%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM393+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:20:53 AM UTC 2025
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM393+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n004.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 01:01:23 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(ordinal_subset_type, type, (
% 0.22/0.40 ordinal_subset: ( $i * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_A_12_type, type, (
% 0.22/0.40 tptp_fun_A_12: $i)).
% 0.22/0.40 tff(tptp_fun_B_13_type, type, (
% 0.22/0.40 tptp_fun_B_13: $i)).
% 0.22/0.40 tff(subset_type, type, (
% 0.22/0.40 subset: ( $i * $i ) > $o)).
% 0.22/0.40 tff(ordinal_type, type, (
% 0.22/0.40 ordinal: $i > $o)).
% 0.22/0.40 tff(inclusion_comparable_type, type, (
% 0.22/0.40 inclusion_comparable: ( $i * $i ) > $o)).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | inclusion_comparable(A, B)))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | inclusion_comparable(A, B))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 ((~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => inclusion_comparable(A, B)))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | inclusion_comparable(A, B))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(3,axiom,(~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => inclusion_comparable(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t25_ordinal1')).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | inclusion_comparable(A, B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | inclusion_comparable(A, B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | inclusion_comparable(A, B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | inclusion_comparable(A, B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.40 tff(8,plain,
% 0.22/0.40 (~((~ordinal(B!13)) | inclusion_comparable(A!12, B!13))),
% 0.22/0.40 inference(and_elim,[status(thm)],[7])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (ordinal(B!13)),
% 0.22/0.40 inference(or_elim,[status(thm)],[8])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (ordinal(A!12)),
% 0.22/0.40 inference(and_elim,[status(thm)],[7])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 (^[A: $i, B: $i] : refl(((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> (((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))))), rewrite((((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.22/0.40 tff(15,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(17,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.40 tff(18,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.22/0.40 tff(19,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.22/0.40 tff(21,plain,(
% 0.22/0.40 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[20])).
% 0.22/0.40 tff(22,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(25,plain,
% 0.22/0.40 (((ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)) | (~ordinal(A!12)) | (~ordinal(B!13))) <=> ((~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)) | (~ordinal(A!12)) | (~ordinal(B!13)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(B!13, A!12) <=> subset(B!13, A!12))))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[25])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)) | (~ordinal(A!12)) | (~ordinal(B!13)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)))),
% 0.22/0.40 inference(transitivity,[status(thm)],[26, 24])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)) | (~ordinal(A!12)) | (~ordinal(B!13)))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(29,plain,
% 0.22/0.40 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(B!13, A!12) <=> subset(B!13, A!12))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 (ordinal_subset(B!13, A!12) <=> subset(B!13, A!12)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[29, 23, 10, 9])).
% 0.22/0.40 tff(31,plain,
% 0.22/0.40 (^[A: $i, B: $i] : refl((inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B))) <=> (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(32,plain,
% 0.22/0.40 (![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B))) <=> ![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.22/0.40 tff(33,plain,
% 0.22/0.40 (![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B))) <=> ![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 (^[A: $i, B: $i] : rewrite((inclusion_comparable(A, B) <=> (subset(A, B) | subset(B, A))) <=> (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 (![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(A, B) | subset(B, A))) <=> ![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.22/0.41 tff(36,axiom,(![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(A, B) | subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_xboole_0')).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 (![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.22/0.41 tff(38,plain,
% 0.22/0.41 (![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.22/0.41 tff(39,plain,(
% 0.22/0.41 ![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[38])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 (![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : (inclusion_comparable(A, B) <=> (subset(B, A) | subset(A, B)))) | (inclusion_comparable(A!12, B!13) <=> (subset(B!13, A!12) | subset(A!12, B!13)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 (inclusion_comparable(A!12, B!13) <=> (subset(B!13, A!12) | subset(A!12, B!13))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.22/0.41 tff(43,plain,
% 0.22/0.41 (~inclusion_comparable(A!12, B!13)),
% 0.22/0.41 inference(or_elim,[status(thm)],[8])).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 ((~(inclusion_comparable(A!12, B!13) <=> (subset(B!13, A!12) | subset(A!12, B!13)))) | inclusion_comparable(A!12, B!13) | (~(subset(B!13, A!12) | subset(A!12, B!13)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(45,plain,
% 0.22/0.41 ((~(inclusion_comparable(A!12, B!13) <=> (subset(B!13, A!12) | subset(A!12, B!13)))) | (~(subset(B!13, A!12) | subset(A!12, B!13)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.22/0.41 tff(46,plain,
% 0.22/0.41 (~(subset(B!13, A!12) | subset(A!12, B!13))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[45, 42])).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 ((subset(B!13, A!12) | subset(A!12, B!13)) | (~subset(B!13, A!12))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 (~subset(B!13, A!12)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.22/0.41 tff(49,plain,
% 0.22/0.41 ((~(ordinal_subset(B!13, A!12) <=> subset(B!13, A!12))) | (~ordinal_subset(B!13, A!12)) | subset(B!13, A!12)),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(50,plain,
% 0.22/0.41 ((~(ordinal_subset(B!13, A!12) <=> subset(B!13, A!12))) | (~ordinal_subset(B!13, A!12))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.22/0.41 tff(51,plain,
% 0.22/0.41 (~ordinal_subset(B!13, A!12)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[50, 30])).
% 0.22/0.41 tff(52,plain,
% 0.22/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(53,plain,
% 0.22/0.41 (((ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)) | (~ordinal(B!13)) | (~ordinal(A!12))) <=> ((~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(54,plain,
% 0.22/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)) | (~ordinal(B!13)) | (~ordinal(A!12)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(A!12, B!13) <=> subset(A!12, B!13))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)) | (~ordinal(B!13)) | (~ordinal(A!12)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[54, 52])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)) | (~ordinal(B!13)) | (~ordinal(A!12)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | (ordinal_subset(A!12, B!13) <=> subset(A!12, B!13))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 (ordinal_subset(A!12, B!13) <=> subset(A!12, B!13)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[57, 23, 10, 9])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 ((subset(B!13, A!12) | subset(A!12, B!13)) | (~subset(A!12, B!13))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(60,plain,
% 0.22/0.41 (~subset(A!12, B!13)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[59, 46])).
% 0.22/0.41 tff(61,plain,
% 0.22/0.41 ((~(ordinal_subset(A!12, B!13) <=> subset(A!12, B!13))) | (~ordinal_subset(A!12, B!13)) | subset(A!12, B!13)),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 ((~(ordinal_subset(A!12, B!13) <=> subset(A!12, B!13))) | (~ordinal_subset(A!12, B!13))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.22/0.41 tff(63,plain,
% 0.22/0.41 (~ordinal_subset(A!12, B!13)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[62, 58])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 (^[A: $i, B: $i] : refl((ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(65,plain,
% 0.22/0.41 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.22/0.41 tff(66,plain,
% 0.22/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), ((ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | ((~ordinal(B)) | (~ordinal(A)))))), rewrite((ordinal_subset(B, A) | ordinal_subset(A, B) | ((~ordinal(B)) | (~ordinal(A)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))), ((ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(67,plain,
% 0.22/0.41 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.22/0.41 tff(68,plain,
% 0.22/0.41 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(69,plain,
% 0.22/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite((ordinal_subset(A, B) | ordinal_subset(B, A)) <=> (ordinal_subset(B, A) | ordinal_subset(A, B))), (((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> ((ordinal(A) & ordinal(B)) => (ordinal_subset(B, A) | ordinal_subset(A, B))))), rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(B, A) | ordinal_subset(A, B))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))), (((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(70,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.22/0.41 tff(71,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','connectedness_r1_ordinal1')).
% 0.22/0.41 tff(72,plain,
% 0.22/0.41 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.22/0.41 tff(73,plain,
% 0.22/0.41 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.22/0.41 tff(74,plain,(
% 0.22/0.41 ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[73])).
% 0.22/0.41 tff(75,plain,
% 0.22/0.41 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.22/0.41 tff(76,plain,
% 0.22/0.41 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.22/0.41 tff(77,plain,
% 0.22/0.41 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!12)) | (~ordinal(B!13)) | ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(78,plain,
% 0.22/0.41 ((ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12) | (~ordinal(A!12)) | (~ordinal(B!13))) <=> ((~ordinal(A!12)) | (~ordinal(B!13)) | ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(79,plain,
% 0.22/0.41 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12) | (~ordinal(A!12)) | (~ordinal(B!13)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!12)) | (~ordinal(B!13)) | ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12)))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[78])).
% 0.22/0.41 tff(80,plain,
% 0.22/0.41 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12) | (~ordinal(A!12)) | (~ordinal(B!13)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12))),
% 0.22/0.41 inference(transitivity,[status(thm)],[79, 77])).
% 0.22/0.41 tff(81,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12) | (~ordinal(A!12)) | (~ordinal(B!13)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(82,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!12)) | (~ordinal(B!13)) | ordinal_subset(A!12, B!13) | ordinal_subset(B!13, A!12)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.41 tff(83,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[82, 76, 10, 9, 63, 51])).
% 0.22/0.41 % SZS output end Proof
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------