%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV366+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:32:18 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV366+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Fri Jun 20 09:48:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(i_type, type, (
% 0.21/0.39 i: $i > $i)).
% 0.21/0.39 tff(triple_type, type, (
% 0.21/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_X3_6_type, type, (
% 0.21/0.39 tptp_fun_X3_6: $i)).
% 0.21/0.39 tff(insert_slb_type, type, (
% 0.21/0.39 insert_slb: ( $i * $i ) > $i)).
% 0.21/0.39 tff(pair_type, type, (
% 0.21/0.39 pair: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_X5_4_type, type, (
% 0.21/0.39 tptp_fun_X5_4: $i)).
% 0.21/0.39 tff(tptp_fun_X4_5_type, type, (
% 0.21/0.39 tptp_fun_X4_5: $i)).
% 0.21/0.39 tff(tptp_fun_U_3_type, type, (
% 0.21/0.39 tptp_fun_U_3: $i)).
% 0.21/0.39 tff(tptp_fun_X1_8_type, type, (
% 0.21/0.39 tptp_fun_X1_8: $i)).
% 0.21/0.39 tff(tptp_fun_X2_7_type, type, (
% 0.21/0.39 tptp_fun_X2_7: $i)).
% 0.21/0.39 tff(tptp_fun_Z_9_type, type, (
% 0.21/0.39 tptp_fun_Z_9: $i)).
% 0.21/0.39 tff(insert_pq_type, type, (
% 0.21/0.39 insert_pq: ( $i * $i ) > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[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)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![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))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![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))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 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')).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![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))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,plain,(
% 0.21/0.39 ![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))),
% 0.21/0.39 inference(skolemize,[status(sab)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![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))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~![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(X1!8, insert_slb(U!3, pair(X4!5, X5!4)), X3!6)) = insert_pq(i(triple(X1!8, U!3, X3!6)), X4!5))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (i(triple(X1!8, insert_slb(U!3, pair(X4!5, X5!4)), X3!6)) = insert_pq(i(triple(X1!8, U!3, X3!6)), X4!5)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (insert_pq(i(triple(X1!8, U!3, X3!6)), X4!5) = i(triple(X1!8, insert_slb(U!3, pair(X4!5, X5!4)), X3!6))),
% 0.21/0.39 inference(symmetry,[status(thm)],[9])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (^[V: $i, W: $i, X: $i, Y: $i] : refl((i(triple(V, U!3, X)) = i(triple(W, U!3, Y))) <=> (i(triple(V, U!3, X)) = i(triple(W, U!3, Y))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U!3, X)) = i(triple(W, U!3, Y))) <=> ![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U!3, X)) = i(triple(W, U!3, Y)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 ((![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U!3, X)) = i(triple(W, U!3, Y))) & (~(i(triple(Z!9, insert_slb(U!3, pair(X4!5, X5!4)), X2!7)) = i(triple(X1!8, insert_slb(U!3, pair(X4!5, X5!4)), X3!6))))) <=> (![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U!3, X)) = i(triple(W, U!3, Y))) & (~(i(triple(Z!9, insert_slb(U!3, pair(X4!5, X5!4)), X2!7)) = i(triple(X1!8, insert_slb(U!3, pair(X4!5, X5!4)), X3!6)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 ((~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y)))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3))))) <=> (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y)))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 ((~![U: $i] : (![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y))) => ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3))))) <=> (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y)))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,axiom,(~![U: $i] : (![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y))) => ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_co')).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y)))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y)))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y)))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (~![U: $i] : ((~![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U, X)) = i(triple(W, U, Y)))) | ![Z: $i, X1: $i, X2: $i, X3: $i, X4: $i, X5: $i] : (i(triple(Z, insert_slb(U, pair(X4, X5)), X2)) = i(triple(X1, insert_slb(U, pair(X4, X5)), X3))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U!3, X)) = i(triple(W, U!3, Y))) & (~(i(triple(Z!9, insert_slb(U!3, pair(X4!5, X5!4)), X2!7)) = i(triple(X1!8, insert_slb(U!3, pair(X4!5, X5!4)), X3!6))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U!3, X)) = i(triple(W, U!3, Y)))),
% 0.21/0.39 inference(and_elim,[status(thm)],[21])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U!3, X)) = i(triple(W, U!3, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 ((~![V: $i, W: $i, X: $i, Y: $i] : (i(triple(V, U!3, X)) = i(triple(W, U!3, Y)))) | (i(triple(Z!9, U!3, X2!7)) = i(triple(X1!8, U!3, X3!6)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (i(triple(Z!9, U!3, X2!7)) = i(triple(X1!8, U!3, X3!6))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (insert_pq(i(triple(Z!9, U!3, X2!7)), X4!5) = insert_pq(i(triple(X1!8, U!3, X3!6)), X4!5)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, insert_slb(V, pair(X, Y)), W)) = insert_pq(i(triple(U, V, W)), X))) | (i(triple(Z!9, insert_slb(U!3, pair(X4!5, X5!4)), X2!7)) = insert_pq(i(triple(Z!9, U!3, X2!7)), X4!5))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (i(triple(Z!9, insert_slb(U!3, pair(X4!5, X5!4)), X2!7)) = insert_pq(i(triple(Z!9, U!3, X2!7)), X4!5)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[27, 7])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (i(triple(Z!9, insert_slb(U!3, pair(X4!5, X5!4)), X2!7)) = i(triple(X1!8, insert_slb(U!3, pair(X4!5, X5!4)), X3!6))),
% 0.21/0.40 inference(transitivity,[status(thm)],[28, 26, 10])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (~(i(triple(Z!9, insert_slb(U!3, pair(X4!5, X5!4)), X2!7)) = i(triple(X1!8, insert_slb(U!3, pair(X4!5, X5!4)), X3!6)))),
% 0.21/0.40 inference(and_elim,[status(thm)],[21])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------