%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM387+1 : TPTP v9.0.0. Released v3.2.0.
% 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 05:20:52 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : NUM387+1 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:02:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(in_type, type, (
% 0.19/0.36 in: ( $i * $i ) > $o)).
% 0.19/0.36 tff(succ_type, type, (
% 0.19/0.36 succ: $i > $i)).
% 0.19/0.36 tff(tptp_fun_A_11_type, type, (
% 0.19/0.36 tptp_fun_A_11: $i)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 ((~![A: $i] : (~(A = succ(A)))) <=> (~![A: $i] : (~(A = succ(A))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(2,axiom,(~![A: $i] : (~(A = succ(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t14_ordinal1')).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (~![A: $i] : (~(A = succ(A)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (~![A: $i] : (~(A = succ(A)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (~![A: $i] : (~(A = succ(A)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (~![A: $i] : (~(A = succ(A)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.36 tff(7,plain,(
% 0.19/0.36 A!11 = succ(A!11)),
% 0.19/0.36 inference(skolemize,[status(sab)],[6])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (succ(A!11) = A!11),
% 0.19/0.36 inference(symmetry,[status(thm)],[7])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (succ(succ(A!11)) = succ(A!11)),
% 0.19/0.36 inference(monotonicity,[status(thm)],[8])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (succ(A!11) = succ(succ(A!11))),
% 0.19/0.36 inference(symmetry,[status(thm)],[9])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (in(succ(A!11), succ(A!11)) <=> in(succ(A!11), succ(succ(A!11)))),
% 0.19/0.36 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (in(succ(A!11), succ(succ(A!11))) <=> in(succ(A!11), succ(A!11))),
% 0.19/0.36 inference(symmetry,[status(thm)],[11])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 (^[A: $i] : refl(in(A, succ(A)) <=> in(A, succ(A)))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(16,axiom,(![A: $i] : in(A, succ(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_ordinal1')).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (![A: $i] : in(A, succ(A))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.36 tff(18,plain,(
% 0.19/0.36 ![A: $i] : in(A, succ(A))),
% 0.19/0.36 inference(skolemize,[status(sab)],[17])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 (![A: $i] : in(A, succ(A))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 ((~![A: $i] : in(A, succ(A))) | in(succ(A!11), succ(succ(A!11)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 (in(succ(A!11), succ(succ(A!11)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 (in(succ(A!11), succ(A!11))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(26,plain,
% 0.19/0.36 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(27,plain,
% 0.19/0.36 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.36 tff(28,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 0.19/0.36 tff(29,plain,
% 0.19/0.36 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.36 tff(30,plain,
% 0.19/0.36 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.36 tff(31,plain,(
% 0.19/0.36 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[30])).
% 0.19/0.36 tff(32,plain,
% 0.19/0.36 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.36 tff(33,plain,
% 0.19/0.36 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(succ(A!11), succ(A!11)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(succ(A!11), succ(A!11))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(34,plain,
% 0.19/0.36 (((~in(succ(A!11), succ(A!11))) | (~in(succ(A!11), succ(A!11)))) <=> (~in(succ(A!11), succ(A!11)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(35,plain,
% 0.19/0.36 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(succ(A!11), succ(A!11))) | (~in(succ(A!11), succ(A!11))))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(succ(A!11), succ(A!11))))),
% 0.19/0.36 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.36 tff(36,plain,
% 0.19/0.36 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(succ(A!11), succ(A!11))) | (~in(succ(A!11), succ(A!11))))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(succ(A!11), succ(A!11))))),
% 0.19/0.36 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.36 tff(37,plain,
% 0.19/0.36 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(succ(A!11), succ(A!11))) | (~in(succ(A!11), succ(A!11))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(38,plain,
% 0.19/0.36 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(succ(A!11), succ(A!11)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.36 tff(39,plain,
% 0.19/0.36 (~in(succ(A!11), succ(A!11))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.19/0.36 tff(40,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[39, 22])).
% 0.19/0.36 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------