%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV415+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV415+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:45:40 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(insert_pq_type, type, (
% 0.11/0.38 insert_pq: ( $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_X_3_type, type, (
% 0.11/0.38 tptp_fun_X_3: $i)).
% 0.11/0.38 tff(i_type, type, (
% 0.11/0.38 i: $i > $i)).
% 0.11/0.38 tff(triple_type, type, (
% 0.11/0.38 triple: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_W_4_type, type, (
% 0.11/0.38 tptp_fun_W_4: $i)).
% 0.11/0.38 tff(tptp_fun_V_5_type, type, (
% 0.11/0.38 tptp_fun_V_5: $i)).
% 0.11/0.38 tff(tptp_fun_U_6_type, type, (
% 0.11/0.38 tptp_fun_U_6: $i)).
% 0.11/0.38 tff(insert_cpq_type, type, (
% 0.11/0.38 insert_cpq: ( $i * $i ) > $i)).
% 0.11/0.38 tff(insert_pqp_type, type, (
% 0.11/0.38 insert_pqp: ( $i * $i ) > $i)).
% 0.11/0.38 tff(insert_slb_type, type, (
% 0.11/0.38 insert_slb: ( $i * $i ) > $i)).
% 0.11/0.38 tff(pair_type, type, (
% 0.11/0.38 pair: ( $i * $i ) > $i)).
% 0.11/0.38 tff(bottom_type, type, (
% 0.11/0.38 bottom: $i)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl((i(triple(U, W, X)) = i(triple(V, W, Y))) <=> (i(triple(U, W, X)) = i(triple(V, W, Y))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main2_l12')).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.38 tff(6,plain,(
% 0.11/0.38 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (i(triple(U, W, X)) = i(triple(V, W, Y)))) | (i(triple(U!6, V!5, W!4)) = i(triple(insert_pqp(U!6, X!3), V!5, W!4)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (i(triple(U!6, V!5, W!4)) = i(triple(insert_pqp(U!6, X!3), V!5, W!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (insert_pq(i(triple(U!6, V!5, W!4)), X!3) = insert_pq(i(triple(insert_pqp(U!6, X!3), V!5, W!4)), X!3)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[9])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (insert_pq(i(triple(insert_pqp(U!6, X!3), V!5, W!4)), X!3) = insert_pq(i(triple(U!6, V!5, W!4)), X!3)),
% 0.11/0.38 inference(symmetry,[status(thm)],[10])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (^[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)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,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')).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,(
% 0.11/0.38 ![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))),
% 0.11/0.39 inference(skolemize,[status(sab)],[16])).
% 0.11/0.39 tff(18,plain,
% 0.11/0.39 (![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))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 ((~![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(insert_pqp(U!6, X!3), insert_slb(V!5, pair(X!3, bottom)), W!4)) = insert_pq(i(triple(insert_pqp(U!6, X!3), V!5, W!4)), X!3))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(20,plain,
% 0.11/0.39 (i(triple(insert_pqp(U!6, X!3), insert_slb(V!5, pair(X!3, bottom)), W!4)) = insert_pq(i(triple(insert_pqp(U!6, X!3), V!5, W!4)), X!3)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 (^[U: $i, V: $i, W: $i, X: $i] : refl((insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)) <=> (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)) <=> ![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)) <=> ![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(24,axiom,(![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax42')).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.39 tff(26,plain,(
% 0.11/0.39 ![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.11/0.39 inference(skolemize,[status(sab)],[25])).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))) | (insert_cpq(triple(U!6, V!5, W!4), X!3) = triple(insert_pqp(U!6, X!3), insert_slb(V!5, pair(X!3, bottom)), W!4))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 (insert_cpq(triple(U!6, V!5, W!4), X!3) = triple(insert_pqp(U!6, X!3), insert_slb(V!5, pair(X!3, bottom)), W!4)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.11/0.39 tff(30,plain,
% 0.11/0.39 (i(insert_cpq(triple(U!6, V!5, W!4), X!3)) = i(triple(insert_pqp(U!6, X!3), insert_slb(V!5, pair(X!3, bottom)), W!4))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[29])).
% 0.11/0.39 tff(31,plain,
% 0.11/0.39 (i(insert_cpq(triple(U!6, V!5, W!4), X!3)) = insert_pq(i(triple(U!6, V!5, W!4)), X!3)),
% 0.11/0.39 inference(transitivity,[status(thm)],[30, 20, 11])).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (i(insert_cpq(triple(U, V, W), X)) = insert_pq(i(triple(U, V, W)), X))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (i(insert_cpq(triple(U, V, W), X)) = insert_pq(i(triple(U, V, W)), X)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(33,axiom,(~![U: $i, V: $i, W: $i, X: $i] : (i(insert_cpq(triple(U, V, W), X)) = insert_pq(i(triple(U, V, W)), X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co2')).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (~![U: $i, V: $i, W: $i, X: $i] : (i(insert_cpq(triple(U, V, W), X)) = insert_pq(i(triple(U, V, W)), X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (~![U: $i, V: $i, W: $i, X: $i] : (i(insert_cpq(triple(U, V, W), X)) = insert_pq(i(triple(U, V, W)), X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 (~![U: $i, V: $i, W: $i, X: $i] : (i(insert_cpq(triple(U, V, W), X)) = insert_pq(i(triple(U, V, W)), X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (~![U: $i, V: $i, W: $i, X: $i] : (i(insert_cpq(triple(U, V, W), X)) = insert_pq(i(triple(U, V, W)), X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.11/0.39 tff(38,plain,(
% 0.11/0.39 ~(i(insert_cpq(triple(U!6, V!5, W!4), X!3)) = insert_pq(i(triple(U!6, V!5, W!4)), X!3))),
% 0.11/0.39 inference(skolemize,[status(sab)],[37])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[38, 31])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------