TSTP Solution File: SWV416+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV416+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV416+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Sep 4 02:57:33 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(contains_pq_type, type, (
% 0.18/0.40 contains_pq: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_X_3_type, type, (
% 0.18/0.40 tptp_fun_X_3: $i)).
% 0.18/0.40 tff(i_type, type, (
% 0.18/0.40 i: $i > $i)).
% 0.18/0.40 tff(triple_type, type, (
% 0.18/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_W_4_type, type, (
% 0.18/0.40 tptp_fun_W_4: $i)).
% 0.18/0.40 tff(tptp_fun_V_5_type, type, (
% 0.18/0.40 tptp_fun_V_5: $i)).
% 0.18/0.40 tff(tptp_fun_U_6_type, type, (
% 0.18/0.40 tptp_fun_U_6: $i)).
% 0.18/0.40 tff(pi_sharp_remove_type, type, (
% 0.18/0.40 pi_sharp_remove: ( $i * $i ) > $o)).
% 0.18/0.40 tff(remove_pq_type, type, (
% 0.18/0.40 remove_pq: ( $i * $i ) > $i)).
% 0.18/0.40 tff(remove_cpq_type, type, (
% 0.18/0.40 remove_cpq: ( $i * $i ) > $i)).
% 0.18/0.40 tff(pi_remove_type, type, (
% 0.18/0.40 pi_remove: ( $i * $i ) > $o)).
% 0.18/0.40 tff(phi_type, type, (
% 0.18/0.40 phi: $i > $o)).
% 0.18/0.40 tff(1,plain,
% 0.18/0.40 (^[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)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![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))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(4,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')).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.40 tff(6,plain,(
% 0.18/0.40 ![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.18/0.40 inference(skolemize,[status(sab)],[5])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 ((~![U: $i, V: $i] : (pi_remove(U, V) <=> pi_sharp_remove(i(U), V))) | (pi_remove(triple(U!6, V!5, W!4), X!3) <=> pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 (pi_remove(triple(U!6, V!5, W!4), X!3) <=> pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 ((~((pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) & (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))) | (~phi(remove_cpq(triple(U!6, V!5, W!4), X!3))) | (~pi_remove(triple(U!6, V!5, W!4), X!3)))) <=> (~((pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) & (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))) | (~phi(remove_cpq(triple(U!6, V!5, W!4), X!3))) | (~pi_remove(triple(U!6, V!5, W!4), X!3))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 ((~![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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 ((~![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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(13,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')).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (~![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (~![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (~![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (~![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 (~![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (~![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 (~![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.18/0.40 tff(21,plain,(
% 0.18/0.40 ~((pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) & (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))) | (~phi(remove_cpq(triple(U!6, V!5, W!4), X!3))) | (~pi_remove(triple(U!6, V!5, W!4), X!3)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[20])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (~((pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) & (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))) | (~phi(remove_cpq(triple(U!6, V!5, W!4), X!3))) | (~pi_remove(triple(U!6, V!5, W!4), X!3)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[21, 10])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (pi_remove(triple(U!6, V!5, W!4), X!3)),
% 0.18/0.40 inference(or_elim,[status(thm)],[22])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 ((~(pi_remove(triple(U!6, V!5, W!4), X!3) <=> pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3))) | (~pi_remove(triple(U!6, V!5, W!4), X!3)) | pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 ((~(pi_remove(triple(U!6, V!5, W!4), X!3) <=> pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3))) | pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[25, 9])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 ((~(~((~pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)) | (~(i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))))) <=> ((~pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)) | (~(i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 ((pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) & (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))) <=> (~((~pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)) | (~(i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(29,plain,
% 0.18/0.41 ((~(pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) & (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))) <=> (~(~((~pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)) | (~(i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[28])).
% 0.18/0.41 tff(30,plain,
% 0.18/0.41 ((~(pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) & (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))) <=> ((~pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)) | (~(i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[29, 27])).
% 0.18/0.41 tff(31,plain,
% 0.18/0.41 (~(pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) & (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))),
% 0.18/0.41 inference(or_elim,[status(thm)],[22])).
% 0.18/0.41 tff(32,plain,
% 0.18/0.41 ((~pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)) | (~(i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.41 tff(33,plain,
% 0.18/0.41 (~(i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[32, 26])).
% 0.18/0.41 tff(34,plain,
% 0.18/0.41 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) <=> ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(35,plain,
% 0.18/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(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] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.41 tff(36,plain,
% 0.18/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(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] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(37,plain,
% 0.18/0.41 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((contains_pq(i(triple(U, V, W)), X) => (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))) <=> ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(38,plain,
% 0.18/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_pq(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] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.41 tff(39,axiom,(![U: $i, V: $i, W: $i, X: $i] : (contains_pq(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','main3_li34')).
% 0.18/0.41 tff(40,plain,
% 0.18/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.41 tff(41,plain,
% 0.18/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.18/0.41 tff(42,plain,(
% 0.18/0.41 ![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[41])).
% 0.18/0.41 tff(43,plain,
% 0.18/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.18/0.41 tff(44,plain,
% 0.18/0.41 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))) | ((~contains_pq(i(triple(U!6, V!5, W!4)), X!3)) | (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))) | (~contains_pq(i(triple(U!6, V!5, W!4)), X!3)) | (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(45,plain,
% 0.18/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))) | ((~contains_pq(i(triple(U!6, V!5, W!4)), X!3)) | (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(46,plain,
% 0.18/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_pq(i(triple(U, V, W)), X)) | (i(remove_cpq(triple(U, V, W), X)) = remove_pq(i(triple(U, V, W)), X)))) | (~contains_pq(i(triple(U!6, V!5, W!4)), X!3)) | (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.41 tff(47,plain,
% 0.18/0.41 ((~contains_pq(i(triple(U!6, V!5, W!4)), X!3)) | (i(remove_cpq(triple(U!6, V!5, W!4), X!3)) = remove_pq(i(triple(U!6, V!5, W!4)), X!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.18/0.41 tff(48,plain,
% 0.18/0.41 (~contains_pq(i(triple(U!6, V!5, W!4)), X!3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.18/0.41 tff(49,plain,
% 0.18/0.41 ((~(pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) <=> contains_pq(i(triple(U!6, V!5, W!4)), X!3))) | (~pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3)) | contains_pq(i(triple(U!6, V!5, W!4)), X!3)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(50,plain,
% 0.18/0.41 (~(pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) <=> contains_pq(i(triple(U!6, V!5, W!4)), X!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[49, 26, 48])).
% 0.18/0.41 tff(51,plain,
% 0.18/0.41 (^[U: $i, V: $i] : refl((pi_sharp_remove(U, V) <=> contains_pq(U, V)) <=> (pi_sharp_remove(U, V) <=> contains_pq(U, V)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(52,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.41 tff(53,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(54,axiom,(![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax56')).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.41 tff(56,plain,(
% 0.18/0.41 ![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.18/0.41 inference(skolemize,[status(sab)],[55])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 (![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 ((~![U: $i, V: $i] : (pi_sharp_remove(U, V) <=> contains_pq(U, V))) | (pi_sharp_remove(i(triple(U!6, V!5, W!4)), X!3) <=> contains_pq(i(triple(U!6, V!5, W!4)), X!3))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[58, 57, 50])).
% 0.18/0.41 % SZS output end Proof
%------------------------------------------------------------------------------