%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET019+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:24:50 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET019+4 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:02:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(equal_set_type, type, (
% 0.12/0.37 equal_set: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_B_3_type, type, (
% 0.12/0.37 tptp_fun_B_3: $i)).
% 0.12/0.37 tff(tptp_fun_A_4_type, type, (
% 0.12/0.37 tptp_fun_A_4: $i)).
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))) <=> (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : ((subset(A, B) & subset(B, A)) => equal_set(A, B))) <=> (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,axiom,(~![A: $i, B: $i] : ((subset(A, B) & subset(B, A)) => equal_set(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI02')).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.37 tff(8,plain,(
% 0.12/0.37 ~((~(subset(A!4, B!3) & subset(B!3, A!4))) | equal_set(A!4, B!3))),
% 0.12/0.37 inference(skolemize,[status(sab)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (subset(A!4, B!3) & subset(B!3, A!4)),
% 0.12/0.37 inference(or_elim,[status(thm)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (subset(B!3, A!4)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (subset(A!4, B!3)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 ((~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))) | (~subset(A!4, B!3)) | (~subset(B!3, A!4))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[12, 11, 10])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (~equal_set(A!4, B!3)),
% 0.12/0.37 inference(or_elim,[status(thm)],[8])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((((~subset(A!4, B!3)) | (~subset(B!3, A!4))) <=> equal_set(A!4, B!3)) | ((~subset(A!4, B!3)) | (~subset(B!3, A!4))) | equal_set(A!4, B!3)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (((~subset(A!4, B!3)) | (~subset(B!3, A!4))) <=> equal_set(A!4, B!3)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(22,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.37 tff(24,plain,(
% 0.12/0.37 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[23])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(A!4, B!3)) | (~subset(B!3, A!4))) <=> equal_set(A!4, B!3)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[27, 26, 16])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------