%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM405+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:20:54 AM UTC 2025
% Result : Theorem 1.11s 1.33s
% Output : Proof 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM405+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 01:02:25 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.11/1.33 % SZS status Theorem
% 1.11/1.33 % SZS output start Proof
% 1.11/1.33 tff(in_type, type, (
% 1.11/1.33 in: ( $i * $i ) > $o)).
% 1.11/1.33 tff(tptp_fun_B_14_type, type, (
% 1.11/1.33 tptp_fun_B_14: $i > $i)).
% 1.11/1.33 tff(tptp_fun_A_16_type, type, (
% 1.11/1.33 tptp_fun_A_16: $i)).
% 1.11/1.33 tff(tptp_fun_B_15_type, type, (
% 1.11/1.33 tptp_fun_B_15: $i > $i)).
% 1.11/1.33 tff(ordinal_type, type, (
% 1.11/1.33 ordinal: $i > $o)).
% 1.11/1.33 tff(1,assumption,(~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))), introduced(assumption)).
% 1.11/1.33 tff(2,plain,
% 1.11/1.33 (![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B))) <=> ![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(3,axiom,(![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t37_ordinal1')).
% 1.11/1.33 tff(4,plain,
% 1.11/1.33 (![A: $i] : (~![B: $i] : (in(B, A) <=> ordinal(B)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[3, 2])).
% 1.11/1.33 tff(5,plain,(
% 1.11/1.33 ![A: $i] : (~(in(tptp_fun_B_15(A), A) <=> ordinal(tptp_fun_B_15(A))))),
% 1.11/1.33 inference(skolemize,[status(sab)],[4])).
% 1.11/1.33 tff(6,plain,
% 1.11/1.33 ((~![A: $i] : (~(in(tptp_fun_B_15(A), A) <=> ordinal(tptp_fun_B_15(A))))) | (~(in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))) <=> ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(7,plain,
% 1.11/1.33 (~(in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))) <=> ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[6, 5])).
% 1.11/1.33 tff(8,plain,
% 1.11/1.33 ((in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))) <=> ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))) | ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(tautology,[status(thm)],[])).
% 1.11/1.33 tff(9,plain,
% 1.11/1.33 (in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))) | ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.11/1.33 tff(10,plain,
% 1.11/1.33 (in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[9, 1])).
% 1.11/1.33 tff(11,plain,
% 1.11/1.33 (((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) | ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(tautology,[status(thm)],[])).
% 1.11/1.33 tff(12,plain,
% 1.11/1.33 ((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[11, 1])).
% 1.11/1.33 tff(13,plain,
% 1.11/1.33 (^[A: $i, C: $i] : refl((~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A)))) <=> (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A)))))),
% 1.11/1.33 inference(bind,[status(th)],[])).
% 1.11/1.33 tff(14,plain,
% 1.11/1.33 (![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A)))) <=> ![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))),
% 1.11/1.33 inference(quant_intro,[status(thm)],[13])).
% 1.11/1.33 tff(15,plain,
% 1.11/1.33 (^[A: $i, C: $i] : trans(trans(monotonicity(rewrite((in(C, A) & ordinal(C)) <=> (~((~in(C, A)) | (~ordinal(C))))), ((in(C, tptp_fun_B_14(A)) <=> (in(C, A) & ordinal(C))) <=> (in(C, tptp_fun_B_14(A)) <=> (~((~in(C, A)) | (~ordinal(C))))))), rewrite((in(C, tptp_fun_B_14(A)) <=> (~((~in(C, A)) | (~ordinal(C))))) <=> (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))), ((in(C, tptp_fun_B_14(A)) <=> (in(C, A) & ordinal(C))) <=> (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A)))))), rewrite((~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A)))) <=> (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))), ((in(C, tptp_fun_B_14(A)) <=> (in(C, A) & ordinal(C))) <=> (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))))),
% 1.11/1.33 inference(bind,[status(th)],[])).
% 1.11/1.33 tff(16,plain,
% 1.11/1.33 (![A: $i, C: $i] : (in(C, tptp_fun_B_14(A)) <=> (in(C, A) & ordinal(C))) <=> ![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))),
% 1.11/1.33 inference(quant_intro,[status(thm)],[15])).
% 1.11/1.33 tff(17,plain,
% 1.11/1.33 (![A: $i] : ![C: $i] : (in(C, tptp_fun_B_14(A)) <=> (in(C, A) & ordinal(C))) <=> ![A: $i, C: $i] : (in(C, tptp_fun_B_14(A)) <=> (in(C, A) & ordinal(C)))),
% 1.11/1.33 inference(pull_quant,[status(thm)],[])).
% 1.11/1.33 tff(18,plain,
% 1.11/1.33 (![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C))) <=> ![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(19,axiom,(![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_xboole_0__e2_43__ordinal1')).
% 1.11/1.33 tff(20,plain,
% 1.11/1.33 (![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.11/1.33 tff(21,plain,(
% 1.11/1.33 ![A: $i] : ![C: $i] : (in(C, tptp_fun_B_14(A)) <=> (in(C, A) & ordinal(C)))),
% 1.11/1.33 inference(skolemize,[status(sab)],[20])).
% 1.11/1.33 tff(22,plain,
% 1.11/1.33 (![A: $i, C: $i] : (in(C, tptp_fun_B_14(A)) <=> (in(C, A) & ordinal(C)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[21, 17])).
% 1.11/1.33 tff(23,plain,
% 1.11/1.33 (![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[22, 16])).
% 1.11/1.33 tff(24,plain,
% 1.11/1.33 (![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[23, 14])).
% 1.11/1.33 tff(25,plain,
% 1.11/1.33 (((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(26,plain,
% 1.11/1.33 ((~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))) <=> (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(27,plain,
% 1.11/1.33 ((((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))) <=> (((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(28,plain,
% 1.11/1.33 ((~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))) <=> (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[27])).
% 1.11/1.33 tff(29,plain,
% 1.11/1.33 ((~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))) <=> (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(transitivity,[status(thm)],[28, 26])).
% 1.11/1.33 tff(30,plain,
% 1.11/1.33 (((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[29])).
% 1.11/1.33 tff(31,plain,
% 1.11/1.33 (((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))))),
% 1.11/1.33 inference(transitivity,[status(thm)],[30, 25])).
% 1.11/1.33 tff(32,plain,
% 1.11/1.33 ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(33,plain,
% 1.11/1.33 ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.11/1.33 tff(34,plain,
% 1.11/1.33 (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[33, 24])).
% 1.11/1.33 tff(35,plain,
% 1.11/1.33 ((((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))) | (~((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(tautology,[status(thm)],[])).
% 1.11/1.33 tff(36,plain,
% 1.11/1.33 ((~((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[35, 34])).
% 1.11/1.33 tff(37,plain,
% 1.11/1.33 ($false),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[36, 12, 10])).
% 1.11/1.33 tff(38,plain,(ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.33 tff(39,plain,
% 1.11/1.33 (^[B: $i] : refl(((~ordinal(B)) | in(B, A!16)) <=> ((~ordinal(B)) | in(B, A!16)))),
% 1.11/1.33 inference(bind,[status(th)],[])).
% 1.11/1.33 tff(40,plain,
% 1.11/1.33 (![B: $i] : ((~ordinal(B)) | in(B, A!16)) <=> ![B: $i] : ((~ordinal(B)) | in(B, A!16))),
% 1.11/1.33 inference(quant_intro,[status(thm)],[39])).
% 1.11/1.33 tff(41,plain,
% 1.11/1.33 ((~![A: $i] : (~![B: $i] : ((~ordinal(B)) | in(B, A)))) <=> (~![A: $i] : (~![B: $i] : ((~ordinal(B)) | in(B, A))))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(42,plain,
% 1.11/1.33 ((~![A: $i] : (~![B: $i] : (ordinal(B) => in(B, A)))) <=> (~![A: $i] : (~![B: $i] : ((~ordinal(B)) | in(B, A))))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(43,axiom,(~![A: $i] : (~![B: $i] : (ordinal(B) => in(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_ordinal1')).
% 1.11/1.33 tff(44,plain,
% 1.11/1.33 (~![A: $i] : (~![B: $i] : ((~ordinal(B)) | in(B, A)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.11/1.33 tff(45,plain,
% 1.11/1.33 (~![A: $i] : (~![B: $i] : ((~ordinal(B)) | in(B, A)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[44, 41])).
% 1.11/1.33 tff(46,plain,
% 1.11/1.33 (~![A: $i] : (~![B: $i] : ((~ordinal(B)) | in(B, A)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.11/1.33 tff(47,plain,
% 1.11/1.33 (~![A: $i] : (~![B: $i] : ((~ordinal(B)) | in(B, A)))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[46, 41])).
% 1.11/1.33 tff(48,plain,(
% 1.11/1.33 $oeq((~(~![B: $i] : ((~ordinal(B)) | in(B, A!16)))), ![B: $i] : ((~ordinal(B)) | in(B, A!16)))),
% 1.11/1.33 inference(transitivity,[status(sab)],[47])).
% 1.11/1.33 tff(49,plain,
% 1.11/1.33 (![B: $i] : ((~ordinal(B)) | in(B, A!16))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[48, 40])).
% 1.11/1.33 tff(50,plain,
% 1.11/1.33 (((~![B: $i] : ((~ordinal(B)) | in(B, A!16))) | ((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, A!16))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(51,plain,
% 1.11/1.33 ((~![B: $i] : ((~ordinal(B)) | in(B, A!16))) | ((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(52,plain,
% 1.11/1.33 ((~![B: $i] : ((~ordinal(B)) | in(B, A!16))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.11/1.33 tff(53,plain,
% 1.11/1.33 ((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[52, 49])).
% 1.11/1.33 tff(54,plain,
% 1.11/1.33 (in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[53, 38])).
% 1.11/1.33 tff(55,plain,
% 1.11/1.33 ((~((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))),
% 1.11/1.33 inference(tautology,[status(thm)],[])).
% 1.11/1.33 tff(56,plain,
% 1.11/1.33 (~((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[55, 38, 54])).
% 1.11/1.33 tff(57,plain,
% 1.11/1.33 ((in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16))) <=> ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(tautology,[status(thm)],[])).
% 1.11/1.33 tff(58,plain,
% 1.11/1.33 ((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[57, 7])).
% 1.11/1.33 tff(59,plain,
% 1.11/1.33 (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[58, 38])).
% 1.11/1.33 tff(60,plain,
% 1.11/1.33 ((((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))) | ((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))),
% 1.11/1.33 inference(tautology,[status(thm)],[])).
% 1.11/1.33 tff(61,plain,
% 1.11/1.33 (((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(tptp_fun_B_14(A!16)))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[60, 34])).
% 1.11/1.33 tff(62,plain,
% 1.11/1.33 ((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[61, 59])).
% 1.11/1.33 tff(63,plain,
% 1.11/1.33 ((~((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))),
% 1.11/1.33 inference(tautology,[status(thm)],[])).
% 1.11/1.33 tff(64,plain,
% 1.11/1.33 (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[63, 62, 38])).
% 1.11/1.33 tff(65,plain,
% 1.11/1.33 ((((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))) | ((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) | in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))),
% 1.11/1.33 inference(tautology,[status(thm)],[])).
% 1.11/1.33 tff(66,plain,
% 1.11/1.33 (((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[65, 64, 56])).
% 1.11/1.33 tff(67,plain,
% 1.11/1.33 (((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))) <=> ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(68,plain,
% 1.11/1.33 ((~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(69,plain,
% 1.11/1.33 ((((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))) <=> (((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(70,plain,
% 1.11/1.33 ((~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[69])).
% 1.11/1.33 tff(71,plain,
% 1.11/1.33 ((~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))) <=> (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(transitivity,[status(thm)],[70, 68])).
% 1.11/1.33 tff(72,plain,
% 1.11/1.33 (((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))) <=> ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[71])).
% 1.11/1.33 tff(73,plain,
% 1.11/1.33 (((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))) <=> ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16)))))),
% 1.11/1.33 inference(transitivity,[status(thm)],[72, 67])).
% 1.11/1.33 tff(74,plain,
% 1.11/1.33 ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16)) | (~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16)))))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(75,plain,
% 1.11/1.33 ((~![A: $i, C: $i] : (~(((~in(C, A)) | (~ordinal(C))) <=> in(C, tptp_fun_B_14(A))))) | (~(((~ordinal(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))))) | (~in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), A!16))) <=> in(tptp_fun_B_15(tptp_fun_B_14(tptp_fun_B_14(A!16))), tptp_fun_B_14(A!16))))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.11/1.33 tff(76,plain,
% 1.11/1.33 ($false),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[75, 24, 66])).
% 1.11/1.33 % SZS output end Proof
% 1.11/1.33 % E exiting
%------------------------------------------------------------------------------