%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV152+1 : TPTP v9.0.0. Bugfixed 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 05:31:36 AM UTC 2025
% 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 : SWV152+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.00/0.12 % 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 09:30:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(gt_type, type, (
% 0.19/0.41 gt: ( $i * $i ) > $o)).
% 0.19/0.41 tff(n4_type, type, (
% 0.19/0.41 n4: $i)).
% 0.19/0.41 tff(n5_type, type, (
% 0.19/0.41 n5: $i)).
% 0.19/0.41 tff(succ_type, type, (
% 0.19/0.41 succ: $i > $i)).
% 0.19/0.41 tff(n3_type, type, (
% 0.19/0.41 n3: $i)).
% 0.19/0.41 tff(n0_type, type, (
% 0.19/0.41 n0: $i)).
% 0.19/0.41 tff(tptp_minus_1_type, type, (
% 0.19/0.41 tptp_minus_1: $i)).
% 0.19/0.41 tff(plus_type, type, (
% 0.19/0.41 plus: ( $i * $i ) > $i)).
% 0.19/0.41 tff(leq_type, type, (
% 0.19/0.41 leq: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_A_13_type, type, (
% 0.19/0.41 tptp_fun_A_13: $i)).
% 0.19/0.41 tff(n1_type, type, (
% 0.19/0.41 n1: $i)).
% 0.19/0.41 tff(sum_type, type, (
% 0.19/0.41 sum: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(a_select3_type, type, (
% 0.19/0.41 a_select3: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_sum_index_type, type, (
% 0.19/0.41 tptp_sum_index: $i)).
% 0.19/0.41 tff(q_type, type, (
% 0.19/0.41 q: $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 ((succ(succ(succ(n0))) = n3) <=> (succ(succ(succ(n0))) = n3)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(2,axiom,(succ(succ(succ(n0))) = n3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_3')).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (succ(succ(succ(n0))) = n3),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (n3 = succ(succ(succ(n0)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[3])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (succ(n3) = succ(succ(succ(succ(n0))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[4])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (succ(succ(succ(succ(n0)))) = succ(n3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 ((succ(succ(succ(succ(n0)))) = n4) <=> (succ(succ(succ(succ(n0)))) = n4)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(8,axiom,(succ(succ(succ(succ(n0)))) = n4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_4')).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (succ(succ(succ(succ(n0)))) = n4),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (n4 = succ(succ(succ(succ(n0))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[9])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (n4 = succ(n3)),
% 0.19/0.41 inference(transitivity,[status(thm)],[10, 6])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (gt(n4, n4) <=> gt(succ(n3), n4)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (gt(succ(n3), n4) <=> gt(n4, n4)),
% 0.19/0.41 inference(symmetry,[status(thm)],[12])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((succ(tptp_minus_1) = n0) <=> (succ(tptp_minus_1) = n0)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,axiom,(succ(tptp_minus_1) = n0), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','succ_tptp_minus_1')).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (succ(tptp_minus_1) = n0),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (n0 = succ(tptp_minus_1)),
% 0.19/0.41 inference(symmetry,[status(thm)],[16])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (succ(n0) = succ(succ(tptp_minus_1))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (succ(succ(n0)) = succ(succ(succ(tptp_minus_1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (succ(succ(succ(n0))) = succ(succ(succ(succ(tptp_minus_1))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (succ(succ(succ(succ(tptp_minus_1)))) = succ(succ(succ(n0)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[20])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (succ(succ(succ(succ(succ(tptp_minus_1))))) = succ(succ(succ(succ(n0))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (^[X: $i] : refl((plus(n5, X) = succ(succ(succ(succ(succ(X)))))) <=> (plus(n5, X) = succ(succ(succ(succ(succ(X)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,axiom,(![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','succ_plus_5_l')).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,(
% 0.19/0.41 ![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[27])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 ((~![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))) | (plus(n5, tptp_minus_1) = succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (plus(n5, tptp_minus_1) = succ(succ(succ(succ(succ(tptp_minus_1)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ((~![A: $i] : ((~(leq(n0, A) & leq(A, tptp_minus_1))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))) <=> (~![A: $i] : ((~(leq(n0, A) & leq(A, tptp_minus_1))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 ((~![A: $i] : ((leq(n0, A) & leq(A, tptp_minus_1)) => (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))) <=> (~![A: $i] : ((~(leq(n0, A) & leq(A, tptp_minus_1))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,axiom,(~![A: $i] : ((leq(n0, A) & leq(A, tptp_minus_1)) => (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cl5_nebula_norm_0002')).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (~![A: $i] : ((~(leq(n0, A) & leq(A, tptp_minus_1))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (~![A: $i] : ((~(leq(n0, A) & leq(A, tptp_minus_1))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (~![A: $i] : ((~(leq(n0, A) & leq(A, tptp_minus_1))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (~![A: $i] : ((~(leq(n0, A) & leq(A, tptp_minus_1))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.19/0.41 tff(39,plain,(
% 0.19/0.41 ~((~(leq(n0, A!13) & leq(A!13, tptp_minus_1))) | (sum(n0, n4, a_select3(q, A!13, tptp_sum_index)) = n1))),
% 0.19/0.41 inference(skolemize,[status(sab)],[38])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (leq(n0, A!13) & leq(A!13, tptp_minus_1)),
% 0.19/0.41 inference(or_elim,[status(thm)],[39])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (leq(A!13, tptp_minus_1)),
% 0.19/0.41 inference(and_elim,[status(thm)],[40])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (leq(n0, A!13)),
% 0.19/0.41 inference(and_elim,[status(thm)],[40])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.42 tff(49,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.42 tff(52,plain,(
% 0.19/0.42 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.42 inference(skolemize,[status(sab)],[51])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(n0, A!13)) | leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, A!13)) | leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ((leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1)) | (~leq(n0, A!13))) <=> ((~leq(n0, A!13)) | leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1)) | (~leq(n0, A!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(n0, A!13)) | leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1)) | (~leq(n0, A!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, A!13)) | leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[57, 55])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1)) | (~leq(n0, A!13)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, A!13)) | leq(n0, tptp_minus_1) | (~leq(A!13, tptp_minus_1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (leq(n0, tptp_minus_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[60, 54, 42, 41])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (gt(n0, tptp_minus_1) <=> gt(n0, tptp_minus_1)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(63,axiom,(gt(n0, tptp_minus_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gt_0_tptp_minus_1')).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (gt(n0, tptp_minus_1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl(((~gt(Y, X)) | leq(X, Y)) <=> ((~gt(Y, X)) | leq(X, Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : rewrite((gt(Y, X) => leq(X, Y)) <=> ((~gt(Y, X)) | leq(X, Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (gt(Y, X) => leq(X, Y)) <=> ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.42 tff(70,axiom,(![X: $i, Y: $i] : (gt(Y, X) => leq(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt1')).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.42 tff(73,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.19/0.42 inference(skolemize,[status(sab)],[72])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n0, tptp_minus_1)) | leq(tptp_minus_1, n0))) <=> ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n0, tptp_minus_1)) | leq(tptp_minus_1, n0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | ((~gt(n0, tptp_minus_1)) | leq(tptp_minus_1, n0))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~gt(Y, X)) | leq(X, Y))) | (~gt(n0, tptp_minus_1)) | leq(tptp_minus_1, n0)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (leq(tptp_minus_1, n0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[77, 74, 64])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (^[X: $i] : refl(((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0))) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X) & leq(X, n0)) <=> (~((~leq(n0, X)) | (~leq(X, n0))))), ((~(leq(n0, X) & leq(X, n0))) <=> (~(~((~leq(n0, X)) | (~leq(X, n0))))))), rewrite((~(~((~leq(n0, X)) | (~leq(X, n0))))) <=> ((~leq(n0, X)) | (~leq(X, n0)))), ((~(leq(n0, X) & leq(X, n0))) <=> ((~leq(n0, X)) | (~leq(X, n0))))), (((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> (((~leq(n0, X)) | (~leq(X, n0))) | (X = n0)))), rewrite((((~leq(n0, X)) | (~leq(X, n0))) | (X = n0)) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))), (((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.42 tff(86,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','finite_domain_0')).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.42 tff(89,plain,(
% 0.19/0.42 ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.42 inference(skolemize,[status(sab)],[88])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (((tptp_minus_1 = n0) | (~leq(n0, tptp_minus_1)) | (~leq(tptp_minus_1, n0))) <=> ((~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((tptp_minus_1 = n0) | (~leq(n0, tptp_minus_1)) | (~leq(tptp_minus_1, n0)))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((tptp_minus_1 = n0) | (~leq(n0, tptp_minus_1)) | (~leq(tptp_minus_1, n0)))) <=> ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0))),
% 0.19/0.43 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | ((tptp_minus_1 = n0) | (~leq(n0, tptp_minus_1)) | (~leq(tptp_minus_1, n0)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~![X: $i] : ((X = n0) | (~leq(n0, X)) | (~leq(X, n0)))) | (~leq(tptp_minus_1, n0)) | (~leq(n0, tptp_minus_1)) | (tptp_minus_1 = n0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (tptp_minus_1 = n0),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[97, 91, 78, 61])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (n0 = tptp_minus_1),
% 0.19/0.43 inference(symmetry,[status(thm)],[98])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (plus(n5, n0) = plus(n5, tptp_minus_1)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 ((~![X: $i] : (plus(n5, X) = succ(succ(succ(succ(succ(X))))))) | (plus(n5, n0) = succ(succ(succ(succ(succ(n0))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (plus(n5, n0) = succ(succ(succ(succ(succ(n0)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[101, 29])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (succ(succ(succ(succ(succ(n0))))) = plus(n5, n0)),
% 0.19/0.43 inference(symmetry,[status(thm)],[102])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 ((succ(succ(succ(succ(succ(n0))))) = n5) <=> (succ(succ(succ(succ(succ(n0))))) = n5)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(105,axiom,(succ(succ(succ(succ(succ(n0))))) = n5), file('/export/starexec/sandbox/benchmark/theBenchmark.p','successor_5')).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (succ(succ(succ(succ(succ(n0))))) = n5),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (n5 = succ(succ(succ(succ(succ(n0)))))),
% 0.19/0.43 inference(symmetry,[status(thm)],[106])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (n5 = succ(n3)),
% 0.19/0.43 inference(transitivity,[status(thm)],[107, 103, 100, 31, 22, 6])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (gt(n5, n4) <=> gt(succ(n3), n4)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (gt(n5, n4) <=> gt(n4, n4)),
% 0.19/0.43 inference(transitivity,[status(thm)],[109, 13])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (gt(n5, n4) <=> gt(n5, n4)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(112,axiom,(gt(n5, n4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gt_5_4')).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (gt(n5, n4)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (gt(n4, n4)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(118,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (![X: $i] : (~gt(X, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,(
% 0.19/0.43 ![X: $i] : (~gt(X, X))),
% 0.19/0.43 inference(skolemize,[status(sab)],[119])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (![X: $i] : (~gt(X, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 ((~![X: $i] : (~gt(X, X))) | (~gt(n4, n4))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[122, 121, 114])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------