%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU123+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:26:56 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SEU123+2 : TPTP v9.0.0. Released v3.3.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.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 06:07:31 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_A_6_type, type, (
% 0.13/0.39 tptp_fun_A_6: $i)).
% 0.13/0.39 tff(empty_set_type, type, (
% 0.13/0.39 empty_set: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,(
% 0.13/0.39 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!6, empty_set)) | (~subset(empty_set, A!6))) <=> (A!6 = empty_set)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~(((~subset(A!6, empty_set)) | (~subset(empty_set, A!6))) <=> (A!6 = empty_set))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) <=> (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ((~![A: $i] : (subset(A, empty_set) => (A = empty_set))) <=> (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,axiom,(~![A: $i] : (subset(A, empty_set) => (A = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_xboole_1')).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.13/0.39 tff(20,plain,(
% 0.13/0.39 ~((~subset(A!6, empty_set)) | (A!6 = empty_set))),
% 0.13/0.39 inference(skolemize,[status(sab)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (~(A!6 = empty_set)),
% 0.13/0.39 inference(or_elim,[status(thm)],[20])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((((~subset(A!6, empty_set)) | (~subset(empty_set, A!6))) <=> (A!6 = empty_set)) | ((~subset(A!6, empty_set)) | (~subset(empty_set, A!6))) | (A!6 = empty_set)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ((((~subset(A!6, empty_set)) | (~subset(empty_set, A!6))) <=> (A!6 = empty_set)) | ((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((~subset(A!6, empty_set)) | (~subset(empty_set, A!6))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (subset(A!6, empty_set)),
% 0.13/0.40 inference(or_elim,[status(thm)],[20])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 ((~((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))) | (~subset(A!6, empty_set)) | (~subset(empty_set, A!6))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 ((~((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))) | (~subset(empty_set, A!6))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (~subset(empty_set, A!6)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (^[A: $i] : refl(subset(empty_set, A) <=> subset(empty_set, A))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![A: $i] : subset(empty_set, A) <=> ![A: $i] : subset(empty_set, A)),
% 0.13/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![A: $i] : subset(empty_set, A) <=> ![A: $i] : subset(empty_set, A)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(32,axiom,(![A: $i] : subset(empty_set, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_xboole_1')).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![A: $i] : subset(empty_set, A)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.13/0.40 tff(34,plain,(
% 0.13/0.40 ![A: $i] : subset(empty_set, A)),
% 0.13/0.40 inference(skolemize,[status(sab)],[33])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![A: $i] : subset(empty_set, A)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 ((~![A: $i] : subset(empty_set, A)) | subset(empty_set, A!6)),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[36, 35, 28])).
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------