TSTP Solution File: SWV370+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV370+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 15:11:31 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV370+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 02:44:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(contains_pq_type, type, (
% 0.19/0.41 contains_pq: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_X3_4_type, type, (
% 0.19/0.41 tptp_fun_X3_4: $i)).
% 0.19/0.41 tff(insert_pq_type, type, (
% 0.19/0.41 insert_pq: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X1_6_type, type, (
% 0.19/0.41 tptp_fun_X1_6: $i)).
% 0.19/0.41 tff(i_type, type, (
% 0.19/0.41 i: $i > $i)).
% 0.19/0.41 tff(triple_type, type, (
% 0.19/0.41 triple: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Z_7_type, type, (
% 0.19/0.41 tptp_fun_Z_7: $i)).
% 0.19/0.41 tff(tptp_fun_U_3_type, type, (
% 0.19/0.41 tptp_fun_U_3: $i)).
% 0.19/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.19/0.41 tptp_fun_Y_8: $i)).
% 0.19/0.41 tff(insert_slb_type, type, (
% 0.19/0.41 insert_slb: ( $i * $i ) > $i)).
% 0.19/0.41 tff(pair_type, type, (
% 0.19/0.41 pair: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X2_5_type, type, (
% 0.19/0.41 tptp_fun_X2_5: $i)).
% 0.19/0.41 tff(contains_slb_type, type, (
% 0.19/0.41 contains_slb: ( $i * $i ) > $o)).
% 0.19/0.41 tff(contains_cpq_type, type, (
% 0.19/0.41 contains_cpq: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 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/sandbox/benchmark/Axioms/SWV007+4.ax','ax55')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![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))),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![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(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)) = insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)) = insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6) = i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7))),
% 0.19/0.41 inference(symmetry,[status(thm)],[9])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4) <=> contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4) <=> contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)),
% 0.19/0.41 inference(symmetry,[status(thm)],[11])).
% 0.19/0.41 tff(13,assumption,(~(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_slb(U!3, X3!4))), introduced(assumption)).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(17,axiom,(![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax39')).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.41 tff(19,plain,(
% 0.19/0.41 ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.41 inference(skolemize,[status(sab)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))) | (contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_slb(U!3, X3!4))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[21, 20, 13])).
% 0.19/0.41 tff(23,plain,(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_slb(U!3, X3!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(24,assumption,(~contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)), introduced(assumption)).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X)) & (~(contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) <=> contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)))) <=> (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X)) & ((~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) <=> contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))) <=> (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~![U: $i] : (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X)) => ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))) <=> (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(28,axiom,(~![U: $i] : (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X)) => ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l6_co')).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (~![U: $i] : ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U, W), X) <=> contains_pq(i(triple(V, U, W)), X))) | ![Y: $i, Z: $i, X1: $i, X2: $i, X3: $i] : (contains_cpq(triple(Y, insert_slb(U, pair(X1, X2)), Z), X3) <=> contains_pq(i(triple(Y, insert_slb(U, pair(X1, X2)), Z)), X3)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X)) & ((~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) <=> contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) <=> contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)),
% 0.19/0.41 inference(and_elim,[status(thm)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) | contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4) | (~((~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) <=> contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) | contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[39, 24])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))) | (contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) <=> contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) <=> contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[41, 20])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~(contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) <=> contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4))) | (~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) | contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 ((~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) | contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[44, 40])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))) <=> (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((contains_slb(insert_slb(U, pair(V, X)), W) <=> (contains_slb(U, W) | (V = W))) <=> (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> (contains_slb(U, W) | (V = W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.42 tff(51,axiom,(![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> (contains_slb(U, W) | (V = W)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax21')).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.42 tff(54,plain,(
% 0.19/0.42 ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[53])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))) | (contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4) <=> ((X1!6 = X3!4) | contains_slb(U!3, X3!4)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4) <=> ((X1!6 = X3!4) | contains_slb(U!3, X3!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~(contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4) <=> ((X1!6 = X3!4) | contains_slb(U!3, X3!4)))) | (~contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)) | ((X1!6 = X3!4) | contains_slb(U!3, X3!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)) | ((X1!6 = X3!4) | contains_slb(U!3, X3!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((X1!6 = X3!4) | contains_slb(U!3, X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[59, 45])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 ((~contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)) <=> (~contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (~contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[24, 61])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.42 tff(68,axiom,(![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> (contains_pq(U, W) | (V = W)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+1.ax','ax9')).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.19/0.42 tff(71,plain,(
% 0.19/0.42 ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[70])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ((~![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(Y!8, U!3, Z!7)), X1!6), X3!4) <=> ((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4) <=> ((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((~(contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4) <=> ((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)))) | contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4) | (~((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4) | (~((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (~((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[76, 62])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)) | (~(X1!6 = X3!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (~(X1!6 = X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 ((~((X1!6 = X3!4) | contains_slb(U!3, X3!4))) | (X1!6 = X3!4) | contains_slb(U!3, X3!4)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (contains_slb(U!3, X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[80, 79, 60])).
% 0.19/0.42 tff(82,assumption,(~(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))), introduced(assumption)).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (^[V: $i, W: $i, X: $i] : refl((contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X)) <=> (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X)) <=> ![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X))),
% 0.19/0.42 inference(and_elim,[status(thm)],[36])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X))) | (contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 86, 82])).
% 0.19/0.42 tff(89,plain,(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)) | (~contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (~contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[90, 77])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))) | (~contains_cpq(triple(Y!8, U!3, Z!7), X3!4)) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (~contains_cpq(triple(Y!8, U!3, Z!7), X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[92, 91, 89])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((~(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_slb(U!3, X3!4))) | contains_cpq(triple(Y!8, U!3, Z!7), X3!4) | (~contains_slb(U!3, X3!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[94, 93, 81, 23])).
% 0.19/0.42 tff(96,plain,(contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[96, 12])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) | (~contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)) | (~((~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) <=> contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 ((~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)) | (~contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[98, 37])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((~(contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) <=> contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4))) | contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) | (~contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4) | (~contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[101, 42])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (~contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[102, 100])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~(contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4) <=> ((X1!6 = X3!4) | contains_slb(U!3, X3!4)))) | contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4) | (~((X1!6 = X3!4) | contains_slb(U!3, X3!4)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4) | (~((X1!6 = X3!4) | contains_slb(U!3, X3!4)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 57])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (~((X1!6 = X3!4) | contains_slb(U!3, X3!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 103])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (((X1!6 = X3!4) | contains_slb(U!3, X3!4)) | (~(X1!6 = X3!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (~(X1!6 = X3!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (((X1!6 = X3!4) | contains_slb(U!3, X3!4)) | (~contains_slb(U!3, X3!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (~contains_slb(U!3, X3!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 ((~(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_slb(U!3, X3!4))) | (~contains_cpq(triple(Y!8, U!3, Z!7), X3!4)) | contains_slb(U!3, X3!4)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (~contains_cpq(triple(Y!8, U!3, Z!7), X3!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[111, 110, 23])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))) | contains_cpq(triple(Y!8, U!3, Z!7), X3!4) | (~contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (~contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[113, 112, 89])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))) | (X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (~((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[115, 114, 108])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~(contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4) <=> ((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)))) | (~contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)) | ((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 ((~contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)) | ((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[117, 74])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (~contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[118, 116])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[119, 97])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------