%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV370+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 : Sat Jun 21 05:32:19 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV370+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:44:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(contains_pq_type, type, (
% 0.21/0.40 contains_pq: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_X3_4_type, type, (
% 0.21/0.40 tptp_fun_X3_4: $i)).
% 0.21/0.40 tff(insert_pq_type, type, (
% 0.21/0.40 insert_pq: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_X1_6_type, type, (
% 0.21/0.40 tptp_fun_X1_6: $i)).
% 0.21/0.40 tff(i_type, type, (
% 0.21/0.40 i: $i > $i)).
% 0.21/0.40 tff(triple_type, type, (
% 0.21/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_Z_7_type, type, (
% 0.21/0.40 tptp_fun_Z_7: $i)).
% 0.21/0.40 tff(tptp_fun_U_3_type, type, (
% 0.21/0.40 tptp_fun_U_3: $i)).
% 0.21/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.21/0.40 tptp_fun_Y_8: $i)).
% 0.21/0.40 tff(insert_slb_type, type, (
% 0.21/0.40 insert_slb: ( $i * $i ) > $i)).
% 0.21/0.40 tff(pair_type, type, (
% 0.21/0.40 pair: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_X2_5_type, type, (
% 0.21/0.40 tptp_fun_X2_5: $i)).
% 0.21/0.40 tff(contains_slb_type, type, (
% 0.21/0.40 contains_slb: ( $i * $i ) > $o)).
% 0.21/0.40 tff(contains_cpq_type, type, (
% 0.21/0.40 contains_cpq: ( $i * $i ) > $o)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[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)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 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')).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.40 tff(6,plain,(
% 0.21/0.40 ![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))),
% 0.21/0.40 inference(skolemize,[status(sab)],[5])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 ((~![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))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (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)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (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))),
% 0.21/0.40 inference(symmetry,[status(thm)],[9])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (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)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (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)),
% 0.21/0.40 inference(symmetry,[status(thm)],[11])).
% 0.21/0.40 tff(13,assumption,(~(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_slb(U!3, X3!4))), introduced(assumption)).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (^[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)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 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')).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.41 tff(19,plain,(
% 0.21/0.41 ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.21/0.41 inference(skolemize,[status(sab)],[18])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))) | (contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_slb(U!3, X3!4))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[21, 20, 13])).
% 0.21/0.41 tff(23,plain,(contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_slb(U!3, X3!4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(24,assumption,(~contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)), introduced(assumption)).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 ((![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 ((~![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 ((~![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 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')).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (~![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (~![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (~![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (~![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (~(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))),
% 0.21/0.41 inference(and_elim,[status(thm)],[33])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((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)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (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)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[36, 24])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((~![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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (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)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[38, 20])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 ((~(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)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 ((~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)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[41, 37])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.41 tff(48,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')).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.41 tff(51,plain,(
% 0.21/0.41 ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[50])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(insert_slb(U, pair(V, X)), W) <=> ((V = W) | contains_slb(U, W)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 ((~![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)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4) <=> ((X1!6 = X3!4) | contains_slb(U!3, X3!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 ((~(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))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ((~contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)) | ((X1!6 = X3!4) | contains_slb(U!3, X3!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 ((X1!6 = X3!4) | contains_slb(U!3, X3!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[56, 42])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 ((~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))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (~contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 58])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.42 tff(65,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')).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.42 tff(68,plain,(
% 0.21/0.42 ![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[67])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i] : (contains_pq(insert_pq(U, V), W) <=> ((V = W) | contains_pq(U, W)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 ((~![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)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (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))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 ((~(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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (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)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (~((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[73, 59])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)) | (~(X1!6 = X3!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (~(X1!6 = X3!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 ((~((X1!6 = X3!4) | contains_slb(U!3, X3!4))) | (X1!6 = X3!4) | contains_slb(U!3, X3!4)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (contains_slb(U!3, X3!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[77, 76, 57])).
% 0.21/0.42 tff(79,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)).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (^[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)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X))),
% 0.21/0.42 inference(and_elim,[status(thm)],[33])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((~![V: $i, W: $i, X: $i] : (contains_cpq(triple(V, U!3, W), X) <=> contains_pq(i(triple(V, U!3, W)), X))) | (contains_cpq(triple(Y!8, U!3, Z!7), X3!4) <=> contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[84, 83, 79])).
% 0.21/0.42 tff(86,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,[]))).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (((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))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (~contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[87, 74])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 ((~(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)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (~contains_cpq(triple(Y!8, U!3, Z!7), X3!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 88, 86])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 ((~(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))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[91, 90, 78, 23])).
% 0.21/0.42 tff(93,plain,(contains_pq(i(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7)), X3!4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[93, 12])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((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))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ((~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))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 34])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (~contains_cpq(triple(Y!8, insert_slb(U!3, pair(X1!6, X2!5)), Z!7), X3!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~(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))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (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))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[98, 39])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (~contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 97])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ((~(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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (contains_slb(insert_slb(U!3, pair(X1!6, X2!5)), X3!4) | (~((X1!6 = X3!4) | contains_slb(U!3, X3!4)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[101, 54])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (~((X1!6 = X3!4) | contains_slb(U!3, X3!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[102, 100])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (((X1!6 = X3!4) | contains_slb(U!3, X3!4)) | (~(X1!6 = X3!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (~(X1!6 = X3!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (((X1!6 = X3!4) | contains_slb(U!3, X3!4)) | (~contains_slb(U!3, X3!4))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (~contains_slb(U!3, X3!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 ((~(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)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (~contains_cpq(triple(Y!8, U!3, Z!7), X3!4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[108, 107, 23])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 ((~(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))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 (~contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[110, 109, 86])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 ((~((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)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (~((X1!6 = X3!4) | contains_pq(i(triple(Y!8, U!3, Z!7)), X3!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[112, 111, 105])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 ((~(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))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 ((~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))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[114, 71])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (~contains_pq(insert_pq(i(triple(Y!8, U!3, Z!7)), X1!6), X3!4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[115, 113])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[116, 94])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------