%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV415+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:32:24 AM UTC 2025
% Result : Theorem 0.13s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWV415+2 : TPTP v9.0.0. Released v3.3.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 09:47:01 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(insert_pq_type, type, (
% 0.13/0.41 insert_pq: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_X_14_type, type, (
% 0.13/0.41 tptp_fun_X_14: $i)).
% 0.13/0.41 tff(i_type, type, (
% 0.13/0.41 i: $i > $i)).
% 0.13/0.41 tff(triple_type, type, (
% 0.13/0.41 triple: ( $i * $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_W_15_type, type, (
% 0.13/0.41 tptp_fun_W_15: $i)).
% 0.13/0.41 tff(tptp_fun_V_16_type, type, (
% 0.13/0.41 tptp_fun_V_16: $i)).
% 0.13/0.41 tff(tptp_fun_U_17_type, type, (
% 0.13/0.41 tptp_fun_U_17: $i)).
% 0.13/0.41 tff(insert_cpq_type, type, (
% 0.13/0.41 insert_cpq: ( $i * $i ) > $i)).
% 0.13/0.41 tff(insert_pqp_type, type, (
% 0.13/0.41 insert_pqp: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_X7_10_type, type, (
% 0.13/0.41 tptp_fun_X7_10: $i)).
% 0.13/0.41 tff(insert_slb_type, type, (
% 0.13/0.41 insert_slb: ( $i * $i ) > $i)).
% 0.13/0.41 tff(pair_type, type, (
% 0.13/0.41 pair: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_X9_8_type, type, (
% 0.13/0.41 tptp_fun_X9_8: $i)).
% 0.13/0.41 tff(tptp_fun_X8_9_type, type, (
% 0.13/0.41 tptp_fun_X8_9: $i)).
% 0.13/0.41 tff(tptp_fun_Y_7_type, type, (
% 0.13/0.41 tptp_fun_Y_7: $i)).
% 0.13/0.41 tff(tptp_fun_X5_12_type, type, (
% 0.13/0.41 tptp_fun_X5_12: $i)).
% 0.13/0.41 tff(tptp_fun_X6_11_type, type, (
% 0.13/0.41 tptp_fun_X6_11: $i)).
% 0.13/0.41 tff(tptp_fun_X4_13_type, type, (
% 0.13/0.41 tptp_fun_X4_13: $i)).
% 0.13/0.41 tff(tptp_fun_X_3_type, type, (
% 0.13/0.41 tptp_fun_X_3: $i)).
% 0.13/0.41 tff(create_slb_type, type, (
% 0.13/0.41 create_slb: $i)).
% 0.13/0.41 tff(tptp_fun_V_5_type, type, (
% 0.13/0.41 tptp_fun_V_5: $i)).
% 0.13/0.41 tff(tptp_fun_W_4_type, type, (
% 0.13/0.41 tptp_fun_W_4: $i)).
% 0.13/0.41 tff(tptp_fun_U_6_type, type, (
% 0.13/0.41 tptp_fun_U_6: $i)).
% 0.13/0.41 tff(create_pq_type, type, (
% 0.13/0.41 create_pq: $i)).
% 0.13/0.41 tff(bottom_type, type, (
% 0.13/0.41 bottom: $i)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[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)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![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))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (![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))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 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')).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![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))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.41 tff(6,plain,(
% 0.13/0.41 ![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))),
% 0.13/0.41 inference(skolemize,[status(sab)],[5])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![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))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 ((~![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(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)) = insert_pq(i(triple(X5!12, Y!7, X7!10)), X8!9))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)) = insert_pq(i(triple(X5!12, Y!7, X7!10)), X8!9)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (insert_pq(i(triple(X5!12, Y!7, X7!10)), X8!9) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))),
% 0.13/0.41 inference(symmetry,[status(thm)],[9])).
% 0.13/0.41 tff(11,assumption,(~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))), introduced(assumption)).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))) | ![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X5!12, Y!7, X7!10)) = i(triple(X4!13, Y!7, X6!11)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (i(triple(X5!12, Y!7, X7!10)) = i(triple(X4!13, Y!7, X6!11))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (insert_pq(i(triple(X5!12, Y!7, X7!10)), X8!9) = insert_pq(i(triple(X4!13, Y!7, X6!11)), X8!9)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[15])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (insert_pq(i(triple(X4!13, Y!7, X6!11)), X8!9) = insert_pq(i(triple(X5!12, Y!7, X7!10)), X8!9)),
% 0.13/0.41 inference(symmetry,[status(thm)],[16])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 ((~![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(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = insert_pq(i(triple(X4!13, Y!7, X6!11)), X8!9))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = insert_pq(i(triple(X4!13, Y!7, X6!11)), X8!9)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[18, 7])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))),
% 0.13/0.41 inference(transitivity,[status(thm)],[19, 17, 10])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))) | (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[21, 11])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[22, 20])).
% 0.13/0.41 tff(24,plain,((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (^[U: $i, V: $i] : refl((i(triple(U, create_slb, V)) = create_pq) <=> (i(triple(U, create_slb, V)) = create_pq))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq) <=> ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.13/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq) <=> ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(28,axiom,(![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+4.ax','ax54')).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.41 tff(30,plain,(
% 0.13/0.41 ![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.13/0.41 inference(skolemize,[status(sab)],[29])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 ((~![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)) | (i(triple(V!5, create_slb, X!3)) = create_pq)),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (i(triple(V!5, create_slb, X!3)) = create_pq),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.42 tff(34,plain,
% 0.13/0.42 ((i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3))) <=> (i(triple(U!6, create_slb, W!4)) = create_pq)),
% 0.13/0.42 inference(monotonicity,[status(thm)],[33])).
% 0.13/0.42 tff(35,plain,
% 0.13/0.42 ((i(triple(U!6, create_slb, W!4)) = create_pq) <=> (i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))),
% 0.13/0.42 inference(symmetry,[status(thm)],[34])).
% 0.13/0.42 tff(36,plain,
% 0.13/0.42 ((~![U: $i, V: $i] : (i(triple(U, create_slb, V)) = create_pq)) | (i(triple(U!6, create_slb, W!4)) = create_pq)),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(37,plain,
% 0.13/0.42 (i(triple(U!6, create_slb, W!4)) = create_pq),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[36, 31])).
% 0.13/0.42 tff(38,plain,
% 0.13/0.42 (i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.13/0.42 tff(39,assumption,(~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))), introduced(assumption)).
% 0.13/0.42 tff(40,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.13/0.42 tff(41,plain,(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(42,plain,
% 0.13/0.42 ((![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) <=> ((~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(43,plain,
% 0.13/0.42 ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) <=> (~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(44,plain,
% 0.13/0.42 (((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))) <=> ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[43])).
% 0.13/0.42 tff(45,plain,
% 0.13/0.42 ((~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))) <=> (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[44])).
% 0.13/0.42 tff(46,plain,
% 0.13/0.42 ((![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) <=> (![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[45])).
% 0.13/0.42 tff(47,plain,
% 0.13/0.42 ((![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) <=> ((~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[46, 42])).
% 0.13/0.42 tff(48,plain,
% 0.13/0.42 ((![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) <=> (![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(49,plain,
% 0.13/0.42 ((![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) <=> (![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(50,plain,
% 0.13/0.42 ((![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))) <=> (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(51,plain,
% 0.13/0.42 ((![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) <=> (![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[50])).
% 0.13/0.42 tff(52,plain,
% 0.13/0.42 ((![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) <=> (![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (~((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3)))) | (i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[51, 49])).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 ((((~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))) <=> (![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 ((![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))) <=> (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(55,plain,
% 0.22/0.43 (((~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) <=> ((~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[54])).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 ((((~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))) <=> (((~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[55])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 ((((~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))) <=> (![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))) | (~(i(triple(U!6, create_slb, W!4)) = i(triple(V!5, create_slb, X!3)))) | (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y!7, X2)) = i(triple(X1, Y!7, X3))) & (~(i(triple(X4!13, insert_slb(Y!7, pair(X8!9, X9!8)), X6!11)) = i(triple(X5!12, insert_slb(Y!7, pair(X8!9, X9!8)), X7!10))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[56, 53])).
% 0.22/0.43 tff(58,plain,
% 0.22/0.43 (((~(![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))) <=> ((~(![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 (((![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7))))) => ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))) <=> ((~(![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 ((![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3))) => ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7))))) <=> (![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 (((![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3))) => ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7))))) => ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))) <=> ((![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7))))) => ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[60])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 (((![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3))) => ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7))))) => ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))) <=> ((~(![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[61, 59])).
% 0.22/0.43 tff(63,axiom,((![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : (![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3))) => ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7))))) => ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','big2_induction')).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 ((~(![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 ((~(![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 ((~(![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 ((~(![U: $i, V: $i, W: $i, X: $i] : (i(triple(U, create_slb, W)) = i(triple(V, create_slb, X))) & ![Y: $i] : ((~![Z: $i, X1: $i, X2: $i, X3: $i] : (i(triple(Z, Y, X2)) = i(triple(X1, Y, X3)))) | ![X4: $i, X5: $i, X6: $i, X7: $i, X8: $i, X9: $i] : (i(triple(X4, insert_slb(Y, pair(X8, X9)), X6)) = i(triple(X5, insert_slb(Y, pair(X8, X9)), X7)))))) | ![X10: $i, X11: $i, X12: $i, X13: $i, X14: $i] : (i(triple(X10, X12, X13)) = i(triple(X11, X12, X14)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.22/0.43 Proof display could not be completed: monotonicity rule is not handled
% 0.22/0.44 % E exiting
%------------------------------------------------------------------------------