TSTP Solution File: SWV416+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV416+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 15:11:42 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV416+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 02:48:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(remove_pq_type, type, (
% 0.19/0.44 remove_pq: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_X4_20_type, type, (
% 0.19/0.44 tptp_fun_X4_20: $i)).
% 0.19/0.44 tff(i_type, type, (
% 0.19/0.44 i: $i > $i)).
% 0.19/0.44 tff(triple_type, type, (
% 0.19/0.44 triple: ( $i * $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_X3_21_type, type, (
% 0.19/0.44 tptp_fun_X3_21: $i)).
% 0.19/0.44 tff(insert_slb_type, type, (
% 0.19/0.44 insert_slb: ( $i * $i ) > $i)).
% 0.19/0.44 tff(pair_type, type, (
% 0.19/0.44 pair: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_X6_18_type, type, (
% 0.19/0.44 tptp_fun_X6_18: $i)).
% 0.19/0.44 tff(tptp_fun_X5_19_type, type, (
% 0.19/0.44 tptp_fun_X5_19: $i)).
% 0.19/0.44 tff(tptp_fun_X_17_type, type, (
% 0.19/0.44 tptp_fun_X_17: $i)).
% 0.19/0.44 tff(tptp_fun_X2_22_type, type, (
% 0.19/0.44 tptp_fun_X2_22: $i)).
% 0.19/0.44 tff(remove_cpq_type, type, (
% 0.19/0.44 remove_cpq: ( $i * $i ) > $i)).
% 0.19/0.44 tff(insert_pq_type, type, (
% 0.19/0.44 insert_pq: ( $i * $i ) > $i)).
% 0.19/0.44 tff(contains_pq_type, type, (
% 0.19/0.44 contains_pq: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_W_14_type, type, (
% 0.19/0.44 tptp_fun_W_14: $i)).
% 0.19/0.44 tff(tptp_fun_V_15_type, type, (
% 0.19/0.44 tptp_fun_V_15: $i)).
% 0.19/0.44 tff(create_slb_type, type, (
% 0.19/0.44 create_slb: $i)).
% 0.19/0.44 tff(tptp_fun_U_16_type, type, (
% 0.19/0.44 tptp_fun_U_16: $i)).
% 0.19/0.44 tff(create_pq_type, type, (
% 0.19/0.44 create_pq: $i)).
% 0.19/0.44 tff(tptp_fun_X_32_type, type, (
% 0.19/0.44 tptp_fun_X_32: $i)).
% 0.19/0.44 tff(tptp_fun_W_33_type, type, (
% 0.19/0.44 tptp_fun_W_33: $i)).
% 0.19/0.44 tff(tptp_fun_V_34_type, type, (
% 0.19/0.44 tptp_fun_V_34: $i)).
% 0.19/0.44 tff(tptp_fun_U_35_type, type, (
% 0.19/0.44 tptp_fun_U_35: $i)).
% 0.19/0.44 tff(pi_sharp_remove_type, type, (
% 0.19/0.44 pi_sharp_remove: ( $i * $i ) > $o)).
% 0.19/0.44 tff(pi_remove_type, type, (
% 0.19/0.44 pi_remove: ( $i * $i ) > $o)).
% 0.19/0.44 tff(phi_type, type, (
% 0.19/0.44 phi: $i > $o)).
% 0.19/0.44 tff(bad_type, type, (
% 0.19/0.44 bad: $i)).
% 0.19/0.44 tff(remove_slb_type, type, (
% 0.19/0.44 remove_slb: ( $i * $i ) > $i)).
% 0.19/0.44 tff(remove_pqp_type, type, (
% 0.19/0.44 remove_pqp: ( $i * $i ) > $i)).
% 0.19/0.44 tff(strictly_less_than_type, type, (
% 0.19/0.44 strictly_less_than: ( $i * $i ) > $o)).
% 0.19/0.44 tff(lookup_slb_type, type, (
% 0.19/0.44 lookup_slb: ( $i * $i ) > $i)).
% 0.19/0.44 tff(contains_slb_type, type, (
% 0.19/0.44 contains_slb: ( $i * $i ) > $o)).
% 0.19/0.44 tff(contains_cpq_type, type, (
% 0.19/0.44 contains_cpq: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_W_23_type, type, (
% 0.19/0.44 tptp_fun_W_23: $i)).
% 0.19/0.44 tff(tptp_fun_V_24_type, type, (
% 0.19/0.44 tptp_fun_V_24: $i)).
% 0.19/0.44 tff(tptp_fun_U_25_type, type, (
% 0.19/0.44 tptp_fun_U_25: $i)).
% 0.19/0.44 tff(tptp_fun_X6_27_type, type, (
% 0.19/0.44 tptp_fun_X6_27: $i)).
% 0.19/0.44 tff(tptp_fun_X3_30_type, type, (
% 0.19/0.44 tptp_fun_X3_30: $i)).
% 0.19/0.44 tff(tptp_fun_X5_28_type, type, (
% 0.19/0.44 tptp_fun_X5_28: $i)).
% 0.19/0.44 tff(tptp_fun_X4_29_type, type, (
% 0.19/0.44 tptp_fun_X4_29: $i)).
% 0.19/0.44 tff(tptp_fun_X_26_type, type, (
% 0.19/0.44 tptp_fun_X_26: $i)).
% 0.19/0.44 tff(tptp_fun_X2_31_type, type, (
% 0.19/0.44 tptp_fun_X2_31: $i)).
% 0.19/0.44 tff(less_than_type, type, (
% 0.19/0.44 less_than: ( $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_X7_10_type, type, (
% 0.19/0.44 tptp_fun_X7_10: $i)).
% 0.19/0.44 tff(tptp_fun_X9_8_type, type, (
% 0.19/0.44 tptp_fun_X9_8: $i)).
% 0.19/0.44 tff(tptp_fun_X8_9_type, type, (
% 0.19/0.44 tptp_fun_X8_9: $i)).
% 0.19/0.44 tff(tptp_fun_Y_7_type, type, (
% 0.19/0.44 tptp_fun_Y_7: $i)).
% 0.19/0.44 tff(tptp_fun_X5_12_type, type, (
% 0.19/0.44 tptp_fun_X5_12: $i)).
% 0.19/0.44 tff(tptp_fun_X6_11_type, type, (
% 0.19/0.44 tptp_fun_X6_11: $i)).
% 0.19/0.44 tff(tptp_fun_X4_13_type, type, (
% 0.19/0.44 tptp_fun_X4_13: $i)).
% 0.19/0.44 tff(tptp_fun_X_3_type, type, (
% 0.19/0.44 tptp_fun_X_3: $i)).
% 0.19/0.44 tff(tptp_fun_V_5_type, type, (
% 0.19/0.44 tptp_fun_V_5: $i)).
% 0.19/0.44 tff(tptp_fun_W_4_type, type, (
% 0.19/0.44 tptp_fun_W_4: $i)).
% 0.19/0.44 tff(tptp_fun_U_6_type, type, (
% 0.19/0.44 tptp_fun_U_6: $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl((i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X)) <=> (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X)) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(4,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax55')).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.45 tff(6,plain,(
% 0.19/0.45 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.19/0.45 inference(skolemize,[status(sab)],[5])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))) | (i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)) = insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)) = insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19) = i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21))),
% 0.19/0.45 inference(symmetry,[status(thm)],[9])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (remove_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.45 tff(12,assumption,(~(X5!19 = X4!20)), introduced(assumption)).
% 0.19/0.45 tff(13,assumption,(~(remove_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) = insert_pq(remove_pq(i(triple(X2!22, X!17, X3!21)), X4!20), X5!19))), introduced(assumption)).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (^[U: $i, V: $i, W: $i] : refl(((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W))) <=> ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W))) <=> ![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_pq(U, W) & (~(V = W))) <=> (~((~contains_pq(U, W)) | (V = W)))), ((~(contains_pq(U, W) & (~(V = W)))) <=> (~(~((~contains_pq(U, W)) | (V = W)))))), rewrite((~(~((~contains_pq(U, W)) | (V = W)))) <=> ((~contains_pq(U, W)) | (V = W))), ((~(contains_pq(U, W) & (~(V = W)))) <=> ((~contains_pq(U, W)) | (V = W)))), (((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))) <=> (((~contains_pq(U, W)) | (V = W)) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))))), rewrite((((~contains_pq(U, W)) | (V = W)) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))) <=> ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))), (((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))) <=> ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : ((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))) <=> ![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : ((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))) <=> ![U: $i, V: $i, W: $i] : ((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (^[U: $i, V: $i, W: $i] : rewrite(((contains_pq(U, W) & (~(V = W))) => (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))) <=> ((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : ((contains_pq(U, W) & (~(V = W))) => (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V))) <=> ![U: $i, V: $i, W: $i] : ((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.45 tff(21,axiom,(![U: $i, V: $i, W: $i] : ((contains_pq(U, W) & (~(V = W))) => (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax','ax12')).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : ((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : ((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.45 tff(24,plain,(
% 0.19/0.45 ![U: $i, V: $i, W: $i] : ((~(contains_pq(U, W) & (~(V = W)))) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[23])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (((~![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))) | ((X5!19 = X4!20) | (remove_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) = insert_pq(remove_pq(i(triple(X2!22, X!17, X3!21)), X4!20), X5!19)) | (~contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))) | (X5!19 = X4!20) | (remove_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) = insert_pq(remove_pq(i(triple(X2!22, X!17, X3!21)), X4!20), X5!19)) | (~contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 ((~![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))) | ((X5!19 = X4!20) | (remove_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) = insert_pq(remove_pq(i(triple(X2!22, X!17, X3!21)), X4!20), X5!19)) | (~contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 ((~![U: $i, V: $i, W: $i] : ((V = W) | (remove_pq(insert_pq(U, V), W) = insert_pq(remove_pq(U, W), V)) | (~contains_pq(U, W)))) | (X5!19 = X4!20) | (remove_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) = insert_pq(remove_pq(i(triple(X2!22, X!17, X3!21)), X4!20), X5!19)) | (~contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 ((X5!19 = X4!20) | (remove_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) = insert_pq(remove_pq(i(triple(X2!22, X!17, X3!21)), X4!20), X5!19)) | (~contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (~contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[30, 12, 13])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (^[U: $i, V: $i, W: $i] : refl((contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))) <=> (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))) <=> ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))) <=> ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (^[U: $i, V: $i, W: $i] : rewrite((contains_pq(insert_pq(U, V), W) <=> (contains_pq(U, W) | (V = W))) <=> (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> (contains_pq(U, W) | (V = W))) <=> ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.45 tff(37,axiom,(![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> (contains_pq(U, W) | (V = W)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax','ax9')).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.45 tff(40,plain,(
% 0.19/0.45 ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[39])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 ((~![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))) | (contains_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) <=> ((X5!19 = X4!20) | contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (contains_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) <=> ((X5!19 = X4!20) | contains_pq(i(triple(X2!22, X!17, X3!21)), X4!20))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (contains_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20) <=> contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20) <=> contains_pq(insert_pq(i(triple(X2!22, X!17, X3!21)), X5!19), X4!20)),
% 0.19/0.45 inference(symmetry,[status(thm)],[44])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (^[U: $i, V: $i] : refl((i(triple(U, create_slb, V)) = create_pq) <=> (i(triple(U, create_slb, V)) = create_pq))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq) <=> ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq) <=> ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(49,axiom,(![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax54')).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.45 tff(51,plain,(
% 0.19/0.45 ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.19/0.45 inference(skolemize,[status(sab)],[50])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)) | (i(triple(U!16, create_slb, V!15)) = create_pq)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (i(triple(U!16, create_slb, V!15)) = create_pq),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (create_pq = i(triple(U!16, create_slb, V!15))),
% 0.19/0.45 inference(symmetry,[status(thm)],[54])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (contains_pq(create_pq, W!14) <=> contains_pq(i(triple(U!16, create_slb, V!15)), W!14)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (contains_pq(i(triple(U!16, create_slb, V!15)), W!14) <=> contains_pq(create_pq, W!14)),
% 0.19/0.45 inference(symmetry,[status(thm)],[56])).
% 0.19/0.45 tff(58,assumption,(contains_pq(i(triple(U!16, create_slb, V!15)), W!14)), introduced(assumption)).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (contains_pq(create_pq, W!14)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (^[U: $i] : refl((~contains_pq(create_pq, U)) <=> (~contains_pq(create_pq, U)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (![U: $i] : (~contains_pq(create_pq, U)) <=> ![U: $i] : (~contains_pq(create_pq, U))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (![U: $i] : (~contains_pq(create_pq, U)) <=> ![U: $i] : (~contains_pq(create_pq, U))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(63,axiom,(![U: $i] : (~contains_pq(create_pq, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax','ax8')).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (![U: $i] : (~contains_pq(create_pq, U))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.45 tff(65,plain,(
% 0.19/0.45 ![U: $i] : (~contains_pq(create_pq, U))),
% 0.19/0.45 inference(skolemize,[status(sab)],[64])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (![U: $i] : (~contains_pq(create_pq, U))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 ((~![U: $i] : (~contains_pq(create_pq, U))) | (~contains_pq(create_pq, W!14))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (~contains_pq(create_pq, W!14)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[68, 59])).
% 0.19/0.45 tff(70,plain,(~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14))) | contains_pq(i(triple(U!16, create_slb, V!15)), W!14)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 ((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (^[U: $i, V: $i] : refl((pi_sharp_remove(U, V) <=> contains_pq(U, V)) <=> (pi_sharp_remove(U, V) <=> contains_pq(U, V)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V)) <=> ![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V)) <=> ![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(76,axiom,(![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax56')).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.45 tff(78,plain,(
% 0.19/0.45 ![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.19/0.45 inference(skolemize,[status(sab)],[77])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 ((~![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))) | (pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) <=> contains_pq(i(triple(U!35, V!34, W!33)), X!32))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) <=> contains_pq(i(triple(U!35, V!34, W!33)), X!32)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (^[U: $i, V: $i] : refl((pi_remove(U, V) <=> pi_sharp_remove(i(U), V)) <=> (pi_remove(U, V) <=> pi_sharp_remove(i(U), V)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V)) <=> ![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V)) <=> ![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(85,axiom,(![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax57')).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.45 tff(87,plain,(
% 0.19/0.45 ![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.19/0.45 inference(skolemize,[status(sab)],[86])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 ((~![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))) | (pi_remove(triple(U!35, V!34, W!33), X!32) <=> pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 (pi_remove(triple(U!35, V!34, W!33), X!32) <=> pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 ((~((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~phi(remove_cpq(triple(U!35, V!34, W!33), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32)))) <=> (~((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~phi(remove_cpq(triple(U!35, V!34, W!33), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 ((~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 ((~![U: $i, V: $i, W: $i, X: $i] : (pi_remove(triple(U, V, W), X) => (phi(remove_cpq(triple(U, V, W), X)) => (pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(94,axiom,(~![U: $i, V: $i, W: $i, X: $i] : (pi_remove(triple(U, V, W), X) => (phi(remove_cpq(triple(U, V, W), X)) => (pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co3')).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[95, 92])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[97, 92])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[98, 92])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (~![U: $i, V: $i, W: $i, X: $i] : ((pi_sharp_remove(i(triple(U, V, W)), X) & (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) | (~phi(remove_cpq(triple(U, V, W), X))) | (~pi_remove(triple(U, V, W), X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[100, 92])).
% 0.19/0.46 tff(102,plain,(
% 0.19/0.46 ~((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~phi(remove_cpq(triple(U!35, V!34, W!33), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[101])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (~((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~phi(remove_cpq(triple(U!35, V!34, W!33), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[102, 91])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 (pi_remove(triple(U!35, V!34, W!33), X!32)),
% 0.19/0.46 inference(or_elim,[status(thm)],[103])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 ((~(pi_remove(triple(U!35, V!34, W!33), X!32) <=> pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32))) | (~pi_remove(triple(U!35, V!34, W!33), X!32)) | pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(106,plain,
% 0.19/0.46 ((~(pi_remove(triple(U!35, V!34, W!33), X!32) <=> pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32))) | pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 (pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[106, 90])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 ((~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) <=> contains_pq(i(triple(U!35, V!34, W!33)), X!32))) | (~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | contains_pq(i(triple(U!35, V!34, W!33)), X!32)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 ((~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) <=> contains_pq(i(triple(U!35, V!34, W!33)), X!32))) | contains_pq(i(triple(U!35, V!34, W!33)), X!32)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 (contains_pq(i(triple(U!35, V!34, W!33)), X!32)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[109, 81])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 ((~(~((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))))) <=> ((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 ((pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))) <=> (~((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 ((~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))) <=> (~(~((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 ((~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))) <=> ((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 (~(pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32) & (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))),
% 0.19/0.46 inference(or_elim,[status(thm)],[103])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 ((~pi_sharp_remove(i(triple(U!35, V!34, W!33)), X!32)) | (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 (~(i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[116, 107])).
% 0.19/0.46 tff(118,assumption,(![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))), introduced(assumption)).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) | ((~contains_pq(i(triple(U!35, V!34, W!33)), X!32)) | (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))) <=> ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) | (~contains_pq(i(triple(U!35, V!34, W!33)), X!32)) | (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(120,plain,
% 0.19/0.46 ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) | ((~contains_pq(i(triple(U!35, V!34, W!33)), X!32)) | (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(121,plain,
% 0.19/0.46 ((~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) | (~contains_pq(i(triple(U!35, V!34, W!33)), X!32)) | (i(remove_cpq(triple(U!35, V!34, W!33), X!32)) = remove_pq(i(triple(U!35, V!34, W!33)), X!32))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[121, 118, 117, 110])).
% 0.19/0.46 tff(123,plain,(~![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))))))) <=> ((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 ((~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))) <=> (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> ((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 ((![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 ((![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (~((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1)))) | (~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[131, 129])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 ((((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 ((![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))) <=> (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) <=> ((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 ((((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> (((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 ((((~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> (![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) | (~((~contains_pq(i(triple(U!16, create_slb, V!15)), W!14)) | (i(remove_cpq(triple(U!16, create_slb, V!15), W!14)) = remove_pq(i(triple(U!16, create_slb, V!15)), W!14)))) | (![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X!17, Z)), X1)) | (i(remove_cpq(triple(Y, X!17, Z), X1)) = remove_pq(i(triple(Y, X!17, Z)), X1))) & (~((~contains_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20)) | (i(remove_cpq(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21), X4!20)) = remove_pq(i(triple(X2!22, insert_slb(X!17, pair(X5!19, X6!18)), X3!21)), X4!20))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[136, 133])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (((![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (^[X7: $i, X8: $i, X9: $i, X10: $i] : rewrite((contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) <=> ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 (![X7: $i, X8: $i, X9: $i, X10: $i] : (contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))) <=> ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 ((![U: $i, V: $i, W: $i] : (contains_pq(i(triple(U, create_slb, V)), W) => (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : (![Y: $i, Z: $i, X1: $i] : (contains_pq(i(triple(Y, X, Z)), X1) => (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1))) => ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : (contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4) => (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) <=> (![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (((![U: $i, V: $i, W: $i] : (contains_pq(i(triple(U, create_slb, V)), W) => (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : (![Y: $i, Z: $i, X1: $i] : (contains_pq(i(triple(Y, X, Z)), X1) => (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1))) => ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : (contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4) => (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : (contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> ((![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[142, 141])).
% 0.19/0.48 tff(144,plain,
% 0.19/0.48 (((![U: $i, V: $i, W: $i] : (contains_pq(i(triple(U, create_slb, V)), W) => (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : (![Y: $i, Z: $i, X1: $i] : (contains_pq(i(triple(Y, X, Z)), X1) => (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1))) => ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : (contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4) => (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : (contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))) <=> ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[143, 139])).
% 0.19/0.48 tff(145,axiom,((![U: $i, V: $i, W: $i] : (contains_pq(i(triple(U, create_slb, V)), W) => (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : (![Y: $i, Z: $i, X1: $i] : (contains_pq(i(triple(Y, X, Z)), X1) => (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1))) => ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : (contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4) => (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4))))) => ![X7: $i, X8: $i, X9: $i, X10: $i] : (contains_pq(i(triple(X7, X8, X9)), X10) => (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','big3_induction2')).
% 0.19/0.48 tff(146,plain,
% 0.19/0.48 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.48 tff(147,plain,
% 0.19/0.48 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[146, 138])).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[147, 138])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[148, 138])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[149, 138])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[150, 138])).
% 0.19/0.48 tff(152,plain,
% 0.19/0.48 ((~(![U: $i, V: $i, W: $i] : ((~contains_pq(i(triple(U, create_slb, V)), W)) | (i(remove_cpq(triple(U, create_slb, V), W)) = remove_pq(i(triple(U, create_slb, V)), W))) & ![X: $i] : ((~![Y: $i, Z: $i, X1: $i] : ((~contains_pq(i(triple(Y, X, Z)), X1)) | (i(remove_cpq(triple(Y, X, Z), X1)) = remove_pq(i(triple(Y, X, Z)), X1)))) | ![X2: $i, X3: $i, X4: $i, X5: $i, X6: $i] : ((~contains_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)) | (i(remove_cpq(triple(X2, insert_slb(X, pair(X5, X6)), X3), X4)) = remove_pq(i(triple(X2, insert_slb(X, pair(X5, X6)), X3)), X4)))))) | ![X7: $i, X8: $i, X9: $i, X10: $i] : ((~contains_pq(i(triple(X7, X8, X9)), X10)) | (i(remove_cpq(triple(X7, X8, X9), X10)) = remove_pq(i(triple(X7, X8, X9)), X10)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[151, 138])).
% 0.19/0.48 Proof display could not be completed: monotonicity rule is not handled
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