TSTP Solution File: SWW602_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW602_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 20:59:24 EDT 2022
% Result : Theorem 124.49s 80.02s
% Output : Proof 124.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW602_2 : TPTP v8.1.0. Released v6.1.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n019.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun Sep 4 20:19:05 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.15/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.30 Usage: tptp [options] [-file:]file
% 0.15/0.30 -h, -? prints this message.
% 0.15/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.30 -m, -model generate model.
% 0.15/0.30 -p, -proof generate proof.
% 0.15/0.30 -c, -core generate unsat core of named formulas.
% 0.15/0.30 -st, -statistics display statistics.
% 0.15/0.30 -t:timeout set timeout (in second).
% 0.15/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.30 -<param>:<value> configuration parameter and value.
% 0.15/0.30 -o:<output-file> file to place output in.
% 124.49/80.02 % SZS status Theorem
% 124.49/80.02 % SZS output start Proof
% 124.49/80.02 tff(size1_type, type, (
% 124.49/80.02 size1: tree1 > $int)).
% 124.49/80.02 tff(tptp_fun_T_20_type, type, (
% 124.49/80.02 tptp_fun_T_20: tree1)).
% 124.49/80.02 tff(tptp_fun_I_11_type, type, (
% 124.49/80.02 tptp_fun_I_11: $int)).
% 124.49/80.02 tff(node1_type, type, (
% 124.49/80.02 node1: ( tree1 * tree1 ) > tree1)).
% 124.49/80.02 tff(tptp_fun_R_17_type, type, (
% 124.49/80.02 tptp_fun_R_17: tree1 > tree1)).
% 124.49/80.02 tff(tptp_fun_L_18_type, type, (
% 124.49/80.02 tptp_fun_L_18: tree1 > tree1)).
% 124.49/80.02 tff(tptp_fun_J_14_type, type, (
% 124.49/80.02 tptp_fun_J_14: $int)).
% 124.49/80.02 tff(mem_type, type, (
% 124.49/80.02 mem: ( ty * uni * uni ) > $o)).
% 124.49/80.02 tff(t2tb1_type, type, (
% 124.49/80.02 t2tb1: list_tree > uni)).
% 124.49/80.02 tff(tptp_fun_O_16_type, type, (
% 124.49/80.02 tptp_fun_O_16: list_tree)).
% 124.49/80.02 tff(t2tb2_type, type, (
% 124.49/80.02 t2tb2: tree1 > uni)).
% 124.49/80.02 tff(tree_type, type, (
% 124.49/80.02 tree: ty)).
% 124.49/80.02 tff(get_type, type, (
% 124.49/80.02 get: ( ty * ty * uni * uni ) > uni)).
% 124.49/80.02 tff(t2tb_type, type, (
% 124.49/80.02 t2tb: $int > uni)).
% 124.49/80.02 tff(t2tb3_type, type, (
% 124.49/80.02 t2tb3: map_int_lplist_treerp > uni)).
% 124.49/80.02 tff(tptp_fun_A3_15_type, type, (
% 124.49/80.02 tptp_fun_A3_15: map_int_lplist_treerp)).
% 124.49/80.02 tff(int_type, type, (
% 124.49/80.02 int: ty)).
% 124.49/80.02 tff(list_type, type, (
% 124.49/80.02 list: ty > ty)).
% 124.49/80.02 tff(tptp_fun_R_21_type, type, (
% 124.49/80.02 tptp_fun_R_21: tree1 > tree1)).
% 124.49/80.02 tff(tptp_fun_L_22_type, type, (
% 124.49/80.02 tptp_fun_L_22: tree1 > tree1)).
% 124.49/80.02 tff(distinct_type, type, (
% 124.49/80.02 distinct: ( ty * uni ) > $o)).
% 124.49/80.02 tff(all_trees1_type, type, (
% 124.49/80.02 all_trees1: ( $int * list_tree ) > $o)).
% 124.49/80.02 tff(tb2t1_type, type, (
% 124.49/80.02 tb2t1: uni > list_tree)).
% 124.49/80.02 tff(tptp_fun_A4_19_type, type, (
% 124.49/80.02 tptp_fun_A4_19: map_int_lplist_treerp)).
% 124.49/80.02 tff(tb2t3_type, type, (
% 124.49/80.02 tb2t3: uni > map_int_lplist_treerp)).
% 124.49/80.02 tff(set_type, type, (
% 124.49/80.02 set: ( ty * ty * uni * uni * uni ) > uni)).
% 124.49/80.02 tff(infix_plpl_type, type, (
% 124.49/80.02 infix_plpl: ( ty * uni * uni ) > uni)).
% 124.49/80.02 tff(tptp_fun_N_9_type, type, (
% 124.49/80.02 tptp_fun_N_9: $int)).
% 124.49/80.02 tff(nil_type, type, (
% 124.49/80.02 nil: ty > uni)).
% 124.49/80.02 tff(tptp_fun_A1_12_type, type, (
% 124.49/80.02 tptp_fun_A1_12: map_int_lplist_treerp)).
% 124.49/80.02 tff(tptp_fun_A2_13_type, type, (
% 124.49/80.02 tptp_fun_A2_13: map_int_lplist_treerp)).
% 124.49/80.02 tff(cons_type, type, (
% 124.49/80.02 cons: ( ty * uni * uni ) > uni)).
% 124.49/80.02 tff(empty1_type, type, (
% 124.49/80.02 empty1: tree1)).
% 124.49/80.02 tff(const_type, type, (
% 124.49/80.02 const: ( ty * ty * uni ) > uni)).
% 124.49/80.02 tff(tptp_fun_A_10_type, type, (
% 124.49/80.02 tptp_fun_A_10: map_int_lplist_treerp)).
% 124.49/80.02 tff(sort1_type, type, (
% 124.49/80.02 sort1: ( ty * uni ) > $o)).
% 124.49/80.02 tff(1,assumption,($greatereq($sum(I!11, $product(-1, size1(T!20))), 0)), introduced(assumption)).
% 124.49/80.02 tff(2,assumption,(~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))), introduced(assumption)).
% 124.49/80.02 tff(3,plain,
% 124.49/80.02 (((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20))))) | (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0))),
% 124.49/80.02 inference(tautology,[status(thm)],[])).
% 124.49/80.02 tff(4,plain,
% 124.49/80.02 (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0)),
% 124.49/80.02 inference(unit_resolution,[status(thm)],[3, 2])).
% 124.49/80.02 tff(5,plain,
% 124.49/80.02 ($greatereq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0)),
% 124.49/80.02 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.02 tff(6,plain,
% 124.49/80.02 ($greatereq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0)),
% 124.49/80.02 inference(unit_resolution,[status(thm)],[5, 4])).
% 124.49/80.02 tff(7,plain,
% 124.49/80.02 ((~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), -1)) | (~$greatereq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0))),
% 124.49/80.02 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.02 tff(8,plain,
% 124.49/80.02 (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), -1)),
% 124.49/80.02 inference(unit_resolution,[status(thm)],[7, 6])).
% 124.49/80.02 tff(9,plain,
% 124.49/80.02 (((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20))))) | (T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))),
% 124.49/80.02 inference(tautology,[status(thm)],[])).
% 124.49/80.02 tff(10,plain,
% 124.49/80.02 (T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20))),
% 124.49/80.02 inference(unit_resolution,[status(thm)],[9, 2])).
% 124.49/80.02 tff(11,plain,
% 124.49/80.02 (((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20))))) | ($sum(I!11, $product(-1, size1(T!20))) = 0)),
% 124.49/80.02 inference(tautology,[status(thm)],[])).
% 124.49/80.02 tff(12,plain,
% 124.49/80.02 ($sum(I!11, $product(-1, size1(T!20))) = 0),
% 124.49/80.02 inference(unit_resolution,[status(thm)],[11, 2])).
% 124.49/80.02 tff(13,plain,
% 124.49/80.02 (^[L: tree1, R: tree1] : refl(((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1)) <=> ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1)))),
% 124.49/80.02 inference(bind,[status(th)],[])).
% 124.49/80.02 tff(14,plain,
% 124.49/80.02 (![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1)) <=> ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))),
% 124.49/80.02 inference(quant_intro,[status(thm)],[13])).
% 124.49/80.02 tff(15,plain,
% 124.49/80.02 (^[L: tree1, R: tree1] : trans(monotonicity(rewrite(((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))) <=> (~((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1)))), ((~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) <=> (~(~((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1)))))), rewrite((~(~((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1)))) <=> ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))), ((~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) <=> ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))))),
% 124.49/80.02 inference(bind,[status(th)],[])).
% 124.49/80.02 tff(16,plain,
% 124.49/80.02 (![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) <=> ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))),
% 124.49/80.02 inference(quant_intro,[status(thm)],[15])).
% 124.49/80.02 tff(17,plain,
% 124.49/80.02 (($greatereq(N!9, 0) & (~$lesseq(N!9, -1)) & $greatereq(N!9, -1) & ($greatereq(N!9, 1) & $greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))) <=> ($greatereq(N!9, 0) & (~$lesseq(N!9, -1)) & $greatereq(N!9, -1) & $greatereq(N!9, 1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.02 inference(rewrite,[status(thm)],[])).
% 124.49/80.02 tff(18,plain,
% 124.49/80.02 (($greatereq(N!9, 1) & ($greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))) & ($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))) <=> ($greatereq(N!9, 1) & $greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(19,plain,
% 124.49/80.03 ((($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & ($greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0)) & ($greatereq(I!11, 1) & $greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))) <=> ($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(20,plain,
% 124.49/80.03 (($greatereq(I!11, 1) & ($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))) & ($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & $greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))) <=> ($greatereq(I!11, 1) & $greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(21,plain,
% 124.49/80.03 ((($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14)))))))) & ($greatereq(J!14, 0) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1))) & ($greatereq($sum(I!11, $product(-1, J!14)), 1) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2))) & ($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 1)) & ($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & $greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))) <=> ($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & $greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(22,plain,
% 124.49/80.03 ((![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) <=> (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(23,plain,
% 124.49/80.03 ((($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))) <=> ($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & $greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(24,plain,
% 124.49/80.03 ((($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))) & (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))) <=> ($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(25,plain,
% 124.49/80.03 (((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))) <=> (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(26,plain,
% 124.49/80.03 ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) <=> ($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(27,plain,
% 124.49/80.03 (((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))) <=> (($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))) & (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))),
% 124.49/80.03 inference(monotonicity,[status(thm)],[26, 25])).
% 124.49/80.03 tff(28,plain,
% 124.49/80.03 (((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))) <=> ($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))),
% 124.49/80.03 inference(transitivity,[status(thm)],[27, 24])).
% 124.49/80.03 tff(29,plain,
% 124.49/80.03 ((distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) <=> (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(30,plain,
% 124.49/80.03 ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) <=> ($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)))),
% 124.49/80.03 inference(rewrite,[status(thm)],[])).
% 124.49/80.03 tff(31,plain,
% 124.49/80.03 (((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) <=> (($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))),
% 124.49/80.03 inference(monotonicity,[status(thm)],[30, 29, 28])).
% 124.49/80.03 tff(32,plain,
% 124.49/80.03 (((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) <=> ($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & $greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))))),
% 124.49/80.04 inference(transitivity,[status(thm)],[31, 23])).
% 124.49/80.04 tff(33,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 1)))) <=> ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 1))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(34,plain,
% 124.49/80.04 ((~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1))) <=> (~($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 1)))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(35,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) <=> (~(~($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 1))))),
% 124.49/80.04 inference(monotonicity,[status(thm)],[34])).
% 124.49/80.04 tff(36,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) <=> ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 1))),
% 124.49/80.04 inference(transitivity,[status(thm)],[35, 33])).
% 124.49/80.04 tff(37,plain,
% 124.49/80.04 ((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) <=> ($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(38,plain,
% 124.49/80.04 ((~(~($greatereq($sum(I!11, $product(-1, J!14)), 1) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2))))) <=> ($greatereq($sum(I!11, $product(-1, J!14)), 1) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(39,plain,
% 124.49/80.04 ((~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2)))) <=> (~($greatereq($sum(I!11, $product(-1, J!14)), 1) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2))))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(40,plain,
% 124.49/80.04 ((~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) <=> (~(~($greatereq($sum(I!11, $product(-1, J!14)), 1) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)))))),
% 124.49/80.04 inference(monotonicity,[status(thm)],[39])).
% 124.49/80.04 tff(41,plain,
% 124.49/80.04 ((~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) <=> ($greatereq($sum(I!11, $product(-1, J!14)), 1) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)))),
% 124.49/80.04 inference(transitivity,[status(thm)],[40, 38])).
% 124.49/80.04 tff(42,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1))))) <=> ($greatereq(J!14, 0) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(43,plain,
% 124.49/80.04 ((~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1)))) <=> (~($greatereq(J!14, 0) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1))))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(44,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) <=> (~(~($greatereq(J!14, 0) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)))))),
% 124.49/80.04 inference(monotonicity,[status(thm)],[43])).
% 124.49/80.04 tff(45,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) <=> ($greatereq(J!14, 0) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)))),
% 124.49/80.04 inference(transitivity,[status(thm)],[44, 42])).
% 124.49/80.04 tff(46,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14)))))))))) <=> ($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(47,plain,
% 124.49/80.04 ((~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11)))))))) <=> (~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14)))))))))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(48,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) <=> (~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))))))),
% 124.49/80.04 inference(monotonicity,[status(thm)],[47])).
% 124.49/80.04 tff(49,plain,
% 124.49/80.04 ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) <=> ($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))))),
% 124.49/80.04 inference(transitivity,[status(thm)],[48, 46])).
% 124.49/80.04 tff(50,plain,
% 124.49/80.04 (((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))) <=> (($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14)))))))) & ($greatereq(J!14, 0) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1))) & ($greatereq($sum(I!11, $product(-1, J!14)), 1) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2))) & ($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))) & ($greatereq(J!14, 0) & $greatereq($sum(I!11, $product(-1, J!14)), 1)) & ($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & $greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))),
% 124.49/80.04 inference(monotonicity,[status(thm)],[49, 45, 41, 37, 36, 32, 22])).
% 124.49/80.04 tff(51,plain,
% 124.49/80.04 (((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))) <=> ($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & $greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.04 inference(transitivity,[status(thm)],[50, 21])).
% 124.49/80.04 tff(52,plain,
% 124.49/80.04 ((~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) <=> ($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))))),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(53,plain,
% 124.49/80.04 ((~(~$greatereq(I!11, 1))) <=> $greatereq(I!11, 1)),
% 124.49/80.04 inference(rewrite,[status(thm)],[])).
% 124.49/80.04 tff(54,plain,
% 124.49/80.04 (((~(~$greatereq(I!11, 1))) & (~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) & ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))) <=> ($greatereq(I!11, 1) & ($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))) & ($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & $greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))),
% 124.49/80.04 inference(monotonicity,[status(thm)],[53, 52, 51])).
% 124.49/80.04 tff(55,plain,
% 124.49/80.04 (((~(~$greatereq(I!11, 1))) & (~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) & ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))) <=> ($greatereq(I!11, 1) & $greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.05 inference(transitivity,[status(thm)],[54, 20])).
% 124.49/80.05 tff(56,plain,
% 124.49/80.05 ((~(~($greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0)))) <=> ($greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0))),
% 124.49/80.05 inference(rewrite,[status(thm)],[])).
% 124.49/80.05 tff(57,plain,
% 124.49/80.05 ((~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0))) <=> (~($greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0)))),
% 124.49/80.05 inference(rewrite,[status(thm)],[])).
% 124.49/80.05 tff(58,plain,
% 124.49/80.05 ((~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0)))) <=> (~(~($greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0))))),
% 124.49/80.05 inference(monotonicity,[status(thm)],[57])).
% 124.49/80.05 tff(59,plain,
% 124.49/80.05 ((~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0)))) <=> ($greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0))),
% 124.49/80.05 inference(transitivity,[status(thm)],[58, 56])).
% 124.49/80.05 tff(60,plain,
% 124.49/80.05 (^[K: $int] : rewrite(((~($greatereq(K, 0) & (~$lesseq($sum(I!11, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) <=> ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))))),
% 124.49/80.05 inference(bind,[status(th)],[])).
% 124.49/80.05 tff(61,plain,
% 124.49/80.05 (![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I!11, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) <=> ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K)))))),
% 124.49/80.05 inference(quant_intro,[status(thm)],[60])).
% 124.49/80.05 tff(62,plain,
% 124.49/80.05 ((~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1)))) <=> (~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))),
% 124.49/80.05 inference(rewrite,[status(thm)],[])).
% 124.49/80.05 tff(63,plain,
% 124.49/80.05 ((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1))))) <=> (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)))))),
% 124.49/80.05 inference(monotonicity,[status(thm)],[62])).
% 124.49/80.05 tff(64,plain,
% 124.49/80.05 ((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1))))) <=> ($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)))),
% 124.49/80.05 inference(transitivity,[status(thm)],[63, 37])).
% 124.49/80.05 tff(65,plain,
% 124.49/80.05 (((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1))))) & ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I!11, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0)))) & ((~(~$greatereq(I!11, 1))) & (~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) & ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))))) <=> (($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & ($greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0)) & ($greatereq(I!11, 1) & $greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))),
% 124.49/80.05 inference(monotonicity,[status(thm)],[64, 61, 59, 55])).
% 124.49/80.05 tff(66,plain,
% 124.49/80.05 (((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1))))) & ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I!11, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0)))) & ((~(~$greatereq(I!11, 1))) & (~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) & ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))))) <=> ($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.05 inference(transitivity,[status(thm)],[65, 19])).
% 124.49/80.05 tff(67,plain,
% 124.49/80.05 ((~(~($greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) <=> ($greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))),
% 124.49/80.05 inference(rewrite,[status(thm)],[])).
% 124.49/80.05 tff(68,plain,
% 124.49/80.05 ((~(~$greatereq(N!9, 1))) <=> $greatereq(N!9, 1)),
% 124.49/80.05 inference(rewrite,[status(thm)],[])).
% 124.49/80.05 tff(69,plain,
% 124.49/80.05 (((~(~$greatereq(N!9, 1))) & (~(~($greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) & ((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1))))) & ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I!11, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0)))) & ((~(~$greatereq(I!11, 1))) & (~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) & ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))))) <=> ($greatereq(N!9, 1) & ($greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))) & ($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))),
% 124.49/80.05 inference(monotonicity,[status(thm)],[68, 67, 66])).
% 124.49/80.05 tff(70,plain,
% 124.49/80.05 (((~(~$greatereq(N!9, 1))) & (~(~($greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) & ((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1))))) & ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I!11, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0)))) & ((~(~$greatereq(I!11, 1))) & (~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) & ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))))) <=> ($greatereq(N!9, 1) & $greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.05 inference(transitivity,[status(thm)],[69, 18])).
% 124.49/80.05 tff(71,plain,
% 124.49/80.05 ((~(~$greatereq(N!9, -1))) <=> $greatereq(N!9, -1)),
% 124.49/80.05 inference(rewrite,[status(thm)],[])).
% 124.49/80.05 tff(72,plain,
% 124.49/80.05 ((~(~$greatereq(N!9, 0))) <=> $greatereq(N!9, 0)),
% 124.49/80.05 inference(rewrite,[status(thm)],[])).
% 124.49/80.05 tff(73,plain,
% 124.49/80.05 (((~(~$greatereq(N!9, 0))) & (~$lesseq(N!9, -1)) & (~(~$greatereq(N!9, -1))) & ((~(~$greatereq(N!9, 1))) & (~(~($greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) & ((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1))))) & ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I!11, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0)))) & ((~(~$greatereq(I!11, 1))) & (~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) & ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))))))) <=> ($greatereq(N!9, 0) & (~$lesseq(N!9, -1)) & $greatereq(N!9, -1) & ($greatereq(N!9, 1) & $greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))),
% 124.49/80.06 inference(monotonicity,[status(thm)],[72, 71, 70])).
% 124.49/80.06 tff(74,plain,
% 124.49/80.06 (((~(~$greatereq(N!9, 0))) & (~$lesseq(N!9, -1)) & (~(~$greatereq(N!9, -1))) & ((~(~$greatereq(N!9, 1))) & (~(~($greatereq(N!9, -1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) & ((~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$greatereq($sum(I!11, $product(-1, N!9)), 1))))) & ![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I!11, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & (~(~($greatereq(I!11, 1) & $lesseq($sum(I!11, $product(-1, N!9)), 0)))) & ((~(~$greatereq(I!11, 1))) & (~(~($greatereq(N!9, -1) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree))))))) & ((~(~($greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $lesseq($sum(J!14, $product(-1, I!11)), -1) & all_trees1($sum(-1, $sum($product(-1, J!14), I!11)), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum($product(-1, J!14), I!11))))))))) & (~(~($greatereq(J!14, 0) & (~$greatereq($sum(J!14, $product(-1, N!9)), 1))))) & (~(~($lesseq($sum(J!14, $product(-1, I!11)), -1) & (~$lesseq($sum(J!14, $sum(N!9, $product(-1, I!11))), -2))))) & (~(~($greatereq(N!9, -1) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (~(~($greatereq(J!14, 0) & $lesseq($sum(J!14, $product(-1, I!11)), -1)))) & ((~(~($greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1))))) & (distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(size1(tptp_fun_L_18(T)), $product(-1, J!14)) = 0) & ($sum(size1(tptp_fun_R_17(T)), $sum($product(-1, I!11), J!14)) = -1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) & ((~(~($greatereq(N!9, -1) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))))) & ((~(~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(size1(T!20), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))))) & (![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(tptp_fun_L_22(T)), $product(-1, J!14)), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))))))) <=> ($greatereq(N!9, 0) & (~$lesseq(N!9, -1)) & $greatereq(N!9, -1) & $greatereq(N!9, 1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.06 inference(transitivity,[status(thm)],[73, 17])).
% 124.49/80.06 tff(75,plain,
% 124.49/80.06 ((~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 1)))) | (~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq($sum(J, $product(-1, I)), -1) & all_trees1($sum(-1, $sum($product(-1, J), I)), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum($product(-1, J), I)))))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 1)))) | (~($lesseq($sum(J, $product(-1, I)), -1) & (~$lesseq($sum(J, $sum(N, $product(-1, I))), -2)))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1))))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 1)))))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 0)))))))))))) <=> (~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 1)))) | (~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq($sum(J, $product(-1, I)), -1) & all_trees1($sum(-1, $sum($product(-1, J), I)), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum($product(-1, J), I)))))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 1)))) | (~($lesseq($sum(J, $product(-1, I)), -1) & (~$lesseq($sum(J, $sum(N, $product(-1, I))), -2)))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1))))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 1)))))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 0))))))))))))),
% 124.49/80.06 inference(rewrite,[status(thm)],[])).
% 124.49/80.06 tff(76,plain,
% 124.49/80.06 ((~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | (~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $greatereq($sum(I, $product(-1, J)), 1) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$lesseq($sum(J, $product(-1, size1(L))), -1))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1)))))) | (~($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -1)))) | (~($greatereq($sum(I, $product(-1, J)), 1) & (~$lesseq($sum(N, $sum($product(-1, I), J)), -2)))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$lesseq($sum(J, $product(-1, size1(L))), 0)))))))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))))))) <=> (~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 1)))) | (~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq($sum(J, $product(-1, I)), -1) & all_trees1($sum(-1, $sum($product(-1, J), I)), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum($product(-1, J), I)))))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 1)))) | (~($lesseq($sum(J, $product(-1, I)), -1) & (~$lesseq($sum(J, $sum(N, $product(-1, I))), -2)))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1))))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 1)))))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 0))))))))))))),
% 124.49/80.06 inference(rewrite,[status(thm)],[])).
% 124.49/80.06 tff(77,plain,
% 124.49/80.06 ((~![N: $int] : ((~$lesseq(0, N)) | $lesseq(N, -1) | ![A: map_int_lplist_treerp] : ((~$lesseq(1, N)) | ![A1: map_int_lplist_treerp, I: $int] : (![A2: map_int_lplist_treerp] : ((~$lesseq(1, I)) | ![A3: map_int_lplist_treerp, J: $int] : ((~($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq(1, $sum(I, $product(-1, J))) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : (![A4: map_int_lplist_treerp] : ((~($lesseq(-1, N) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, $sum(-1, size1(L))))))) | (~($lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(L) = J) & (size1(R) = $sum(-1, $sum(I, $product(-1, J))))))))) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-1, J))))) | (~($lesseq(1, $sum(I, $product(-1, J))) & (~$lesseq(N, $sum(-2, $sum(I, $product(-1, J))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, size1(L))))))) | (~($lesseq(0, J) & $lesseq(J, $sum(-1, I))))) | (~($lesseq(-1, N) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($lesseq(1, I) & $lesseq(I, N)))) | (~($lesseq(-1, N) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) | (~$lesseq(-1, N)))) <=> (~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | (~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $greatereq($sum(I, $product(-1, J)), 1) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$lesseq($sum(J, $product(-1, size1(L))), -1))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1)))))) | (~($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -1)))) | (~($greatereq($sum(I, $product(-1, J)), 1) & (~$lesseq($sum(N, $sum($product(-1, I), J)), -2)))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$lesseq($sum(J, $product(-1, size1(L))), 0)))))))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1))))))))),
% 124.49/80.06 inference(rewrite,[status(thm)],[])).
% 124.49/80.06 tff(78,plain,
% 124.49/80.06 ((~![N: $int] : ((~$lesseq(0, N)) | $lesseq(N, -1) | ![A: map_int_lplist_treerp] : ((~$lesseq(1, N)) | ![A1: map_int_lplist_treerp, I: $int] : (![A2: map_int_lplist_treerp] : ((~$lesseq(1, I)) | ![A3: map_int_lplist_treerp, J: $int] : ((~($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq(1, $sum(I, $product(-1, J))) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : (![A4: map_int_lplist_treerp] : ((~($lesseq(-1, N) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, $sum(-1, size1(L))))))) | (~($lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(L) = J) & (size1(R) = $sum(-1, $sum(I, $product(-1, J))))))))) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-1, J))))) | (~($lesseq(1, $sum(I, $product(-1, J))) & (~$lesseq(N, $sum(-2, $sum(I, $product(-1, J))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, size1(L))))))) | (~($lesseq(0, J) & $lesseq(J, $sum(-1, I))))) | (~($lesseq(-1, N) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($lesseq(1, I) & $lesseq(I, N)))) | (~($lesseq(-1, N) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) | (~$lesseq(-1, N)))) <=> (~![N: $int] : ((~$lesseq(0, N)) | $lesseq(N, -1) | ![A: map_int_lplist_treerp] : ((~$lesseq(1, N)) | ![A1: map_int_lplist_treerp, I: $int] : (![A2: map_int_lplist_treerp] : ((~$lesseq(1, I)) | ![A3: map_int_lplist_treerp, J: $int] : ((~($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq(1, $sum(I, $product(-1, J))) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : (![A4: map_int_lplist_treerp] : ((~($lesseq(-1, N) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, $sum(-1, size1(L))))))) | (~($lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(L) = J) & (size1(R) = $sum(-1, $sum(I, $product(-1, J))))))))) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-1, J))))) | (~($lesseq(1, $sum(I, $product(-1, J))) & (~$lesseq(N, $sum(-2, $sum(I, $product(-1, J))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, size1(L))))))) | (~($lesseq(0, J) & $lesseq(J, $sum(-1, I))))) | (~($lesseq(-1, N) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($lesseq(1, I) & $lesseq(I, N)))) | (~($lesseq(-1, N) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) | (~$lesseq(-1, N))))),
% 124.49/80.06 inference(rewrite,[status(thm)],[])).
% 124.49/80.06 tff(79,plain,
% 124.49/80.06 ((~![N: $int] : ($lesseq(0, N) => ($lesseq(0, $sum(N, 1)) => ($lesseq(0, $sum(N, 1)) => (($lesseq(0, 0) & $less(0, $sum(N, 1))) => ![A: map_int_lplist_treerp] : (($lesseq(0, $sum(N, 1)) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))) => ($lesseq(1, N) => ![A1: map_int_lplist_treerp, I: $int] : (($lesseq(1, I) & $lesseq(I, N)) => (![K: $int] : (($lesseq(0, K) & $less(K, I)) => all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K))))) => ((($lesseq(0, $sum(N, 1)) & $lesseq(0, I)) & $less(I, $sum(N, 1))) => ![A2: map_int_lplist_treerp] : (($lesseq(0, $sum(N, 1)) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))) => ($lesseq(0, $difference(I, 1)) => ![A3: map_int_lplist_treerp, J: $int] : (($lesseq(0, J) & $lesseq(J, $difference(I, 1))) => (((![K: $int] : (($lesseq(0, K) & $less(K, I)) => all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I)))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : (((T = node1(L, R)) & (size1(T) = I)) & $less(size1(L), J)))) => ((($lesseq(0, $sum(N, 1)) & $lesseq(0, I)) & $less(I, $sum(N, 1))) => (($lesseq(0, $difference($difference(I, 1), J)) & $less($difference($difference(I, 1), J), $sum(N, 1))) => (($lesseq(0, J) & $less(J, $sum(N, 1))) => (((($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J))))) & $lesseq(0, $difference($difference(I, 1), J))) & all_trees1($difference($difference(I, 1), J), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($difference($difference(I, 1), J)))))) => ![O: list_tree] : ((distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : (((T = node1(L, R)) & (size1(L) = J)) & (size1(R) = $difference($difference(I, 1), J))))) => (($lesseq(0, I) & $less(I, $sum(N, 1))) => ![A4: map_int_lplist_treerp] : (($lesseq(0, $sum(N, 1)) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I))))))) => ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I))) => ?[L: tree1, R: tree1] : (((T = node1(L, R)) & (size1(T) = I)) & $less(size1(L), $sum(J, 1))))))))))))))))))))))))) <=> (~![N: $int] : ((~$lesseq(0, N)) | $lesseq(N, -1) | ![A: map_int_lplist_treerp] : ((~$lesseq(1, N)) | ![A1: map_int_lplist_treerp, I: $int] : (![A2: map_int_lplist_treerp] : ((~$lesseq(1, I)) | ![A3: map_int_lplist_treerp, J: $int] : ((~($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq(1, $sum(I, $product(-1, J))) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : (![A4: map_int_lplist_treerp] : ((~($lesseq(-1, N) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, $sum(-1, size1(L))))))) | (~($lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(L) = J) & (size1(R) = $sum(-1, $sum(I, $product(-1, J))))))))) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-1, J))))) | (~($lesseq(1, $sum(I, $product(-1, J))) & (~$lesseq(N, $sum(-2, $sum(I, $product(-1, J))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, size1(L))))))) | (~($lesseq(0, J) & $lesseq(J, $sum(-1, I))))) | (~($lesseq(-1, N) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($lesseq(1, I) & $lesseq(I, N)))) | (~($lesseq(-1, N) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) | (~$lesseq(-1, N))))),
% 124.49/80.06 inference(rewrite,[status(thm)],[])).
% 124.49/80.06 tff(80,axiom,(~![N: $int] : ($lesseq(0, N) => ($lesseq(0, $sum(N, 1)) => ($lesseq(0, $sum(N, 1)) => (($lesseq(0, 0) & $less(0, $sum(N, 1))) => ![A: map_int_lplist_treerp] : (($lesseq(0, $sum(N, 1)) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))) => ($lesseq(1, N) => ![A1: map_int_lplist_treerp, I: $int] : (($lesseq(1, I) & $lesseq(I, N)) => (![K: $int] : (($lesseq(0, K) & $less(K, I)) => all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K))))) => ((($lesseq(0, $sum(N, 1)) & $lesseq(0, I)) & $less(I, $sum(N, 1))) => ![A2: map_int_lplist_treerp] : (($lesseq(0, $sum(N, 1)) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))) => ($lesseq(0, $difference(I, 1)) => ![A3: map_int_lplist_treerp, J: $int] : (($lesseq(0, J) & $lesseq(J, $difference(I, 1))) => (((![K: $int] : (($lesseq(0, K) & $less(K, I)) => all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I)))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : (((T = node1(L, R)) & (size1(T) = I)) & $less(size1(L), J)))) => ((($lesseq(0, $sum(N, 1)) & $lesseq(0, I)) & $less(I, $sum(N, 1))) => (($lesseq(0, $difference($difference(I, 1), J)) & $less($difference($difference(I, 1), J), $sum(N, 1))) => (($lesseq(0, J) & $less(J, $sum(N, 1))) => (((($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J))))) & $lesseq(0, $difference($difference(I, 1), J))) & all_trees1($difference($difference(I, 1), J), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($difference($difference(I, 1), J)))))) => ![O: list_tree] : ((distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : (((T = node1(L, R)) & (size1(L) = J)) & (size1(R) = $difference($difference(I, 1), J))))) => (($lesseq(0, I) & $less(I, $sum(N, 1))) => ![A4: map_int_lplist_treerp] : (($lesseq(0, $sum(N, 1)) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I))))))) => ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I))) => ?[L: tree1, R: tree1] : (((T = node1(L, R)) & (size1(T) = I)) & $less(size1(L), $sum(J, 1))))))))))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_all_trees')).
% 124.49/80.06 tff(81,plain,
% 124.49/80.06 (~![N: $int] : ((~$lesseq(0, N)) | $lesseq(N, -1) | ![A: map_int_lplist_treerp] : ((~$lesseq(1, N)) | ![A1: map_int_lplist_treerp, I: $int] : (![A2: map_int_lplist_treerp] : ((~$lesseq(1, I)) | ![A3: map_int_lplist_treerp, J: $int] : ((~($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq(1, $sum(I, $product(-1, J))) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : (![A4: map_int_lplist_treerp] : ((~($lesseq(-1, N) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, $sum(-1, size1(L))))))) | (~($lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(L) = J) & (size1(R) = $sum(-1, $sum(I, $product(-1, J))))))))) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-1, J))))) | (~($lesseq(1, $sum(I, $product(-1, J))) & (~$lesseq(N, $sum(-2, $sum(I, $product(-1, J))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, size1(L))))))) | (~($lesseq(0, J) & $lesseq(J, $sum(-1, I))))) | (~($lesseq(-1, N) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($lesseq(1, I) & $lesseq(I, N)))) | (~($lesseq(-1, N) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) | (~$lesseq(-1, N)))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[80, 79])).
% 124.49/80.07 tff(82,plain,
% 124.49/80.07 (~![N: $int] : ((~$lesseq(0, N)) | $lesseq(N, -1) | ![A: map_int_lplist_treerp] : ((~$lesseq(1, N)) | ![A1: map_int_lplist_treerp, I: $int] : (![A2: map_int_lplist_treerp] : ((~$lesseq(1, I)) | ![A3: map_int_lplist_treerp, J: $int] : ((~($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq(1, $sum(I, $product(-1, J))) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : (![A4: map_int_lplist_treerp] : ((~($lesseq(-1, N) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, $sum(-1, size1(L))))))) | (~($lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(L) = J) & (size1(R) = $sum(-1, $sum(I, $product(-1, J))))))))) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-1, J))))) | (~($lesseq(1, $sum(I, $product(-1, J))) & (~$lesseq(N, $sum(-2, $sum(I, $product(-1, J))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, size1(L))))))) | (~($lesseq(0, J) & $lesseq(J, $sum(-1, I))))) | (~($lesseq(-1, N) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($lesseq(1, I) & $lesseq(I, N)))) | (~($lesseq(-1, N) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) | (~$lesseq(-1, N)))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[81, 78])).
% 124.49/80.07 tff(83,plain,
% 124.49/80.07 (~![N: $int] : ((~$lesseq(0, N)) | $lesseq(N, -1) | ![A: map_int_lplist_treerp] : ((~$lesseq(1, N)) | ![A1: map_int_lplist_treerp, I: $int] : (![A2: map_int_lplist_treerp] : ((~$lesseq(1, I)) | ![A3: map_int_lplist_treerp, J: $int] : ((~($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq(1, $sum(I, $product(-1, J))) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : (![A4: map_int_lplist_treerp] : ((~($lesseq(-1, N) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, $sum(-1, size1(L))))))) | (~($lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(L) = J) & (size1(R) = $sum(-1, $sum(I, $product(-1, J))))))))) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-1, J))))) | (~($lesseq(1, $sum(I, $product(-1, J))) & (~$lesseq(N, $sum(-2, $sum(I, $product(-1, J))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, size1(L))))))) | (~($lesseq(0, J) & $lesseq(J, $sum(-1, I))))) | (~($lesseq(-1, N) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($lesseq(1, I) & $lesseq(I, N)))) | (~($lesseq(-1, N) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) | (~$lesseq(-1, N)))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[82, 78])).
% 124.49/80.07 tff(84,plain,
% 124.49/80.07 (~![N: $int] : ((~$lesseq(0, N)) | $lesseq(N, -1) | ![A: map_int_lplist_treerp] : ((~$lesseq(1, N)) | ![A1: map_int_lplist_treerp, I: $int] : (![A2: map_int_lplist_treerp] : ((~$lesseq(1, I)) | ![A3: map_int_lplist_treerp, J: $int] : ((~($lesseq(0, J) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq(1, $sum(I, $product(-1, J))) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : (![A4: map_int_lplist_treerp] : ((~($lesseq(-1, N) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, $sum(-1, size1(L))))))) | (~($lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(L) = J) & (size1(R) = $sum(-1, $sum(I, $product(-1, J))))))))) | (~($lesseq(0, J) & (~$lesseq(N, $sum(-1, J))))) | (~($lesseq(1, $sum(I, $product(-1, J))) & (~$lesseq(N, $sum(-2, $sum(I, $product(-1, J))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~(![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & (size1(T) = I) & (~$lesseq(J, size1(L))))))) | (~($lesseq(0, J) & $lesseq(J, $sum(-1, I))))) | (~($lesseq(-1, N) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree))))))) | (~($lesseq(-1, N) & $lesseq(0, I) & (~$lesseq(N, $sum(-1, I))))) | (~![K: $int] : ((~($lesseq(0, K) & (~$lesseq(I, K)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($lesseq(1, I) & $lesseq(I, N)))) | (~($lesseq(-1, N) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree)))))))) | (~$lesseq(-1, N)))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[83, 78])).
% 124.49/80.07 tff(85,plain,
% 124.49/80.07 (~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | (~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $greatereq($sum(I, $product(-1, J)), 1) & all_trees1($sum(-1, $sum(I, $product(-1, J))), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum(I, $product(-1, J))))))))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$lesseq($sum(J, $product(-1, size1(L))), -1))))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1)))))) | (~($greatereq(J, 0) & (~$lesseq($sum(N, $product(-1, J)), -1)))) | (~($greatereq($sum(I, $product(-1, J)), 1) & (~$lesseq($sum(N, $sum($product(-1, I), J)), -2)))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$lesseq($sum(J, $product(-1, size1(L))), 0)))))))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))))))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[84, 77])).
% 124.49/80.07 tff(86,plain,
% 124.49/80.07 (~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 1)))) | (~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq($sum(J, $product(-1, I)), -1) & all_trees1($sum(-1, $sum($product(-1, J), I)), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum($product(-1, J), I)))))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 1)))) | (~($lesseq($sum(J, $product(-1, I)), -1) & (~$lesseq($sum(J, $sum(N, $product(-1, I))), -2)))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1))))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 1)))))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 0)))))))))))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[85, 76])).
% 124.49/80.07 tff(87,plain,
% 124.49/80.07 (~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 1)))) | (~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq($sum(J, $product(-1, I)), -1) & all_trees1($sum(-1, $sum($product(-1, J), I)), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum($product(-1, J), I)))))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 1)))) | (~($lesseq($sum(J, $product(-1, I)), -1) & (~$lesseq($sum(J, $sum(N, $product(-1, I))), -2)))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1))))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 1)))))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 0)))))))))))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[86, 75])).
% 124.49/80.07 tff(88,plain,
% 124.49/80.07 (~![N: $int] : ((~$greatereq(N, 0)) | $lesseq(N, -1) | (~$greatereq(N, -1)) | ![A: map_int_lplist_treerp] : ((~$greatereq(N, 1)) | (~($greatereq(N, -1) & (A = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))))) | ![A1: map_int_lplist_treerp, I: $int] : ((~($greatereq(N, -1) & $greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N)), 1)))) | (~![K: $int] : ((~($greatereq(K, 0) & (~$lesseq($sum(I, $product(-1, K)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1), t2tb(K)))))) | (~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, N)), 0))) | ![A2: map_int_lplist_treerp] : ((~$greatereq(I, 1)) | (~($greatereq(N, -1) & (A2 = tb2t3(set(list(tree), int, t2tb3(A1), t2tb(I), nil(tree)))))) | ![A3: map_int_lplist_treerp, J: $int] : ((~($greatereq(J, 0) & all_trees1(J, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(J)))) & $lesseq($sum(J, $product(-1, I)), -1) & all_trees1($sum(-1, $sum($product(-1, J), I)), tb2t1(get(list(tree), int, t2tb3(A3), t2tb($sum(-1, $sum($product(-1, J), I)))))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, N)), 1)))) | (~($lesseq($sum(J, $product(-1, I)), -1) & (~$lesseq($sum(J, $sum(N, $product(-1, I))), -2)))) | (~($greatereq(N, -1) & $greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~($greatereq(J, 0) & $lesseq($sum(J, $product(-1, I)), -1))) | ![O: list_tree] : ((~($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), -1)))) | (~(distinct(tree, t2tb1(O)) & ![T: tree1] : (mem(tree, t2tb2(T), t2tb1(O)) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(L), $product(-1, J)) = 0) & ($sum(size1(R), $sum($product(-1, I), J)) = -1))))) | ![A4: map_int_lplist_treerp] : ((~($greatereq(N, -1) & (A4 = tb2t3(set(list(tree), int, t2tb3(A3), t2tb(I), infix_plpl(tree, t2tb1(O), get(list(tree), int, t2tb3(A3), t2tb(I)))))))) | ![T: tree1] : ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A4), t2tb(I)))) | ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 1)))))) | (~(![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3), t2tb(I))) & ![T: tree1] : (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3), t2tb(I))) <=> ?[L: tree1, R: tree1] : ((T = node1(L, R)) & ($sum(size1(T), $product(-1, I)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J)), 0)))))))))))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[87, 75])).
% 124.49/80.07 tff(89,plain,
% 124.49/80.07 ($greatereq(N!9, 0) & (~$lesseq(N!9, -1)) & $greatereq(N!9, -1) & $greatereq(N!9, 1) & (A!10 = tb2t3(set(list(tree), int, const(list(tree), int, nil(tree)), t2tb(0), cons(tree, t2tb2(empty1), nil(tree))))) & $greatereq(I!11, 0) & (~$lesseq($sum(N!9, $product(-1, I!11)), -1)) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A1!12), t2tb(K))))) & $greatereq(I!11, 1) & $greatereq($sum(N!9, $product(-1, I!11)), 0) & (A2!13 = tb2t3(set(list(tree), int, t2tb3(A1!12), t2tb(I!11), nil(tree)))) & $greatereq(J!14, 0) & all_trees1(J!14, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(J!14)))) & $greatereq($sum(I!11, $product(-1, J!14)), 1) & all_trees1($sum(-1, $sum(I!11, $product(-1, J!14))), tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb($sum(-1, $sum(I!11, $product(-1, J!14))))))) & (~$lesseq($sum(N!9, $product(-1, J!14)), -1)) & (~$lesseq($sum(N!9, $sum($product(-1, I!11), J!14)), -2)) & distinct(tree, t2tb1(O!16)) & ![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) & (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) & mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) & ![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1)))) & ![K: $int] : ((~($greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, I!11)), 0)))) | all_trees1(K, tb2t1(get(list(tree), int, t2tb3(A3!15), t2tb(K))))) & distinct(tree, get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) & ![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[88, 74])).
% 124.49/80.07 tff(90,plain,
% 124.49/80.07 (![L: tree1, R: tree1] : (~((T!20 = node1(L, R)) & ($sum(I!11, $product(-1, size1(T!20))) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 1))))),
% 124.49/80.07 inference(and_elim,[status(thm)],[89])).
% 124.49/80.07 tff(91,plain,
% 124.49/80.07 (![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[90, 16])).
% 124.49/80.07 tff(92,plain,
% 124.49/80.07 (![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[91, 14])).
% 124.49/80.07 tff(93,plain,
% 124.49/80.07 (((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), -1))) <=> ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), -1))),
% 124.49/80.07 inference(rewrite,[status(thm)],[])).
% 124.49/80.07 tff(94,plain,
% 124.49/80.07 (((~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(tptp_fun_L_22(T!20)), $product(-1, J!14)), 1)) <=> ((~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), -1))),
% 124.49/80.07 inference(rewrite,[status(thm)],[])).
% 124.49/80.07 tff(95,plain,
% 124.49/80.07 (((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(tptp_fun_L_22(T!20)), $product(-1, J!14)), 1))) <=> ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), -1)))),
% 124.49/80.07 inference(monotonicity,[status(thm)],[94])).
% 124.49/80.07 tff(96,plain,
% 124.49/80.07 (((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(tptp_fun_L_22(T!20)), $product(-1, J!14)), 1))) <=> ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), -1))),
% 124.49/80.07 inference(transitivity,[status(thm)],[95, 93])).
% 124.49/80.07 tff(97,plain,
% 124.49/80.07 ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(tptp_fun_L_22(T!20)), $product(-1, J!14)), 1))),
% 124.49/80.07 inference(quant_inst,[status(thm)],[])).
% 124.49/80.07 tff(98,plain,
% 124.49/80.07 ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), -1)),
% 124.49/80.07 inference(modus_ponens,[status(thm)],[97, 96])).
% 124.49/80.07 tff(99,plain,
% 124.49/80.07 ($false),
% 124.49/80.07 inference(unit_resolution,[status(thm)],[98, 92, 12, 10, 8])).
% 124.49/80.07 tff(100,plain,((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20))))), inference(lemma,lemma(discharge,[]))).
% 124.49/80.07 tff(101,plain,
% 124.49/80.07 (^[T: tree1] : refl((~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.07 inference(bind,[status(th)],[])).
% 124.49/80.07 tff(102,plain,
% 124.49/80.07 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> ![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.07 inference(quant_intro,[status(thm)],[101])).
% 124.49/80.07 tff(103,plain,
% 124.49/80.07 (^[T: tree1] : rewrite((~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.07 inference(bind,[status(th)],[])).
% 124.49/80.07 tff(104,plain,
% 124.49/80.07 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> ![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.07 inference(quant_intro,[status(thm)],[103])).
% 124.49/80.07 tff(105,plain,
% 124.49/80.07 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> ![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.07 inference(transitivity,[status(thm)],[104, 102])).
% 124.49/80.07 tff(106,plain,
% 124.49/80.07 (^[T: tree1] : trans(monotonicity(rewrite(((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) <=> ((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))), rewrite((mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))) <=> (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))), ((((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0))))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))), rewrite((((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0))))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))) <=> (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))), ((((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))))),
% 124.49/80.08 inference(bind,[status(th)],[])).
% 124.49/80.08 tff(107,plain,
% 124.49/80.08 (![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> ![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.08 inference(quant_intro,[status(thm)],[106])).
% 124.49/80.08 tff(108,plain,
% 124.49/80.08 (![T: tree1] : (((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | ((T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T))) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0)))) & (mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(T), $product(-1, I!11)) = 0) & (~$greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.08 inference(and_elim,[status(thm)],[89])).
% 124.49/80.08 tff(109,plain,
% 124.49/80.08 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[108, 107])).
% 124.49/80.08 tff(110,plain,
% 124.49/80.08 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[109, 105])).
% 124.49/80.08 tff(111,plain,
% 124.49/80.08 (((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) | (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) <=> ((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) | (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(112,plain,
% 124.49/80.08 ((~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(size1(T!20), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(size1(T!20), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))) <=> (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(113,plain,
% 124.49/80.08 (((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) | (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(size1(T!20), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(size1(T!20), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) <=> ((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) | (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.08 inference(monotonicity,[status(thm)],[112])).
% 124.49/80.08 tff(114,plain,
% 124.49/80.08 (((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) | (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(size1(T!20), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(size1(T!20), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) <=> ((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) | (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))))),
% 124.49/80.08 inference(transitivity,[status(thm)],[113, 111])).
% 124.49/80.08 tff(115,plain,
% 124.49/80.08 ((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) | (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))) | (~($sum(size1(T!20), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(size1(T!20), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.08 inference(quant_inst,[status(thm)],[])).
% 124.49/80.08 tff(116,plain,
% 124.49/80.08 ((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T)))), 0) | (~(T = node1(tptp_fun_L_22(T), tptp_fun_R_21(T)))) | (~($sum(size1(T), $product(-1, I!11)) = 0)))))) | (~(mem(tree, t2tb2(T), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(T), $product(-1, I!11)) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))) | (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[115, 114])).
% 124.49/80.08 tff(117,plain,
% 124.49/80.08 (~((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0)))))),
% 124.49/80.08 inference(unit_resolution,[status(thm)],[116, 110])).
% 124.49/80.08 tff(118,plain,
% 124.49/80.08 (((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 0))))) | ((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))),
% 124.49/80.08 inference(tautology,[status(thm)],[])).
% 124.49/80.08 tff(119,plain,
% 124.49/80.08 ((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20))))))),
% 124.49/80.08 inference(unit_resolution,[status(thm)],[118, 117])).
% 124.49/80.08 tff(120,plain,
% 124.49/80.08 ((~((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20)))))))) | (~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20))))))),
% 124.49/80.08 inference(tautology,[status(thm)],[])).
% 124.49/80.08 tff(121,plain,
% 124.49/80.08 ((~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~((~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_22(T!20)))), 0) | (~(T!20 = node1(tptp_fun_L_22(T!20), tptp_fun_R_21(T!20))))))),
% 124.49/80.08 inference(unit_resolution,[status(thm)],[120, 119])).
% 124.49/80.08 tff(122,plain,
% 124.49/80.08 (~mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))),
% 124.49/80.08 inference(unit_resolution,[status(thm)],[121, 100])).
% 124.49/80.08 tff(123,plain,
% 124.49/80.08 (^[A: ty, X: uni, L1: uni, L2: uni] : refl((mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1))) <=> (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1))))),
% 124.49/80.08 inference(bind,[status(th)],[])).
% 124.49/80.08 tff(124,plain,
% 124.49/80.08 (![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1))) <=> ![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1)))),
% 124.49/80.08 inference(quant_intro,[status(thm)],[123])).
% 124.49/80.08 tff(125,plain,
% 124.49/80.08 (![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1))) <=> ![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1)))),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(126,plain,
% 124.49/80.08 (^[A: ty, X: uni, L1: uni, L2: uni] : rewrite((mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L1) | mem(A, X, L2))) <=> (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1))))),
% 124.49/80.08 inference(bind,[status(th)],[])).
% 124.49/80.08 tff(127,plain,
% 124.49/80.08 (![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L1) | mem(A, X, L2))) <=> ![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1)))),
% 124.49/80.08 inference(quant_intro,[status(thm)],[126])).
% 124.49/80.08 tff(128,axiom,(![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L1) | mem(A, X, L2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mem_append')).
% 124.49/80.08 tff(129,plain,
% 124.49/80.08 (![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1)))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[128, 127])).
% 124.49/80.08 tff(130,plain,
% 124.49/80.08 (![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1)))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[129, 125])).
% 124.49/80.08 tff(131,plain,(
% 124.49/80.08 ![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1)))),
% 124.49/80.08 inference(skolemize,[status(sab)],[130])).
% 124.49/80.08 tff(132,plain,
% 124.49/80.08 (![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1)))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[131, 124])).
% 124.49/80.08 tff(133,plain,
% 124.49/80.08 ((~![A: ty, X: uni, L1: uni, L2: uni] : (mem(A, X, infix_plpl(A, L1, L2)) <=> (mem(A, X, L2) | mem(A, X, L1)))) | (mem(tree, t2tb2(T!20), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) <=> (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | mem(tree, t2tb2(T!20), t2tb1(O!16))))),
% 124.49/80.08 inference(quant_inst,[status(thm)],[])).
% 124.49/80.08 tff(134,plain,
% 124.49/80.08 (mem(tree, t2tb2(T!20), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) <=> (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | mem(tree, t2tb2(T!20), t2tb1(O!16)))),
% 124.49/80.08 inference(unit_resolution,[status(thm)],[133, 132])).
% 124.49/80.08 tff(135,plain,
% 124.49/80.08 (A4!19 = tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))),
% 124.49/80.08 inference(and_elim,[status(thm)],[89])).
% 124.49/80.08 tff(136,plain,
% 124.49/80.08 (t2tb3(A4!19) = t2tb3(tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))),
% 124.49/80.08 inference(monotonicity,[status(thm)],[135])).
% 124.49/80.08 tff(137,plain,
% 124.49/80.08 (t2tb3(tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) = t2tb3(A4!19)),
% 124.49/80.08 inference(symmetry,[status(thm)],[136])).
% 124.49/80.08 tff(138,plain,
% 124.49/80.08 (![J: uni] : (t2tb3(tb2t3(J)) = J) <=> ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(139,plain,
% 124.49/80.08 (![J: uni] : (t2tb3(tb2t3(J)) = J) <=> ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(140,axiom,(![J: uni] : (t2tb3(tb2t3(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR3')).
% 124.49/80.08 tff(141,plain,
% 124.49/80.08 (![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[140, 139])).
% 124.49/80.08 tff(142,plain,(
% 124.49/80.08 ![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 124.49/80.08 inference(skolemize,[status(sab)],[141])).
% 124.49/80.08 tff(143,plain,
% 124.49/80.08 (![J: uni] : (t2tb3(tb2t3(J)) = J)),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[142, 138])).
% 124.49/80.08 tff(144,plain,
% 124.49/80.08 ((~![J: uni] : (t2tb3(tb2t3(J)) = J)) | (t2tb3(tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) = set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))),
% 124.49/80.08 inference(quant_inst,[status(thm)],[])).
% 124.49/80.08 tff(145,plain,
% 124.49/80.08 (t2tb3(tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) = set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))),
% 124.49/80.08 inference(unit_resolution,[status(thm)],[144, 143])).
% 124.49/80.08 tff(146,plain,
% 124.49/80.08 (set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) = t2tb3(tb2t3(set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))),
% 124.49/80.08 inference(symmetry,[status(thm)],[145])).
% 124.49/80.08 tff(147,plain,
% 124.49/80.08 (set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) = t2tb3(A4!19)),
% 124.49/80.08 inference(transitivity,[status(thm)],[146, 137])).
% 124.49/80.08 tff(148,plain,
% 124.49/80.08 (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = get(list(tree), int, t2tb3(A4!19), t2tb(I!11))),
% 124.49/80.08 inference(monotonicity,[status(thm)],[147])).
% 124.49/80.08 tff(149,plain,
% 124.49/80.08 (^[A: ty, X: uni, X1: uni] : refl(sort1(list(A), infix_plpl(A, X, X1)) <=> sort1(list(A), infix_plpl(A, X, X1)))),
% 124.49/80.08 inference(bind,[status(th)],[])).
% 124.49/80.08 tff(150,plain,
% 124.49/80.08 (![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1)) <=> ![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1))),
% 124.49/80.08 inference(quant_intro,[status(thm)],[149])).
% 124.49/80.08 tff(151,plain,
% 124.49/80.08 (![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1)) <=> ![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1))),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(152,axiom,(![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','infix_plpl_sort2')).
% 124.49/80.08 tff(153,plain,
% 124.49/80.08 (![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[152, 151])).
% 124.49/80.08 tff(154,plain,(
% 124.49/80.08 ![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1))),
% 124.49/80.08 inference(skolemize,[status(sab)],[153])).
% 124.49/80.08 tff(155,plain,
% 124.49/80.08 (![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[154, 150])).
% 124.49/80.08 tff(156,plain,
% 124.49/80.08 ((~![A: ty, X: uni, X1: uni] : sort1(list(A), infix_plpl(A, X, X1))) | sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))),
% 124.49/80.08 inference(quant_inst,[status(thm)],[])).
% 124.49/80.08 tff(157,plain,
% 124.49/80.08 (sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))),
% 124.49/80.08 inference(unit_resolution,[status(thm)],[156, 155])).
% 124.49/80.08 tff(158,plain,
% 124.49/80.08 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : refl(((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))))),
% 124.49/80.08 inference(bind,[status(th)],[])).
% 124.49/80.08 tff(159,plain,
% 124.49/80.08 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 124.49/80.08 inference(quant_intro,[status(thm)],[158])).
% 124.49/80.08 tff(160,plain,
% 124.49/80.08 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(161,plain,
% 124.49/80.08 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : trans(monotonicity(rewrite(((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)) <=> ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> (sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))))), rewrite((sort1(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))), ((sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))))),
% 124.49/80.08 inference(bind,[status(th)],[])).
% 124.49/80.08 tff(162,plain,
% 124.49/80.08 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 124.49/80.08 inference(quant_intro,[status(thm)],[161])).
% 124.49/80.08 tff(163,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort1(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','select_eq')).
% 124.49/80.08 tff(164,plain,
% 124.49/80.08 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[163, 162])).
% 124.49/80.08 tff(165,plain,
% 124.49/80.08 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[164, 160])).
% 124.49/80.08 tff(166,plain,(
% 124.49/80.08 ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 124.49/80.08 inference(skolemize,[status(sab)],[165])).
% 124.49/80.08 tff(167,plain,
% 124.49/80.08 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))),
% 124.49/80.08 inference(modus_ponens,[status(thm)],[166, 159])).
% 124.49/80.08 tff(168,plain,
% 124.49/80.08 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))) | (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))) | (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(169,plain,
% 124.49/80.08 (((get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | $false | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) <=> ((~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))) | (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(170,plain,
% 124.49/80.08 ((~$true) <=> $false),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(171,plain,
% 124.49/80.08 ((t2tb(I!11) = t2tb(I!11)) <=> $true),
% 124.49/80.08 inference(rewrite,[status(thm)],[])).
% 124.49/80.08 tff(172,plain,
% 124.49/80.08 ((~(t2tb(I!11) = t2tb(I!11))) <=> (~$true)),
% 124.49/80.09 inference(monotonicity,[status(thm)],[171])).
% 124.49/80.09 tff(173,plain,
% 124.49/80.09 ((~(t2tb(I!11) = t2tb(I!11))) <=> $false),
% 124.49/80.09 inference(transitivity,[status(thm)],[172, 170])).
% 124.49/80.09 tff(174,plain,
% 124.49/80.09 (((get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~(t2tb(I!11) = t2tb(I!11))) | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) <=> ((get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | $false | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))),
% 124.49/80.09 inference(monotonicity,[status(thm)],[173])).
% 124.49/80.09 tff(175,plain,
% 124.49/80.09 (((get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~(t2tb(I!11) = t2tb(I!11))) | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))) <=> ((~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))) | (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))),
% 124.49/80.09 inference(transitivity,[status(thm)],[174, 169])).
% 124.49/80.09 tff(176,plain,
% 124.49/80.09 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~(t2tb(I!11) = t2tb(I!11))) | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))) | (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))),
% 124.49/80.09 inference(monotonicity,[status(thm)],[175])).
% 124.49/80.09 tff(177,plain,
% 124.49/80.09 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~(t2tb(I!11) = t2tb(I!11))) | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))) | (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))))),
% 124.49/80.09 inference(transitivity,[status(thm)],[176, 168])).
% 124.49/80.09 tff(178,plain,
% 124.49/80.09 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | ((get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) | (~(t2tb(I!11) = t2tb(I!11))) | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))))),
% 124.49/80.09 inference(quant_inst,[status(thm)],[])).
% 124.49/80.09 tff(179,plain,
% 124.49/80.09 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort1(B, B1)))) | (~sort1(list(tree), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))) | (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[178, 177])).
% 124.49/80.09 tff(180,plain,
% 124.49/80.09 (get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11)) = infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[179, 167, 157])).
% 124.49/80.09 tff(181,plain,
% 124.49/80.09 (infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) = get(list(tree), int, set(list(tree), int, t2tb3(A3!15), t2tb(I!11), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))), t2tb(I!11))),
% 124.49/80.09 inference(symmetry,[status(thm)],[180])).
% 124.49/80.09 tff(182,plain,
% 124.49/80.09 (infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) = get(list(tree), int, t2tb3(A4!19), t2tb(I!11))),
% 124.49/80.09 inference(transitivity,[status(thm)],[181, 148])).
% 124.49/80.09 tff(183,plain,
% 124.49/80.09 (mem(tree, t2tb2(T!20), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) <=> mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11)))),
% 124.49/80.09 inference(monotonicity,[status(thm)],[182])).
% 124.49/80.09 tff(184,plain,
% 124.49/80.09 (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11))) <=> mem(tree, t2tb2(T!20), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))),
% 124.49/80.09 inference(symmetry,[status(thm)],[183])).
% 124.49/80.09 tff(185,plain,
% 124.49/80.09 (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A4!19), t2tb(I!11)))),
% 124.49/80.09 inference(and_elim,[status(thm)],[89])).
% 124.49/80.09 tff(186,plain,
% 124.49/80.09 (mem(tree, t2tb2(T!20), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[185, 184])).
% 124.49/80.09 tff(187,plain,
% 124.49/80.09 ((~(mem(tree, t2tb2(T!20), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11)))) <=> (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | mem(tree, t2tb2(T!20), t2tb1(O!16))))) | (~mem(tree, t2tb2(T!20), infix_plpl(tree, t2tb1(O!16), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))))) | (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | mem(tree, t2tb2(T!20), t2tb1(O!16)))),
% 124.49/80.09 inference(tautology,[status(thm)],[])).
% 124.49/80.09 tff(188,plain,
% 124.49/80.09 (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | mem(tree, t2tb2(T!20), t2tb1(O!16))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[187, 186, 134])).
% 124.49/80.09 tff(189,plain,
% 124.49/80.09 ((~(mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | mem(tree, t2tb2(T!20), t2tb1(O!16)))) | mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | mem(tree, t2tb2(T!20), t2tb1(O!16))),
% 124.49/80.09 inference(tautology,[status(thm)],[])).
% 124.49/80.09 tff(190,plain,
% 124.49/80.09 (mem(tree, t2tb2(T!20), get(list(tree), int, t2tb3(A3!15), t2tb(I!11))) | mem(tree, t2tb2(T!20), t2tb1(O!16))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[189, 188])).
% 124.49/80.09 tff(191,plain,
% 124.49/80.09 (mem(tree, t2tb2(T!20), t2tb1(O!16))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[190, 122])).
% 124.49/80.09 tff(192,plain,
% 124.49/80.09 (^[T: tree1] : refl((~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))) <=> (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))))),
% 124.49/80.09 inference(bind,[status(th)],[])).
% 124.49/80.09 tff(193,plain,
% 124.49/80.09 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))) <=> ![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))),
% 124.49/80.09 inference(quant_intro,[status(thm)],[192])).
% 124.49/80.09 tff(194,plain,
% 124.49/80.09 (^[T: tree1] : rewrite((~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))) <=> (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))))),
% 124.49/80.09 inference(bind,[status(th)],[])).
% 124.49/80.09 tff(195,plain,
% 124.49/80.09 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))) <=> ![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))),
% 124.49/80.09 inference(quant_intro,[status(thm)],[194])).
% 124.49/80.09 tff(196,plain,
% 124.49/80.09 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))) <=> ![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))),
% 124.49/80.09 inference(transitivity,[status(thm)],[195, 193])).
% 124.49/80.09 tff(197,plain,
% 124.49/80.09 (^[T: tree1] : trans(monotonicity(rewrite(((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) <=> ((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))), rewrite((mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))) <=> (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))), ((((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) <=> (((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))), rewrite((((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) <=> (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))), ((((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) <=> (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))))),
% 124.49/80.09 inference(bind,[status(th)],[])).
% 124.49/80.09 tff(198,plain,
% 124.49/80.09 (![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))) <=> ![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))),
% 124.49/80.09 inference(quant_intro,[status(thm)],[197])).
% 124.49/80.09 tff(199,plain,
% 124.49/80.09 (![T: tree1] : (((~mem(tree, t2tb2(T), t2tb1(O!16))) | ((T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T))) & ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0) & ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1))) & (mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : (~((T = node1(L, R)) & ($sum(size1(L), $product(-1, J!14)) = 0) & ($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))),
% 124.49/80.09 inference(and_elim,[status(thm)],[89])).
% 124.49/80.09 tff(200,plain,
% 124.49/80.09 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[199, 198])).
% 124.49/80.09 tff(201,plain,
% 124.49/80.09 (![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[200, 196])).
% 124.49/80.09 tff(202,plain,
% 124.49/80.09 ((~![T: tree1] : (~((~((~mem(tree, t2tb2(T), t2tb1(O!16))) | (~((~(T = node1(tptp_fun_L_18(T), tptp_fun_R_17(T)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T))))) = 1)))))) | (~(mem(tree, t2tb2(T), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))) | (~((~((~mem(tree, t2tb2(T!20), t2tb1(O!16))) | (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)))))) | (~(mem(tree, t2tb2(T!20), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))))),
% 124.49/80.09 inference(quant_inst,[status(thm)],[])).
% 124.49/80.09 tff(203,plain,
% 124.49/80.09 (~((~((~mem(tree, t2tb2(T!20), t2tb1(O!16))) | (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)))))) | (~(mem(tree, t2tb2(T!20), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1))))))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[202, 201])).
% 124.49/80.09 tff(204,plain,
% 124.49/80.09 (((~((~mem(tree, t2tb2(T!20), t2tb1(O!16))) | (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)))))) | (~(mem(tree, t2tb2(T!20), t2tb1(O!16)) | ![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(size1(L), $product(-1, J!14)) = 0)) | (~($sum(size1(R), $sum($product(-1, I!11), J!14)) = -1)))))) | ((~mem(tree, t2tb2(T!20), t2tb1(O!16))) | (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)))))),
% 124.49/80.09 inference(tautology,[status(thm)],[])).
% 124.49/80.09 tff(205,plain,
% 124.49/80.09 ((~mem(tree, t2tb2(T!20), t2tb1(O!16))) | (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1))))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[204, 203])).
% 124.49/80.09 tff(206,plain,
% 124.49/80.09 ((~((~mem(tree, t2tb2(T!20), t2tb1(O!16))) | (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)))))) | (~mem(tree, t2tb2(T!20), t2tb1(O!16))) | (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1))))),
% 124.49/80.09 inference(tautology,[status(thm)],[])).
% 124.49/80.09 tff(207,plain,
% 124.49/80.09 ((~mem(tree, t2tb2(T!20), t2tb1(O!16))) | (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1))))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[206, 205])).
% 124.49/80.09 tff(208,plain,
% 124.49/80.09 (~((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[207, 191])).
% 124.49/80.09 tff(209,plain,
% 124.49/80.09 (((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1))) | (T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))),
% 124.49/80.09 inference(tautology,[status(thm)],[])).
% 124.49/80.09 tff(210,plain,
% 124.49/80.09 (T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[209, 208])).
% 124.49/80.09 tff(211,plain,
% 124.49/80.09 (node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)) = T!20),
% 124.49/80.09 inference(symmetry,[status(thm)],[210])).
% 124.49/80.09 tff(212,plain,
% 124.49/80.09 (size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))) = size1(T!20)),
% 124.49/80.09 inference(monotonicity,[status(thm)],[211])).
% 124.49/80.09 tff(213,plain,
% 124.49/80.09 (size1(T!20) = size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))),
% 124.49/80.09 inference(symmetry,[status(thm)],[212])).
% 124.49/80.09 tff(214,plain,
% 124.49/80.09 ((~(size1(T!20) = size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))))) | $greatereq($sum(size1(T!20), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))))), 0)),
% 124.49/80.09 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.09 tff(215,plain,
% 124.49/80.09 ($greatereq($sum(size1(T!20), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))))), 0)),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[214, 213])).
% 124.49/80.09 tff(216,plain,
% 124.49/80.09 (^[X: tree1, X1: tree1] : refl(($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1) <=> ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1))),
% 124.49/80.09 inference(bind,[status(th)],[])).
% 124.49/80.09 tff(217,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1) <=> ![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)),
% 124.49/80.09 inference(quant_intro,[status(thm)],[216])).
% 124.49/80.09 tff(218,plain,
% 124.49/80.09 (^[X: tree1, X1: tree1] : trans(monotonicity(rewrite($sum(size1(node1(X, X1)), $sum($product(-1, size1(X)), $product(-1, size1(X1)))) = $sum($product(-1, size1(X1)), $sum($product(-1, size1(X)), size1(node1(X, X1))))), (($sum(size1(node1(X, X1)), $sum($product(-1, size1(X)), $product(-1, size1(X1)))) = 1) <=> ($sum($product(-1, size1(X1)), $sum($product(-1, size1(X)), size1(node1(X, X1)))) = 1))), rewrite(($sum($product(-1, size1(X1)), $sum($product(-1, size1(X)), size1(node1(X, X1)))) = 1) <=> ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)), (($sum(size1(node1(X, X1)), $sum($product(-1, size1(X)), $product(-1, size1(X1)))) = 1) <=> ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)))),
% 124.49/80.09 inference(bind,[status(th)],[])).
% 124.49/80.09 tff(219,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : ($sum(size1(node1(X, X1)), $sum($product(-1, size1(X)), $product(-1, size1(X1)))) = 1) <=> ![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)),
% 124.49/80.09 inference(quant_intro,[status(thm)],[218])).
% 124.49/80.09 tff(220,plain,
% 124.49/80.09 (^[X: tree1, X1: tree1] : rewrite((size1(node1(X, X1)) = $sum(1, $sum(size1(X), size1(X1)))) <=> ($sum(size1(node1(X, X1)), $sum($product(-1, size1(X)), $product(-1, size1(X1)))) = 1))),
% 124.49/80.09 inference(bind,[status(th)],[])).
% 124.49/80.09 tff(221,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum(1, $sum(size1(X), size1(X1)))) <=> ![X: tree1, X1: tree1] : ($sum(size1(node1(X, X1)), $sum($product(-1, size1(X)), $product(-1, size1(X1)))) = 1)),
% 124.49/80.09 inference(quant_intro,[status(thm)],[220])).
% 124.49/80.09 tff(222,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum(1, $sum(size1(X), size1(X1)))) <=> ![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum(1, $sum(size1(X), size1(X1))))),
% 124.49/80.09 inference(rewrite,[status(thm)],[])).
% 124.49/80.09 tff(223,plain,
% 124.49/80.09 (^[X: tree1, X1: tree1] : rewrite((size1(node1(X, X1)) = $sum($sum(1, size1(X)), size1(X1))) <=> (size1(node1(X, X1)) = $sum(1, $sum(size1(X), size1(X1)))))),
% 124.49/80.09 inference(bind,[status(th)],[])).
% 124.49/80.09 tff(224,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum($sum(1, size1(X)), size1(X1))) <=> ![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum(1, $sum(size1(X), size1(X1))))),
% 124.49/80.09 inference(quant_intro,[status(thm)],[223])).
% 124.49/80.09 tff(225,axiom,((size1(empty1) = 0) & ![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum($sum(1, size1(X)), size1(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','size_def')).
% 124.49/80.09 tff(226,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum($sum(1, size1(X)), size1(X1)))),
% 124.49/80.09 inference(and_elim,[status(thm)],[225])).
% 124.49/80.09 tff(227,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum(1, $sum(size1(X), size1(X1))))),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[226, 224])).
% 124.49/80.09 tff(228,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : (size1(node1(X, X1)) = $sum(1, $sum(size1(X), size1(X1))))),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[227, 222])).
% 124.49/80.09 tff(229,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : ($sum(size1(node1(X, X1)), $sum($product(-1, size1(X)), $product(-1, size1(X1)))) = 1)),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[228, 221])).
% 124.49/80.09 tff(230,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[229, 219])).
% 124.49/80.09 tff(231,plain,(
% 124.49/80.09 ![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)),
% 124.49/80.09 inference(skolemize,[status(sab)],[230])).
% 124.49/80.09 tff(232,plain,
% 124.49/80.09 (![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[231, 217])).
% 124.49/80.09 tff(233,plain,
% 124.49/80.09 (((~![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)) | ($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1)) <=> ((~![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)) | ($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1))),
% 124.49/80.09 inference(rewrite,[status(thm)],[])).
% 124.49/80.09 tff(234,plain,
% 124.49/80.09 (($sum(size1(tptp_fun_R_17(T!20)), $sum(size1(tptp_fun_L_18(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1) <=> ($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1)),
% 124.49/80.09 inference(rewrite,[status(thm)],[])).
% 124.49/80.09 tff(235,plain,
% 124.49/80.09 (((~![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)) | ($sum(size1(tptp_fun_R_17(T!20)), $sum(size1(tptp_fun_L_18(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1)) <=> ((~![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)) | ($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1))),
% 124.49/80.09 inference(monotonicity,[status(thm)],[234])).
% 124.49/80.09 tff(236,plain,
% 124.49/80.09 (((~![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)) | ($sum(size1(tptp_fun_R_17(T!20)), $sum(size1(tptp_fun_L_18(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1)) <=> ((~![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)) | ($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1))),
% 124.49/80.09 inference(transitivity,[status(thm)],[235, 233])).
% 124.49/80.09 tff(237,plain,
% 124.49/80.09 ((~![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)) | ($sum(size1(tptp_fun_R_17(T!20)), $sum(size1(tptp_fun_L_18(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1)),
% 124.49/80.09 inference(quant_inst,[status(thm)],[])).
% 124.49/80.09 tff(238,plain,
% 124.49/80.09 ((~![X: tree1, X1: tree1] : ($sum(size1(X1), $sum(size1(X), $product(-1, size1(node1(X, X1))))) = -1)) | ($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1)),
% 124.49/80.09 inference(modus_ponens,[status(thm)],[237, 236])).
% 124.49/80.09 tff(239,plain,
% 124.49/80.09 ($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[238, 232])).
% 124.49/80.09 tff(240,plain,
% 124.49/80.09 ((~($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1)) | $lesseq($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))), -1)),
% 124.49/80.09 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.09 tff(241,plain,
% 124.49/80.09 ($lesseq($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))), -1)),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[240, 239])).
% 124.49/80.09 tff(242,plain,
% 124.49/80.09 (((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1))) | ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)),
% 124.49/80.09 inference(tautology,[status(thm)],[])).
% 124.49/80.09 tff(243,plain,
% 124.49/80.09 ($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1),
% 124.49/80.09 inference(unit_resolution,[status(thm)],[242, 208])).
% 124.49/80.09 tff(244,plain,
% 124.49/80.09 ((~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)) | $lesseq($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))), 1)),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(245,plain,
% 124.49/80.10 ($lesseq($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))), 1)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[244, 243])).
% 124.49/80.10 tff(246,plain,
% 124.49/80.10 (((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | (~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1))) | ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)),
% 124.49/80.10 inference(tautology,[status(thm)],[])).
% 124.49/80.10 tff(247,plain,
% 124.49/80.10 ($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[246, 208])).
% 124.49/80.10 tff(248,plain,
% 124.49/80.10 ((~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), 0)),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(249,plain,
% 124.49/80.10 ($lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), 0)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[248, 247])).
% 124.49/80.10 tff(250,plain,
% 124.49/80.10 ($lesseq($sum(I!11, $product(-1, size1(T!20))), 0) | (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), 0)) | (~$greatereq($sum(size1(T!20), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))))), 0)) | (~$lesseq($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))), -1)) | (~$lesseq($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))), 1))),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(251,plain,
% 124.49/80.10 ($lesseq($sum(I!11, $product(-1, size1(T!20))), 0)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[250, 249, 245, 241, 215])).
% 124.49/80.10 tff(252,plain,
% 124.49/80.10 ((~($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))) = 0)) | $greatereq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), 0)),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(253,plain,
% 124.49/80.10 ($greatereq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), 0)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[252, 247])).
% 124.49/80.10 tff(254,plain,
% 124.49/80.10 ((~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), -1)) | (~$greatereq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), 0))),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(255,plain,
% 124.49/80.10 (~$lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), -1)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[254, 253])).
% 124.49/80.10 tff(256,plain,
% 124.49/80.10 (((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), -1))) <=> ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | (~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), -1))),
% 124.49/80.10 inference(rewrite,[status(thm)],[])).
% 124.49/80.10 tff(257,plain,
% 124.49/80.10 (((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(tptp_fun_L_18(T!20)), $product(-1, J!14)), 1)) <=> ((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), -1))),
% 124.49/80.10 inference(rewrite,[status(thm)],[])).
% 124.49/80.10 tff(258,plain,
% 124.49/80.10 (((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(tptp_fun_L_18(T!20)), $product(-1, J!14)), 1))) <=> ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), -1)))),
% 124.49/80.10 inference(monotonicity,[status(thm)],[257])).
% 124.49/80.10 tff(259,plain,
% 124.49/80.10 (((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(tptp_fun_L_18(T!20)), $product(-1, J!14)), 1))) <=> ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | (~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), -1))),
% 124.49/80.10 inference(transitivity,[status(thm)],[258, 256])).
% 124.49/80.10 tff(260,plain,
% 124.49/80.10 ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | ((~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(tptp_fun_L_18(T!20)), $product(-1, J!14)), 1))),
% 124.49/80.10 inference(quant_inst,[status(thm)],[])).
% 124.49/80.10 tff(261,plain,
% 124.49/80.10 ((~![L: tree1, R: tree1] : ((~(T!20 = node1(L, R))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $greatereq($sum(size1(L), $product(-1, J!14)), 1))) | (~(T!20 = node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))) | (~($sum(I!11, $product(-1, size1(T!20))) = 0)) | $lesseq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), -1)),
% 124.49/80.10 inference(modus_ponens,[status(thm)],[260, 259])).
% 124.49/80.10 tff(262,plain,
% 124.49/80.10 (~($sum(I!11, $product(-1, size1(T!20))) = 0)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[261, 92, 210, 255])).
% 124.49/80.10 tff(263,plain,
% 124.49/80.10 (($sum(I!11, $product(-1, size1(T!20))) = 0) | (~$lesseq($sum(I!11, $product(-1, size1(T!20))), 0)) | (~$greatereq($sum(I!11, $product(-1, size1(T!20))), 0))),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(264,plain,
% 124.49/80.10 ((~$lesseq($sum(I!11, $product(-1, size1(T!20))), 0)) | (~$greatereq($sum(I!11, $product(-1, size1(T!20))), 0))),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[263, 262])).
% 124.49/80.10 tff(265,plain,
% 124.49/80.10 ($false),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[264, 251, 1])).
% 124.49/80.10 tff(266,plain,(~$greatereq($sum(I!11, $product(-1, size1(T!20))), 0)), inference(lemma,lemma(discharge,[]))).
% 124.49/80.10 tff(267,plain,
% 124.49/80.10 ((~(size1(T!20) = size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))))) | $lesseq($sum(size1(T!20), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))))), 0)),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(268,plain,
% 124.49/80.10 ($lesseq($sum(size1(T!20), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))))), 0)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[267, 213])).
% 124.49/80.10 tff(269,plain,
% 124.49/80.10 ((~($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))) = -1)) | $greatereq($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))), -1)),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(270,plain,
% 124.49/80.10 ($greatereq($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))), -1)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[269, 239])).
% 124.49/80.10 tff(271,plain,
% 124.49/80.10 ((~($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))) = 1)) | $greatereq($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))), 1)),
% 124.49/80.10 inference(theory_lemma,[status(thm)],[])).
% 124.49/80.10 tff(272,plain,
% 124.49/80.10 ($greatereq($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))), 1)),
% 124.49/80.10 inference(unit_resolution,[status(thm)],[271, 243])).
% 124.49/80.10 tff(273,plain,
% 124.49/80.10 ($greatereq($sum(I!11, $product(-1, size1(T!20))), 0) | (~$greatereq($sum(J!14, $product(-1, size1(tptp_fun_L_18(T!20)))), 0)) | (~$lesseq($sum(size1(T!20), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20))))), 0)) | (~$greatereq($sum(size1(tptp_fun_L_18(T!20)), $sum(size1(tptp_fun_R_17(T!20)), $product(-1, size1(node1(tptp_fun_L_18(T!20), tptp_fun_R_17(T!20)))))), -1)) | (~$greatereq($sum(I!11, $sum($product(-1, J!14), $product(-1, size1(tptp_fun_R_17(T!20))))), 1))),
% 124.59/80.14 inference(theory_lemma,[status(thm)],[])).
% 124.59/80.14 tff(274,plain,
% 124.59/80.14 ($greatereq($sum(I!11, $product(-1, size1(T!20))), 0)),
% 124.59/80.14 inference(unit_resolution,[status(thm)],[273, 253, 272, 270, 268])).
% 124.59/80.14 tff(275,plain,
% 124.59/80.14 ($false),
% 124.59/80.14 inference(unit_resolution,[status(thm)],[274, 266])).
% 124.59/80.14 % SZS output end Proof
%------------------------------------------------------------------------------