0.57/0.66 tff(628,plain,
% 0.57/0.66 (bst1(X4!11) <=> bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.66 inference(symmetry,[status(thm)],[627])).
% 0.57/0.66 tff(629,plain,
% 0.57/0.66 (bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[213, 628])).
% 0.57/0.66 tff(630,plain,
% 0.57/0.66 (((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))) | (bst1(X6!24) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))))) <=> ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))) | bst1(X6!24) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(631,plain,
% 0.57/0.66 ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))) | (bst1(X6!24) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))))),
% 0.57/0.66 inference(quant_inst,[status(thm)],[])).
% 0.57/0.66 tff(632,plain,
% 0.57/0.66 ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(L) | (~bst1(node1(C, L, K, V, R))))) | bst1(X6!24) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21)))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[631, 630])).
% 0.57/0.66 tff(633,plain,
% 0.57/0.66 (bst1(X6!24) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21)))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[632, 383])).
% 0.57/0.66 tff(634,plain,
% 0.57/0.66 (bst1(X6!24)),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[633, 629])).
% 0.57/0.66 tff(635,plain,
% 0.57/0.66 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14) <=> lt_tree1(X2!13, X1!14)),
% 0.57/0.66 inference(monotonicity,[status(thm)],[157])).
% 0.57/0.66 tff(636,plain,
% 0.57/0.66 (lt_tree1(X2!13, X1!14) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)),
% 0.57/0.66 inference(symmetry,[status(thm)],[635])).
% 0.57/0.66 tff(637,plain,
% 0.57/0.66 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[411, 636])).
% 0.57/0.66 tff(638,plain,
% 0.57/0.66 ((~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))) | (~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.66 inference(tautology,[status(thm)],[])).
% 0.57/0.66 tff(639,plain,
% 0.57/0.66 (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[638, 388, 637, 634, 626])).
% 0.57/0.66 tff(640,plain,
% 0.57/0.66 ((~(bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))))) | bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | ((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))),
% 0.57/0.66 inference(tautology,[status(thm)],[])).
% 0.57/0.66 tff(641,plain,
% 0.57/0.66 ((~(bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> (~((~bst1(X1!14)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | (~bst1(X6!24)) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))))) | bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[640, 639])).
% 0.57/0.66 tff(642,plain,
% 0.57/0.66 (bst1(node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[641, 604])).
% 0.57/0.66 tff(643,plain,
% 0.57/0.66 (bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[642, 597])).
% 0.57/0.66 tff(644,plain,
% 0.57/0.66 (node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7) = node1(black1, X9!21, K!9, V!8, R!7)),
% 0.57/0.66 inference(monotonicity,[status(thm)],[250])).
% 0.57/0.66 tff(645,plain,
% 0.57/0.66 (node1(black1, X9!21, K!9, V!8, R!7) = node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)),
% 0.57/0.66 inference(symmetry,[status(thm)],[644])).
% 0.57/0.66 tff(646,plain,
% 0.57/0.66 (bst1(node1(black1, X9!21, K!9, V!8, R!7)) <=> bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.57/0.66 inference(monotonicity,[status(thm)],[645])).
% 0.57/0.66 tff(647,plain,
% 0.57/0.66 (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> bst1(node1(black1, X9!21, K!9, V!8, R!7))),
% 0.57/0.66 inference(symmetry,[status(thm)],[646])).
% 0.57/0.66 tff(648,plain,
% 0.57/0.66 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7))))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(649,plain,
% 0.57/0.66 ((bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~bst1(R!7)) | (~lt_tree1(K!9, X9!21))))) <=> (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7)))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(650,plain,
% 0.57/0.66 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~bst1(R!7)) | (~lt_tree1(K!9, X9!21)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7))))))),
% 0.57/0.66 inference(monotonicity,[status(thm)],[649])).
% 0.57/0.66 tff(651,plain,
% 0.57/0.66 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~bst1(R!7)) | (~lt_tree1(K!9, X9!21)))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7))))))),
% 0.57/0.66 inference(transitivity,[status(thm)],[650, 648])).
% 0.57/0.66 tff(652,plain,
% 0.57/0.66 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~bst1(R!7)) | (~lt_tree1(K!9, X9!21)))))),
% 0.57/0.66 inference(quant_inst,[status(thm)],[])).
% 0.57/0.66 tff(653,plain,
% 0.57/0.66 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7)))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.57/0.66 tff(654,plain,
% 0.57/0.66 (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7))))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[653, 15])).
% 0.57/0.66 tff(655,plain,
% 0.57/0.66 (lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21)) <=> lt_tree1(K!9, X4!11)),
% 0.57/0.66 inference(monotonicity,[status(thm)],[608])).
% 0.57/0.66 tff(656,plain,
% 0.57/0.66 (lt_tree1(K!9, X4!11) <=> lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.66 inference(symmetry,[status(thm)],[655])).
% 0.57/0.66 tff(657,plain,
% 0.57/0.66 (lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[232, 656])).
% 0.57/0.66 tff(658,plain,
% 0.57/0.66 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))) | lt_tree1(K!9, X9!21))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))) | lt_tree1(K!9, X9!21))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(659,plain,
% 0.57/0.66 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))) | lt_tree1(K!9, X9!21))),
% 0.57/0.66 inference(quant_inst,[status(thm)],[])).
% 0.57/0.66 tff(660,plain,
% 0.57/0.66 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))) | lt_tree1(K!9, X9!21)),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.57/0.66 tff(661,plain,
% 0.57/0.66 ((~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))) | lt_tree1(K!9, X9!21)),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[660, 227])).
% 0.57/0.66 tff(662,plain,
% 0.57/0.66 (lt_tree1(K!9, X9!21)),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[661, 657])).
% 0.57/0.66 tff(663,plain,
% 0.57/0.66 (((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))) | (bst1(X9!21) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))))) <=> ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))) | bst1(X9!21) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(664,plain,
% 0.57/0.66 ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))) | (bst1(X9!21) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))))),
% 0.57/0.66 inference(quant_inst,[status(thm)],[])).
% 0.57/0.66 tff(665,plain,
% 0.57/0.66 ((~![K: $int, V: $int, L: tree1, R: tree1, C: color1] : (bst1(R) | (~bst1(node1(C, L, K, V, R))))) | bst1(X9!21) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21)))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.57/0.66 tff(666,plain,
% 0.57/0.66 (bst1(X9!21) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21)))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[665, 208])).
% 0.57/0.66 tff(667,plain,
% 0.57/0.66 (bst1(X9!21)),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[666, 629])).
% 0.57/0.66 tff(668,plain,
% 0.57/0.66 ((~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7)))) | (~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7))),
% 0.57/0.66 inference(tautology,[status(thm)],[])).
% 0.57/0.66 tff(669,plain,
% 0.57/0.66 (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7)))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[668, 234, 233, 667, 662])).
% 0.57/0.66 tff(670,plain,
% 0.57/0.66 ((~(bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7)))))) | bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | ((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7)))),
% 0.57/0.66 inference(tautology,[status(thm)],[])).
% 0.57/0.66 tff(671,plain,
% 0.57/0.66 ((~(bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> (~((~gt_tree1(K!9, R!7)) | (~bst1(X9!21)) | (~lt_tree1(K!9, X9!21)) | (~bst1(R!7)))))) | bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[670, 669])).
% 0.57/0.66 tff(672,plain,
% 0.57/0.66 (bst1(node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[671, 654])).
% 0.57/0.66 tff(673,plain,
% 0.57/0.66 (bst1(node1(black1, X9!21, K!9, V!8, R!7))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[672, 647])).
% 0.57/0.66 tff(674,plain,
% 0.57/0.66 (lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) <=> lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))),
% 0.57/0.66 inference(monotonicity,[status(thm)],[594])).
% 0.57/0.66 tff(675,plain,
% 0.57/0.66 (lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24)) <=> lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.66 inference(symmetry,[status(thm)],[674])).
% 0.57/0.66 tff(676,plain,
% 0.57/0.66 ((~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))) <=> (~lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)))),
% 0.57/0.66 inference(monotonicity,[status(thm)],[675])).
% 0.57/0.66 tff(677,assumption,(~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))), introduced(assumption)).
% 0.57/0.66 tff(678,plain,
% 0.57/0.66 (~lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.57/0.66 tff(679,assumption,(~lt_tree1(X7!23, X1!14)), introduced(assumption)).
% 0.57/0.66 tff(680,plain,
% 0.57/0.66 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : refl(((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0))) <=> ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0))))),
% 0.57/0.66 inference(bind,[status(th)],[])).
% 0.57/0.66 tff(681,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))),
% 0.57/0.66 inference(quant_intro,[status(thm)],[680])).
% 0.57/0.66 tff(682,plain,
% 0.57/0.66 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : rewrite(((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$lesseq($sum(Y, $product(-1, X)), 0))) <=> ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0))))),
% 0.57/0.66 inference(bind,[status(th)],[])).
% 0.57/0.66 tff(683,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$lesseq($sum(Y, $product(-1, X)), 0))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))),
% 0.57/0.66 inference(quant_intro,[status(thm)],[682])).
% 0.57/0.66 tff(684,plain,
% 0.57/0.66 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(rewrite((~$lesseq(Y, X)) <=> (~$lesseq($sum(Y, $product(-1, X)), 0))), (((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R)))) <=> ((~$lesseq($sum(Y, $product(-1, X)), 0)) | (~gt_tree1(X, node1(C, L, Y, V, R)))))), rewrite(((~$lesseq($sum(Y, $product(-1, X)), 0)) | (~gt_tree1(X, node1(C, L, Y, V, R)))) <=> ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$lesseq($sum(Y, $product(-1, X)), 0)))), (((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R)))) <=> ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$lesseq($sum(Y, $product(-1, X)), 0)))))),
% 0.57/0.66 inference(bind,[status(th)],[])).
% 0.57/0.66 tff(685,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R)))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$lesseq($sum(Y, $product(-1, X)), 0)))),
% 0.57/0.66 inference(quant_intro,[status(thm)],[684])).
% 0.57/0.66 tff(686,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R)))) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(687,plain,
% 0.57/0.66 (^[X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : trans(monotonicity(rewrite($less(X, Y) <=> (~$lesseq(Y, X))), ((gt_tree1(X, node1(C, L, Y, V, R)) => $less(X, Y)) <=> (gt_tree1(X, node1(C, L, Y, V, R)) => (~$lesseq(Y, X))))), rewrite((gt_tree1(X, node1(C, L, Y, V, R)) => (~$lesseq(Y, X))) <=> ((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R))))), ((gt_tree1(X, node1(C, L, Y, V, R)) => $less(X, Y)) <=> ((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R))))))),
% 0.57/0.66 inference(bind,[status(th)],[])).
% 0.57/0.66 tff(688,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) => $less(X, Y)) <=> ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R))))),
% 0.57/0.66 inference(quant_intro,[status(thm)],[687])).
% 0.57/0.66 tff(689,axiom,(![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) => $less(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_node_gt')).
% 0.57/0.66 tff(690,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.57/0.66 tff(691,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq(Y, X)) | (~gt_tree1(X, node1(C, L, Y, V, R))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[690, 686])).
% 0.57/0.66 tff(692,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$lesseq($sum(Y, $product(-1, X)), 0)))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[691, 685])).
% 0.57/0.66 tff(693,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[692, 683])).
% 0.57/0.66 tff(694,plain,(
% 0.57/0.66 ![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))),
% 0.57/0.66 inference(skolemize,[status(sab)],[693])).
% 0.57/0.66 tff(695,plain,
% 0.57/0.66 (![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[694, 681])).
% 0.57/0.66 tff(696,plain,
% 0.57/0.66 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(697,plain,
% 0.57/0.67 (((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0))) <=> ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(698,plain,
% 0.57/0.67 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))))),
% 0.57/0.67 inference(monotonicity,[status(thm)],[697])).
% 0.57/0.67 tff(699,plain,
% 0.57/0.67 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)))),
% 0.57/0.67 inference(transitivity,[status(thm)],[698, 696])).
% 0.57/0.67 tff(700,plain,
% 0.57/0.67 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0)))),
% 0.57/0.67 inference(quant_inst,[status(thm)],[])).
% 0.57/0.67 tff(701,plain,
% 0.57/0.67 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~gt_tree1(X, node1(C, L, Y, V, R))) | (~$greatereq($sum(X, $product(-1, Y)), 0)))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.57/0.67 tff(702,plain,
% 0.57/0.67 ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~$lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[701, 695])).
% 0.57/0.67 tff(703,plain,
% 0.57/0.67 (~$lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[702, 611])).
% 0.57/0.67 tff(704,plain,
% 0.57/0.67 (^[X: $int, Y: $int, T: tree1] : rewrite(($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0)))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(705,plain,
% 0.57/0.67 (![X: $int, Y: $int, T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[704])).
% 0.57/0.67 tff(706,plain,
% 0.57/0.67 (^[X: $int, Y: $int, T: tree1] : refl(($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(707,plain,
% 0.57/0.67 (![X: $int, Y: $int, T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[706])).
% 0.57/0.67 tff(708,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ![T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(pull_quant,[status(thm)],[])).
% 0.57/0.67 tff(709,plain,
% 0.57/0.67 (^[X: $int, Y: $int] : pull_quant(($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(710,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ![T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[709])).
% 0.57/0.67 tff(711,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(transitivity,[status(thm)],[710, 708])).
% 0.57/0.67 tff(712,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(transitivity,[status(thm)],[711, 707])).
% 0.57/0.67 tff(713,plain,
% 0.57/0.67 (^[X: $int, Y: $int] : rewrite(($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(714,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[713])).
% 0.57/0.67 tff(715,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int, T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(transitivity,[status(thm)],[714, 712])).
% 0.57/0.67 tff(716,plain,
% 0.57/0.67 (^[X: $int, Y: $int] : rewrite(($lesseq($sum(Y, $product(-1, X)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(717,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($lesseq($sum(Y, $product(-1, X)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[716])).
% 0.57/0.67 tff(718,plain,
% 0.57/0.67 (^[X: $int, Y: $int] : rewrite(($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ($lesseq($sum(Y, $product(-1, X)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(719,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($lesseq($sum(Y, $product(-1, X)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[718])).
% 0.57/0.67 tff(720,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(721,plain,
% 0.57/0.67 (^[X: $int, Y: $int] : trans(monotonicity(rewrite($less(X, Y) <=> (~$lesseq(Y, X))), quant_intro(proof_bind(^[T: tree1] : rewrite((lt_tree1(X, T) => lt_tree1(Y, T)) <=> ((~lt_tree1(X, T)) | lt_tree1(Y, T)))), (![T: tree1] : (lt_tree1(X, T) => lt_tree1(Y, T)) <=> ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))), (($less(X, Y) => ![T: tree1] : (lt_tree1(X, T) => lt_tree1(Y, T))) <=> ((~$lesseq(Y, X)) => ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))))), rewrite(((~$lesseq(Y, X)) => ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T))) <=> ($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))), (($less(X, Y) => ![T: tree1] : (lt_tree1(X, T) => lt_tree1(Y, T))) <=> ($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(722,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($less(X, Y) => ![T: tree1] : (lt_tree1(X, T) => lt_tree1(Y, T))) <=> ![X: $int, Y: $int] : ($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[721])).
% 0.57/0.67 tff(723,axiom,(![X: $int, Y: $int] : ($less(X, Y) => ![T: tree1] : (lt_tree1(X, T) => lt_tree1(Y, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lt_tree_trans')).
% 0.57/0.67 tff(724,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[723, 722])).
% 0.57/0.67 tff(725,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($lesseq(Y, X) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[724, 720])).
% 0.57/0.67 tff(726,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($lesseq($sum(Y, $product(-1, X)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[725, 719])).
% 0.57/0.67 tff(727,plain,
% 0.57/0.67 (![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[726, 717])).
% 0.57/0.67 tff(728,plain,(
% 0.57/0.67 ![X: $int, Y: $int] : ($greatereq($sum(X, $product(-1, Y)), 0) | ![T: tree1] : ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(skolemize,[status(sab)],[727])).
% 0.57/0.67 tff(729,plain,
% 0.57/0.67 (![X: $int, Y: $int, T: tree1] : ($greatereq($sum(X, $product(-1, Y)), 0) | ((~lt_tree1(X, T)) | lt_tree1(Y, T)))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[728, 715])).
% 0.57/0.67 tff(730,plain,
% 0.57/0.67 (![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[729, 705])).
% 0.57/0.67 tff(731,plain,
% 0.57/0.67 (((~![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, X1!14))) <=> ((~![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, X1!14))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(732,plain,
% 0.57/0.67 ((lt_tree1(X7!23, X1!14) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, X1!14))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(733,plain,
% 0.57/0.67 ($greatereq($sum($product(-1, X7!23), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11))), 0) <=> $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(734,plain,
% 0.57/0.67 ($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)) = $sum($product(-1, X7!23), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(735,plain,
% 0.57/0.67 ($greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0) <=> $greatereq($sum($product(-1, X7!23), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11))), 0)),
% 0.57/0.67 inference(monotonicity,[status(thm)],[734])).
% 0.57/0.67 tff(736,plain,
% 0.57/0.67 ($greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0) <=> $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0)),
% 0.57/0.67 inference(transitivity,[status(thm)],[735, 733])).
% 0.57/0.67 tff(737,plain,
% 0.57/0.67 ((lt_tree1(X7!23, X1!14) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0)) <=> (lt_tree1(X7!23, X1!14) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0))),
% 0.57/0.67 inference(monotonicity,[status(thm)],[736])).
% 0.57/0.67 tff(738,plain,
% 0.57/0.67 ((lt_tree1(X7!23, X1!14) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0)) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, X1!14))),
% 0.57/0.67 inference(transitivity,[status(thm)],[737, 732])).
% 0.57/0.67 tff(739,plain,
% 0.57/0.67 (((~![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))) | (lt_tree1(X7!23, X1!14) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0))) <=> ((~![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, X1!14)))),
% 0.57/0.67 inference(monotonicity,[status(thm)],[738])).
% 0.57/0.67 tff(740,plain,
% 0.57/0.67 (((~![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))) | (lt_tree1(X7!23, X1!14) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0))) <=> ((~![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, X1!14))),
% 0.57/0.67 inference(transitivity,[status(thm)],[739, 731])).
% 0.57/0.67 tff(741,plain,
% 0.57/0.67 ((~![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))) | (lt_tree1(X7!23, X1!14) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $greatereq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, X7!23)), 0))),
% 0.57/0.67 inference(quant_inst,[status(thm)],[])).
% 0.57/0.67 tff(742,plain,
% 0.57/0.67 ((~![X: $int, Y: $int, T: tree1] : (lt_tree1(Y, T) | (~lt_tree1(X, T)) | $greatereq($sum(X, $product(-1, Y)), 0))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X1!14)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, X1!14)),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.57/0.67 tff(743,plain,
% 0.57/0.67 ($false),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[742, 730, 637, 703, 679])).
% 0.57/0.67 tff(744,plain,(lt_tree1(X7!23, X1!14)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.67 tff(745,plain,
% 0.57/0.67 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, X6!24, X7!23, X8!22, X9!21)) <=> (~((~gt_tree1(X7!23, X9!21)) | (~bst1(X6!24)) | (~bst1(X9!21)) | (~lt_tree1(X7!23, X6!24)))))),
% 0.57/0.67 inference(quant_inst,[status(thm)],[])).
% 0.57/0.67 tff(746,plain,
% 0.57/0.67 (bst1(node1(red1, X6!24, X7!23, X8!22, X9!21)) <=> (~((~gt_tree1(X7!23, X9!21)) | (~bst1(X6!24)) | (~bst1(X9!21)) | (~lt_tree1(X7!23, X6!24))))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[745, 15])).
% 0.57/0.67 tff(747,plain,
% 0.57/0.67 ((~(bst1(node1(red1, X6!24, X7!23, X8!22, X9!21)) <=> (~((~gt_tree1(X7!23, X9!21)) | (~bst1(X6!24)) | (~bst1(X9!21)) | (~lt_tree1(X7!23, X6!24)))))) | (~bst1(node1(red1, X6!24, X7!23, X8!22, X9!21))) | (~((~gt_tree1(X7!23, X9!21)) | (~bst1(X6!24)) | (~bst1(X9!21)) | (~lt_tree1(X7!23, X6!24))))),
% 0.57/0.67 inference(tautology,[status(thm)],[])).
% 0.57/0.67 tff(748,plain,
% 0.57/0.67 (~((~gt_tree1(X7!23, X9!21)) | (~bst1(X6!24)) | (~bst1(X9!21)) | (~lt_tree1(X7!23, X6!24)))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[747, 629, 746])).
% 0.57/0.67 tff(749,plain,
% 0.57/0.67 (((~gt_tree1(X7!23, X9!21)) | (~bst1(X6!24)) | (~bst1(X9!21)) | (~lt_tree1(X7!23, X6!24))) | lt_tree1(X7!23, X6!24)),
% 0.57/0.67 inference(tautology,[status(thm)],[])).
% 0.57/0.67 tff(750,plain,
% 0.57/0.67 (lt_tree1(X7!23, X6!24)),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[749, 748])).
% 0.57/0.67 tff(751,plain,
% 0.57/0.67 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | ((~lt_tree1(X7!23, X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~lt_tree1(X7!23, X1!14)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(X7!23, X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~lt_tree1(X7!23, X1!14)))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(752,plain,
% 0.57/0.67 ((lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~lt_tree1(X7!23, X6!24)) | (~lt_tree1(X7!23, X1!14))) <=> ((~lt_tree1(X7!23, X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~lt_tree1(X7!23, X1!14)))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(753,plain,
% 0.57/0.67 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~lt_tree1(X7!23, X6!24)) | (~lt_tree1(X7!23, X1!14)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | ((~lt_tree1(X7!23, X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~lt_tree1(X7!23, X1!14))))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[752])).
% 0.57/0.68 tff(754,plain,
% 0.57/0.68 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~lt_tree1(X7!23, X6!24)) | (~lt_tree1(X7!23, X1!14)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(X7!23, X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~lt_tree1(X7!23, X1!14)))),
% 0.57/0.68 inference(transitivity,[status(thm)],[753, 751])).
% 0.57/0.68 tff(755,plain,
% 0.57/0.68 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | (~lt_tree1(X7!23, X6!24)) | (~lt_tree1(X7!23, X1!14)))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(756,plain,
% 0.57/0.68 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(X7!23, X6!24)) | $lesseq($sum(X7!23, $product(-1, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)))), 0) | lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24)) | (~lt_tree1(X7!23, X1!14))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.57/0.68 tff(757,plain,
% 0.57/0.68 (lt_tree1(X7!23, node1(black1, X1!14, node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X6!24))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[756, 458, 703, 750, 744])).
% 0.57/0.68 tff(758,plain,
% 0.57/0.68 ($false),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[757, 678])).
% 0.57/0.68 tff(759,plain,(lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.68 tff(760,plain,
% 0.57/0.68 (gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) <=> gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[644])).
% 0.57/0.68 tff(761,plain,
% 0.57/0.68 (gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7)) <=> gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.57/0.68 inference(symmetry,[status(thm)],[760])).
% 0.57/0.68 tff(762,plain,
% 0.57/0.68 ((~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) <=> (~gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[761])).
% 0.57/0.68 tff(763,assumption,(~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))), introduced(assumption)).
% 0.57/0.68 tff(764,plain,
% 0.57/0.68 (~gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.57/0.68 tff(765,assumption,(~gt_tree1(X7!23, R!7)), introduced(assumption)).
% 0.57/0.68 tff(766,plain,
% 0.57/0.68 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(K!9, $product(-1, X7!23)), 0)) | (~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~$lesseq($sum(K!9, $product(-1, X7!23)), 0)) | (~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(767,plain,
% 0.57/0.68 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(K!9, $product(-1, X7!23)), 0)) | (~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21))))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(768,plain,
% 0.57/0.68 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~$lesseq($sum(K!9, $product(-1, X7!23)), 0)) | (~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21)))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.57/0.68 tff(769,plain,
% 0.57/0.68 ((~$lesseq($sum(K!9, $product(-1, X7!23)), 0)) | (~lt_tree1(K!9, node1(red1, X6!24, X7!23, X8!22, X9!21)))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[768, 285])).
% 0.57/0.68 tff(770,plain,
% 0.57/0.68 (~$lesseq($sum(K!9, $product(-1, X7!23)), 0)),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[769, 657])).
% 0.57/0.68 tff(771,plain,
% 0.57/0.68 (((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | ((~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, R!7))) <=> ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, R!7))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(772,plain,
% 0.57/0.68 ((gt_tree1(X7!23, R!7) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | (~gt_tree1(K!9, R!7))) <=> ((~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, R!7))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(773,plain,
% 0.57/0.68 (((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (gt_tree1(X7!23, R!7) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | (~gt_tree1(K!9, R!7)))) <=> ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | ((~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, R!7)))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[772])).
% 0.57/0.68 tff(774,plain,
% 0.57/0.68 (((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (gt_tree1(X7!23, R!7) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | (~gt_tree1(K!9, R!7)))) <=> ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, R!7))),
% 0.57/0.68 inference(transitivity,[status(thm)],[773, 771])).
% 0.57/0.68 tff(775,plain,
% 0.57/0.68 ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (gt_tree1(X7!23, R!7) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | (~gt_tree1(K!9, R!7)))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(776,plain,
% 0.57/0.68 ((~![X: $int, Y: $int, T: tree1] : (gt_tree1(Y, T) | $lesseq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, T)))) | (~gt_tree1(K!9, R!7)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, R!7)),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.57/0.68 tff(777,plain,
% 0.57/0.68 ($false),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[776, 314, 234, 770, 765])).
% 0.57/0.68 tff(778,plain,(gt_tree1(X7!23, R!7)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.68 tff(779,plain,
% 0.57/0.68 (((~gt_tree1(X7!23, X9!21)) | (~bst1(X6!24)) | (~bst1(X9!21)) | (~lt_tree1(X7!23, X6!24))) | gt_tree1(X7!23, X9!21)),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(780,plain,
% 0.57/0.68 (gt_tree1(X7!23, X9!21)),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[779, 748])).
% 0.57/0.68 tff(781,plain,
% 0.57/0.68 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | ((~gt_tree1(X7!23, X9!21)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | (~gt_tree1(X7!23, R!7)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (~gt_tree1(X7!23, X9!21)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | (~gt_tree1(X7!23, R!7)))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(782,plain,
% 0.57/0.68 ((gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | (~gt_tree1(X7!23, R!7)) | (~gt_tree1(X7!23, X9!21))) <=> ((~gt_tree1(X7!23, X9!21)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | (~gt_tree1(X7!23, R!7)))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(783,plain,
% 0.57/0.68 ($greatereq($sum($product(-1, K!9), X7!23), 0) <=> $lesseq($sum(K!9, $product(-1, X7!23)), 0)),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(784,plain,
% 0.57/0.68 ($sum(X7!23, $product(-1, K!9)) = $sum($product(-1, K!9), X7!23)),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(785,plain,
% 0.57/0.68 ($greatereq($sum(X7!23, $product(-1, K!9)), 0) <=> $greatereq($sum($product(-1, K!9), X7!23), 0)),
% 0.57/0.68 inference(monotonicity,[status(thm)],[784])).
% 0.57/0.68 tff(786,plain,
% 0.57/0.68 ($greatereq($sum(X7!23, $product(-1, K!9)), 0) <=> $lesseq($sum(K!9, $product(-1, X7!23)), 0)),
% 0.57/0.68 inference(transitivity,[status(thm)],[785, 783])).
% 0.57/0.68 tff(787,plain,
% 0.57/0.68 ((gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(X7!23, $product(-1, K!9)), 0) | (~gt_tree1(X7!23, R!7)) | (~gt_tree1(X7!23, X9!21))) <=> (gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | (~gt_tree1(X7!23, R!7)) | (~gt_tree1(X7!23, X9!21)))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[786])).
% 0.57/0.68 tff(788,plain,
% 0.57/0.68 ((gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(X7!23, $product(-1, K!9)), 0) | (~gt_tree1(X7!23, R!7)) | (~gt_tree1(X7!23, X9!21))) <=> ((~gt_tree1(X7!23, X9!21)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | (~gt_tree1(X7!23, R!7)))),
% 0.57/0.68 inference(transitivity,[status(thm)],[787, 782])).
% 0.57/0.68 tff(789,plain,
% 0.57/0.68 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(X7!23, $product(-1, K!9)), 0) | (~gt_tree1(X7!23, R!7)) | (~gt_tree1(X7!23, X9!21)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | ((~gt_tree1(X7!23, X9!21)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | (~gt_tree1(X7!23, R!7))))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[788])).
% 0.57/0.68 tff(790,plain,
% 0.57/0.68 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(X7!23, $product(-1, K!9)), 0) | (~gt_tree1(X7!23, R!7)) | (~gt_tree1(X7!23, X9!21)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (~gt_tree1(X7!23, X9!21)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | (~gt_tree1(X7!23, R!7)))),
% 0.57/0.68 inference(transitivity,[status(thm)],[789, 781])).
% 0.57/0.68 tff(791,plain,
% 0.57/0.68 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | $greatereq($sum(X7!23, $product(-1, K!9)), 0) | (~gt_tree1(X7!23, R!7)) | (~gt_tree1(X7!23, X9!21)))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(792,plain,
% 0.57/0.68 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (gt_tree1(X, node1(C, L, Y, V, R)) | $greatereq($sum(X, $product(-1, Y)), 0) | (~gt_tree1(X, R)) | (~gt_tree1(X, L)))) | (~gt_tree1(X7!23, X9!21)) | $lesseq($sum(K!9, $product(-1, X7!23)), 0) | gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7)) | (~gt_tree1(X7!23, R!7))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[791, 790])).
% 0.57/0.68 tff(793,plain,
% 0.57/0.68 (gt_tree1(X7!23, node1(black1, X9!21, K!9, node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), R!7))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[792, 347, 770, 780, 778])).
% 0.57/0.68 tff(794,plain,
% 0.57/0.68 ($false),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[793, 764])).
% 0.57/0.68 tff(795,plain,(gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.68 tff(796,plain,
% 0.57/0.68 ((~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))) | (~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24)))),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(797,plain,
% 0.57/0.68 ((~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))) | (~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7)))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[796, 795, 759])).
% 0.57/0.68 tff(798,plain,
% 0.57/0.68 (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[797, 673, 643])).
% 0.57/0.68 tff(799,plain,
% 0.57/0.68 ((~(bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) <=> (~((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))))) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, node_proj_41(node1(X5!25, X6!24, X7!23, X8!22, X9!21)), node1(black1, X9!21, K!9, V!8, R!7))) | ((~bst1(node1(black1, X1!14, X2!13, X3!12, X6!24))) | (~bst1(node1(black1, X9!21, K!9, V!8, R!7))) | (~gt_tree1(X7!23, node1(black1, X9!21, K!9, V!8, R!7))) | (~lt_tree1(X7!23, node1(black1, X1!14, X2!13, X3!12, X6!24))))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(800,plain,
% 0.57/0.69 ($false),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[799, 798, 593, 22])).
% 0.57/0.69 tff(801,plain,(bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7)))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.69 tff(802,plain,
% 0.57/0.69 (((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7)))) | (~bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(803,plain,
% 0.57/0.69 ((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7)))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[802, 801])).
% 0.57/0.69 tff(804,plain,
% 0.57/0.69 (((~(X5!25 = red1)) | (~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))))))))) | ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(805,plain,
% 0.57/0.69 ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[804, 580])).
% 0.57/0.69 tff(806,plain,
% 0.57/0.69 ((~((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))))) | (~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))))))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(807,plain,
% 0.57/0.69 ((~((~(X!15 = red1)) | (~(X1!14 = leaf1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))) | (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[806, 805])).
% 0.57/0.69 tff(808,plain,
% 0.57/0.69 (~((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[807, 803])).
% 0.57/0.69 tff(809,plain,
% 0.57/0.69 (((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))))) | (X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(810,plain,
% 0.57/0.69 (X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26)),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[809, 808])).
% 0.57/0.69 tff(811,plain,
% 0.57/0.69 (node1(X10!30, X11!29, X12!28, X13!27, X14!26) = X1!14),
% 0.57/0.69 inference(symmetry,[status(thm)],[810])).
% 0.57/0.69 tff(812,plain,
% 0.57/0.69 (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))) | (~bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(813,plain,
% 0.57/0.69 ((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[812, 801])).
% 0.57/0.69 tff(814,plain,
% 0.57/0.69 (((~(X1!14 = node1(X10!30, X11!29, X12!28, X13!27, X14!26))) | (~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))))) | ((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(815,plain,
% 0.57/0.69 ((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[814, 808])).
% 0.57/0.69 tff(816,plain,
% 0.57/0.69 ((~((~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1)))))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))) | (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X1!14, X2!13, X3!12, X6!24), X7!23, X8!22, node1(black1, X9!21, K!9, V!8, R!7))) | (~(X10!30 = black1))))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(817,plain,
% 0.57/0.69 (~((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1)))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[816, 815, 813])).
% 0.57/0.69 tff(818,plain,
% 0.57/0.69 (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) | (X10!30 = red1)),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(819,plain,
% 0.57/0.69 (X10!30 = red1),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[818, 817])).
% 0.57/0.69 tff(820,plain,
% 0.57/0.69 (red1 = X10!30),
% 0.57/0.69 inference(symmetry,[status(thm)],[819])).
% 0.57/0.69 tff(821,plain,
% 0.57/0.69 (node1(red1, X11!29, X12!28, X13!27, X14!26) = node1(X10!30, X11!29, X12!28, X13!27, X14!26)),
% 0.57/0.69 inference(monotonicity,[status(thm)],[820])).
% 0.57/0.69 tff(822,plain,
% 0.57/0.69 (node1(red1, X11!29, X12!28, X13!27, X14!26) = X1!14),
% 0.57/0.69 inference(transitivity,[status(thm)],[821, 811])).
% 0.57/0.69 tff(823,plain,
% 0.57/0.69 ((leaf1 = node1(red1, X11!29, X12!28, X13!27, X14!26)) <=> (leaf1 = X1!14)),
% 0.57/0.69 inference(monotonicity,[status(thm)],[822])).
% 0.57/0.69 tff(824,plain,
% 0.57/0.69 ((leaf1 = node1(red1, X11!29, X12!28, X13!27, X14!26)) <=> (X1!14 = leaf1)),
% 0.57/0.69 inference(transitivity,[status(thm)],[823, 1])).
% 0.57/0.69 tff(825,plain,
% 0.57/0.69 ((~(leaf1 = node1(red1, X11!29, X12!28, X13!27, X14!26))) <=> (~(X1!14 = leaf1))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[824])).
% 0.57/0.69 tff(826,plain,
% 0.57/0.69 ((~![V: color1, V1: tree1, V2: $int, V3: $int, V4: tree1] : (~(leaf1 = node1(V, V1, V2, V3, V4)))) | (~(leaf1 = node1(red1, X11!29, X12!28, X13!27, X14!26)))),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(827,plain,
% 0.57/0.69 (~(leaf1 = node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[826, 125])).
% 0.57/0.69 tff(828,plain,
% 0.57/0.69 (~(X1!14 = leaf1)),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[827, 825])).
% 0.57/0.69 tff(829,plain,
% 0.57/0.69 (((~![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))) | ((X1!14 = leaf1) | (X1!14 = node1(node_proj_11(X1!14), node_proj_21(X1!14), node_proj_31(X1!14), node_proj_41(X1!14), node_proj_51(X1!14))))) <=> ((~![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))) | (X1!14 = leaf1) | (X1!14 = node1(node_proj_11(X1!14), node_proj_21(X1!14), node_proj_31(X1!14), node_proj_41(X1!14), node_proj_51(X1!14))))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(830,plain,
% 0.57/0.69 ((~![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))) | ((X1!14 = leaf1) | (X1!14 = node1(node_proj_11(X1!14), node_proj_21(X1!14), node_proj_31(X1!14), node_proj_41(X1!14), node_proj_51(X1!14))))),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(831,plain,
% 0.57/0.69 ((~![U: tree1] : ((U = leaf1) | (U = node1(node_proj_11(U), node_proj_21(U), node_proj_31(U), node_proj_41(U), node_proj_51(U))))) | (X1!14 = leaf1) | (X1!14 = node1(node_proj_11(X1!14), node_proj_21(X1!14), node_proj_31(X1!14), node_proj_41(X1!14), node_proj_51(X1!14)))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[830, 829])).
% 0.57/0.69 tff(832,plain,
% 0.57/0.69 (X1!14 = node1(node_proj_11(X1!14), node_proj_21(X1!14), node_proj_31(X1!14), node_proj_41(X1!14), node_proj_51(X1!14))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[831, 135, 828])).
% 0.57/0.69 tff(833,plain,
% 0.57/0.69 (node1(node_proj_11(X1!14), node_proj_21(X1!14), node_proj_31(X1!14), node_proj_41(X1!14), node_proj_51(X1!14)) = X1!14),
% 0.57/0.69 inference(symmetry,[status(thm)],[832])).
% 0.57/0.69 tff(834,plain,
% 0.57/0.69 (node1(X10!30, X11!29, X12!28, X13!27, X14!26) = node1(red1, X11!29, X12!28, X13!27, X14!26)),
% 0.57/0.69 inference(symmetry,[status(thm)],[821])).
% 0.57/0.69 tff(835,plain,
% 0.57/0.69 (X1!14 = node1(red1, X11!29, X12!28, X13!27, X14!26)),
% 0.57/0.69 inference(transitivity,[status(thm)],[810, 834])).
% 0.57/0.69 tff(836,plain,
% 0.57/0.69 (node_proj_51(X1!14) = node_proj_51(node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[835])).
% 0.57/0.69 tff(837,plain,
% 0.57/0.69 (node_proj_51(node1(red1, X11!29, X12!28, X13!27, X14!26)) = node_proj_51(X1!14)),
% 0.57/0.69 inference(symmetry,[status(thm)],[836])).
% 0.57/0.69 tff(838,plain,
% 0.57/0.69 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_51(node1(U, U1, U2, U3, U4)) = U4)) | (node_proj_51(node1(red1, X11!29, X12!28, X13!27, X14!26)) = X14!26)),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(839,plain,
% 0.57/0.69 (node_proj_51(node1(red1, X11!29, X12!28, X13!27, X14!26)) = X14!26),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[838, 50])).
% 0.57/0.69 tff(840,plain,
% 0.57/0.69 (X14!26 = node_proj_51(node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(symmetry,[status(thm)],[839])).
% 0.57/0.69 tff(841,plain,
% 0.57/0.69 (X14!26 = node_proj_51(X1!14)),
% 0.57/0.69 inference(transitivity,[status(thm)],[840, 837])).
% 0.57/0.69 tff(842,plain,
% 0.57/0.69 (node_proj_41(X1!14) = node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[810])).
% 0.57/0.69 tff(843,plain,
% 0.57/0.69 (node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)) = node_proj_41(X1!14)),
% 0.57/0.69 inference(symmetry,[status(thm)],[842])).
% 0.57/0.69 tff(844,plain,
% 0.57/0.69 (node_proj_31(X1!14) = node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[810])).
% 0.57/0.69 tff(845,plain,
% 0.57/0.69 (node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)) = node_proj_31(X1!14)),
% 0.57/0.69 inference(symmetry,[status(thm)],[844])).
% 0.57/0.69 tff(846,plain,
% 0.57/0.69 (node_proj_21(X1!14) = node_proj_21(node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[835])).
% 0.57/0.69 tff(847,plain,
% 0.57/0.69 (node_proj_21(node1(red1, X11!29, X12!28, X13!27, X14!26)) = node_proj_21(X1!14)),
% 0.57/0.69 inference(symmetry,[status(thm)],[846])).
% 0.57/0.69 tff(848,plain,
% 0.57/0.69 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_21(node1(U, U1, U2, U3, U4)) = U1)) | (node_proj_21(node1(red1, X11!29, X12!28, X13!27, X14!26)) = X11!29)),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(849,plain,
% 0.57/0.69 (node_proj_21(node1(red1, X11!29, X12!28, X13!27, X14!26)) = X11!29),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[848, 88])).
% 0.57/0.69 tff(850,plain,
% 0.57/0.69 (X11!29 = node_proj_21(node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(symmetry,[status(thm)],[849])).
% 0.57/0.69 tff(851,plain,
% 0.57/0.69 (X11!29 = node_proj_21(X1!14)),
% 0.57/0.69 inference(transitivity,[status(thm)],[850, 847])).
% 0.57/0.69 tff(852,plain,
% 0.57/0.69 (node_proj_11(X1!14) = node_proj_11(node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[835])).
% 0.57/0.69 tff(853,plain,
% 0.57/0.69 (node_proj_11(node1(red1, X11!29, X12!28, X13!27, X14!26)) = node_proj_11(X1!14)),
% 0.57/0.69 inference(symmetry,[status(thm)],[852])).
% 0.57/0.69 tff(854,plain,
% 0.57/0.69 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : (node_proj_11(node1(U, U1, U2, U3, U4)) = U)) | (node_proj_11(node1(red1, X11!29, X12!28, X13!27, X14!26)) = red1)),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(855,plain,
% 0.57/0.69 (node_proj_11(node1(red1, X11!29, X12!28, X13!27, X14!26)) = red1),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[854, 97])).
% 0.57/0.69 tff(856,plain,
% 0.57/0.69 (red1 = node_proj_11(node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.69 inference(symmetry,[status(thm)],[855])).
% 0.57/0.69 tff(857,plain,
% 0.57/0.69 (red1 = node_proj_11(X1!14)),
% 0.57/0.69 inference(transitivity,[status(thm)],[856, 853])).
% 0.57/0.69 tff(858,plain,
% 0.57/0.69 (node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26) = node1(node_proj_11(X1!14), node_proj_21(X1!14), node_proj_31(X1!14), node_proj_41(X1!14), node_proj_51(X1!14))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[857, 851, 845, 843, 841])).
% 0.57/0.69 tff(859,plain,
% 0.57/0.69 (node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26) = X1!14),
% 0.57/0.69 inference(transitivity,[status(thm)],[858, 833])).
% 0.57/0.69 tff(860,plain,
% 0.57/0.69 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)) <=> lt_tree1(X2!13, X1!14)),
% 0.57/0.70 inference(monotonicity,[status(thm)],[157, 859])).
% 0.57/0.70 tff(861,plain,
% 0.57/0.70 (lt_tree1(X2!13, X1!14) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))),
% 0.57/0.70 inference(symmetry,[status(thm)],[860])).
% 0.57/0.70 tff(862,plain,
% 0.57/0.70 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[411, 861])).
% 0.57/0.70 tff(863,plain,
% 0.57/0.70 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26)) <=> lt_tree1(X2!13, X1!14)),
% 0.57/0.70 inference(monotonicity,[status(thm)],[157, 822])).
% 0.57/0.70 tff(864,plain,
% 0.57/0.70 (lt_tree1(X2!13, X1!14) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.70 inference(symmetry,[status(thm)],[863])).
% 0.57/0.70 tff(865,plain,
% 0.57/0.70 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[411, 864])).
% 0.57/0.70 tff(866,plain,
% 0.57/0.70 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(867,plain,
% 0.57/0.70 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(868,plain,
% 0.57/0.70 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, L))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[867, 866])).
% 0.57/0.70 tff(869,plain,
% 0.57/0.70 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[868, 435])).
% 0.57/0.70 tff(870,plain,
% 0.57/0.70 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[869, 865])).
% 0.57/0.70 tff(871,plain,
% 0.57/0.70 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(872,plain,
% 0.57/0.70 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(873,plain,
% 0.57/0.70 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~lt_tree1(X, node1(C, L, Y, V, R))) | lt_tree1(X, R))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.57/0.70 tff(874,plain,
% 0.57/0.70 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, X12!28, X13!27, X14!26))) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[873, 227])).
% 0.57/0.70 tff(875,plain,
% 0.57/0.70 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[874, 865])).
% 0.57/0.70 tff(876,plain,
% 0.57/0.70 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)))))))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(877,plain,
% 0.57/0.70 ((bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)))))) <=> (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(878,plain,
% 0.57/0.70 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)))))))),
% 0.57/0.71 inference(monotonicity,[status(thm)],[877])).
% 0.57/0.71 tff(879,plain,
% 0.57/0.71 (((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))))) <=> ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)))))))),
% 0.57/0.71 inference(transitivity,[status(thm)],[878, 876])).
% 0.57/0.71 tff(880,plain,
% 0.57/0.71 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))))),
% 0.57/0.71 inference(quant_inst,[status(thm)],[])).
% 0.57/0.71 tff(881,plain,
% 0.57/0.71 ((~![X: color1, X1: tree1, X2: $int, X3: $int, X4: tree1] : (bst1(node1(X, X1, X2, X3, X4)) <=> (~((~gt_tree1(X2, X4)) | (~bst1(X1)) | (~bst1(X4)) | (~lt_tree1(X2, X1)))))) | (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))))),
% 0.57/0.71 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.57/0.71 tff(882,plain,
% 0.57/0.71 (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)))))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[881, 15])).
% 0.64/0.71 tff(883,plain,
% 0.64/0.71 (node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))) = node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))),
% 0.64/0.71 inference(monotonicity,[status(thm)],[157, 149, 141])).
% 0.64/0.71 tff(884,plain,
% 0.64/0.71 (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))),
% 0.64/0.71 inference(monotonicity,[status(thm)],[883])).
% 0.64/0.71 tff(885,plain,
% 0.64/0.71 (bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) <=> bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.64/0.71 inference(symmetry,[status(thm)],[884])).
% 0.64/0.71 tff(886,plain,
% 0.64/0.71 ((~bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))) <=> (~bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))))),
% 0.64/0.71 inference(monotonicity,[status(thm)],[885])).
% 0.64/0.71 tff(887,plain,
% 0.64/0.71 (((~(X!15 = red1)) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))) | (~(X10!30 = red1))) | (~bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7))))),
% 0.64/0.71 inference(tautology,[status(thm)],[])).
% 0.64/0.71 tff(888,plain,
% 0.64/0.71 (~bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), X2!13, X3!12, node1(black1, X4!11, K!9, V!8, R!7)))),
% 0.64/0.71 inference(unit_resolution,[status(thm)],[887, 817])).
% 0.64/0.71 tff(889,plain,
% 0.64/0.71 (~bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7)))))),
% 0.64/0.71 inference(modus_ponens,[status(thm)],[888, 886])).
% 0.64/0.71 tff(890,plain,
% 0.64/0.71 ((~(bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) <=> (~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))))) | bst1(node1(red1, node1(black1, X11!29, X12!28, X13!27, X14!26), node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node_proj_41(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))),
% 0.64/0.72 inference(tautology,[status(thm)],[])).
% 0.64/0.72 tff(891,plain,
% 0.64/0.72 ((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)))),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[890, 889, 882])).
% 0.64/0.72 tff(892,plain,
% 0.64/0.72 (bst1(node1(red1, X11!29, X12!28, X13!27, X14!26)) <=> bst1(X1!14)),
% 0.64/0.72 inference(monotonicity,[status(thm)],[822])).
% 0.64/0.72 tff(893,plain,
% 0.64/0.72 (bst1(X1!14) <=> bst1(node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.64/0.72 inference(symmetry,[status(thm)],[892])).
% 0.64/0.72 tff(894,plain,
% 0.64/0.72 (bst1(node1(red1, X11!29, X12!28, X13!27, X14!26))),
% 0.64/0.72 inference(modus_ponens,[status(thm)],[388, 893])).
% 0.64/0.72 tff(895,plain,
% 0.64/0.72 (((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | (bst1(node1(black1, X11!29, X12!28, X13!27, X14!26)) | (~bst1(node1(red1, X11!29, X12!28, X13!27, X14!26))))) <=> ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | bst1(node1(black1, X11!29, X12!28, X13!27, X14!26)) | (~bst1(node1(red1, X11!29, X12!28, X13!27, X14!26))))),
% 0.64/0.72 inference(rewrite,[status(thm)],[])).
% 0.64/0.72 tff(896,plain,
% 0.64/0.72 ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | (bst1(node1(black1, X11!29, X12!28, X13!27, X14!26)) | (~bst1(node1(red1, X11!29, X12!28, X13!27, X14!26))))),
% 0.64/0.72 inference(quant_inst,[status(thm)],[])).
% 0.64/0.72 tff(897,plain,
% 0.64/0.72 ((~![C: color1, Cqt: color1, K: $int, V: $int, L: tree1, R: tree1] : (bst1(node1(Cqt, L, K, V, R)) | (~bst1(node1(C, L, K, V, R))))) | bst1(node1(black1, X11!29, X12!28, X13!27, X14!26)) | (~bst1(node1(red1, X11!29, X12!28, X13!27, X14!26)))),
% 0.64/0.72 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.64/0.72 tff(898,plain,
% 0.64/0.72 (bst1(node1(black1, X11!29, X12!28, X13!27, X14!26)) | (~bst1(node1(red1, X11!29, X12!28, X13!27, X14!26)))),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[897, 399])).
% 0.64/0.72 tff(899,plain,
% 0.64/0.72 (bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[898, 894])).
% 0.64/0.72 tff(900,plain,
% 0.64/0.72 ((~((~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))))) | (~gt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(node_proj_11(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_21(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_31(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_41(node1(black1, X4!11, K!9, V!8, R!7)), node_proj_51(node1(black1, X4!11, K!9, V!8, R!7))))) | (~bst1(node1(black1, X11!29, X12!28, X13!27, X14!26))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)))),
% 0.64/0.72 inference(tautology,[status(thm)],[])).
% 0.64/0.72 tff(901,plain,
% 0.64/0.72 (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[900, 899, 363, 240, 891])).
% 0.64/0.72 tff(902,plain,
% 0.64/0.72 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U3, $product(-1, node_proj_41(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X13!27, $product(-1, node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))) = 0)),
% 0.64/0.72 inference(quant_inst,[status(thm)],[])).
% 0.64/0.72 tff(903,plain,
% 0.64/0.72 ($sum(X13!27, $product(-1, node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))) = 0),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[902, 35])).
% 0.64/0.72 tff(904,plain,
% 0.64/0.72 ((~($sum(X13!27, $product(-1, node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))) = 0)) | $lesseq($sum(X13!27, $product(-1, node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.72 inference(theory_lemma,[status(thm)],[])).
% 0.64/0.72 tff(905,plain,
% 0.64/0.72 ($lesseq($sum(X13!27, $product(-1, node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[904, 903])).
% 0.64/0.72 tff(906,plain,
% 0.64/0.72 ((~($sum(X13!27, $product(-1, node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))) = 0)) | $greatereq($sum(X13!27, $product(-1, node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.72 inference(theory_lemma,[status(thm)],[])).
% 0.64/0.72 tff(907,plain,
% 0.64/0.72 ($greatereq($sum(X13!27, $product(-1, node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[906, 903])).
% 0.64/0.72 tff(908,plain,
% 0.64/0.72 (X13!27 = node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26))),
% 0.64/0.72 inference(theory_lemma,[status(thm)],[907, 905])).
% 0.64/0.72 tff(909,plain,
% 0.64/0.72 (node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)) = X13!27),
% 0.64/0.72 inference(symmetry,[status(thm)],[908])).
% 0.64/0.72 tff(910,plain,
% 0.64/0.72 ((~![U: color1, U1: tree1, U2: $int, U3: $int, U4: tree1] : ($sum(U2, $product(-1, node_proj_31(node1(U, U1, U2, U3, U4)))) = 0)) | ($sum(X12!28, $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))) = 0)),
% 0.64/0.72 inference(quant_inst,[status(thm)],[])).
% 0.64/0.72 tff(911,plain,
% 0.64/0.72 ($sum(X12!28, $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))) = 0),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[910, 73])).
% 0.64/0.72 tff(912,plain,
% 0.64/0.72 ((~($sum(X12!28, $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))) = 0)) | $lesseq($sum(X12!28, $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.72 inference(theory_lemma,[status(thm)],[])).
% 0.64/0.72 tff(913,plain,
% 0.64/0.72 ($lesseq($sum(X12!28, $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[912, 911])).
% 0.64/0.72 tff(914,plain,
% 0.64/0.72 ((~($sum(X12!28, $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))) = 0)) | $greatereq($sum(X12!28, $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.72 inference(theory_lemma,[status(thm)],[])).
% 0.64/0.72 tff(915,plain,
% 0.64/0.72 ($greatereq($sum(X12!28, $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.72 inference(unit_resolution,[status(thm)],[914, 911])).
% 0.64/0.72 tff(916,plain,
% 0.64/0.72 (X12!28 = node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26))),
% 0.64/0.72 inference(theory_lemma,[status(thm)],[915, 913])).
% 0.64/0.72 tff(917,plain,
% 0.64/0.72 (node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)) = X12!28),
% 0.64/0.72 inference(symmetry,[status(thm)],[916])).
% 0.64/0.72 tff(918,plain,
% 0.64/0.72 (node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26) = node1(black1, X11!29, X12!28, X13!27, X14!26)),
% 0.64/0.72 inference(monotonicity,[status(thm)],[917, 909])).
% 0.64/0.72 tff(919,plain,
% 0.64/0.72 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))),
% 0.64/0.72 inference(monotonicity,[status(thm)],[918])).
% 0.64/0.72 tff(920,plain,
% 0.64/0.72 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)) <=> lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))),
% 0.64/0.72 inference(symmetry,[status(thm)],[919])).
% 0.64/0.72 tff(921,plain,
% 0.64/0.72 ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))) <=> (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)))),
% 0.64/0.72 inference(monotonicity,[status(thm)],[920])).
% 0.64/0.72 tff(922,assumption,(~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26))), introduced(assumption)).
% 0.64/0.72 tff(923,plain,
% 0.64/0.72 (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))),
% 0.64/0.72 inference(modus_ponens,[status(thm)],[922, 921])).
% 0.64/0.72 tff(924,assumption,(lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)), introduced(assumption)).
% 0.64/0.72 tff(925,assumption,(lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)), introduced(assumption)).
% 0.64/0.72 tff(926,assumption,(~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)), introduced(assumption)).
% 0.64/0.72 tff(927,plain,
% 0.64/0.72 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)))),
% 0.64/0.72 inference(rewrite,[status(thm)],[])).
% 0.64/0.72 tff(928,plain,
% 0.64/0.72 ((lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29))) <=> ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)))),
% 0.64/0.72 inference(rewrite,[status(thm)],[])).
% 0.64/0.72 tff(929,plain,
% 0.64/0.72 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | ((~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))))),
% 0.64/0.72 inference(monotonicity,[status(thm)],[928])).
% 0.64/0.72 tff(930,plain,
% 0.64/0.72 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)))),
% 0.64/0.73 inference(transitivity,[status(thm)],[929, 927])).
% 0.64/0.73 tff(931,plain,
% 0.64/0.73 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)))),
% 0.64/0.73 inference(quant_inst,[status(thm)],[])).
% 0.64/0.73 tff(932,plain,
% 0.64/0.73 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : (lt_tree1(X, node1(C, L, Y, V, R)) | $lesseq($sum(X, $product(-1, Y)), 0) | (~lt_tree1(X, R)) | (~lt_tree1(X, L)))) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))),
% 0.64/0.73 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.64/0.73 tff(933,plain,
% 0.64/0.73 (lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))),
% 0.64/0.73 inference(unit_resolution,[status(thm)],[932, 458, 926, 925, 924])).
% 0.64/0.73 tff(934,plain,
% 0.64/0.73 ($false),
% 0.64/0.73 inference(unit_resolution,[status(thm)],[933, 923])).
% 0.64/0.73 tff(935,plain,(lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(black1, X11!29, X12!28, X13!27, X14!26)) | $lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X14!26)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), X11!29))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.73 tff(936,plain,
% 0.64/0.73 ($lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)),
% 0.64/0.73 inference(unit_resolution,[status(thm)],[935, 901, 875, 870])).
% 0.64/0.73 tff(937,plain,
% 0.64/0.73 (((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))))) <=> ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))))),
% 0.64/0.73 inference(rewrite,[status(thm)],[])).
% 0.64/0.73 tff(938,plain,
% 0.64/0.73 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | ((~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))))),
% 0.64/0.73 inference(quant_inst,[status(thm)],[])).
% 0.64/0.73 tff(939,plain,
% 0.64/0.73 ((~![X: $int, Y: $int, V: $int, L: tree1, R: tree1, C: color1] : ((~$lesseq($sum(X, $product(-1, Y)), 0)) | (~lt_tree1(X, node1(C, L, Y, V, R))))) | (~$lesseq($sum(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), $product(-1, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)))), 0)) | (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26)))),
% 0.64/0.73 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.64/0.73 tff(940,plain,
% 0.64/0.73 (~lt_tree1(node_proj_31(node1(X!15, X1!14, X2!13, X3!12, X4!11)), node1(red1, X11!29, node_proj_31(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), node_proj_41(node1(X10!30, X11!29, X12!28, X13!27, X14!26)), X14!26))),
% 0.64/0.73 inference(unit_resolution,[status(thm)],[939, 285, 936])).
% 0.64/0.73 tff(941,plain,
% 0.64/0.73 ($false),
% 0.64/0.73 inference(unit_resolution,[status(thm)],[940, 862])).
% 0.64/0.73 % SZS output end Proof
%------------------------------------------------------------------------------