%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET595+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:25:56 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET595+4 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.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 05:29:25 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(member_type, type, (
% 0.13/0.39 member: ( $i * $i ) > $o)).
% 0.13/0.39 tff(difference_type, type, (
% 0.13/0.39 difference: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_A_4_type, type, (
% 0.13/0.39 tptp_fun_A_4: $i)).
% 0.13/0.39 tff(tptp_fun_E_3_type, type, (
% 0.13/0.39 tptp_fun_E_3: $i)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(union_type, type, (
% 0.13/0.39 union: ( $i * $i ) > $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(equal_set_type, type, (
% 0.13/0.39 equal_set: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4)) <=> member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[B: $i, A: $i, E: $i] : refl((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (^[B: $i, A: $i, E: $i] : trans(trans(monotonicity(rewrite((member(B, E) & (~member(B, A))) <=> (~((~member(B, E)) | member(B, A)))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))), rewrite((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))), rewrite((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(7,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.39 tff(9,plain,(
% 0.13/0.39 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4)) <=> member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.13/0.39 tff(14,plain,(~(((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4)) <=> member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','union')).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.39 tff(23,plain,(
% 0.13/0.39 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[30, 28])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.13/0.39 tff(37,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.13/0.39 tff(40,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[39])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(E!3, union(difference(E!3, A!4), A!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!4), A!4))))) | (~(subset(E!3, union(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (~((~((~subset(E!3, union(difference(E!3, A!4), A!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!4), A!4))))) | (~(subset(E!3, union(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (((~((~subset(E!3, union(difference(E!3, A!4), A!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!4), A!4))))) | (~(subset(E!3, union(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4))))))) | (subset(E!3, union(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (subset(E!3, union(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.13/0.40 tff(47,assumption,(~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3))), introduced(assumption)).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.13/0.40 tff(50,assumption,(~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))))), introduced(assumption)).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[51, 24, 50])).
% 0.13/0.40 tff(53,plain,(member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[55, 49])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[57, 47])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.13/0.40 tff(61,assumption,(((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) <=> member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))), introduced(assumption)).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) <=> member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[62, 11, 61])).
% 0.13/0.40 tff(64,plain,(~(((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) <=> member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ((((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) <=> member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 ((~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[66, 60])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4)))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), difference(E!3, A!4))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[68, 67, 56])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (~((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[70, 42])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 (((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3)))))) | ((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 ((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 ((~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(union(difference(E, A), A), E))) <=> (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(union(difference(E, A), A), E)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 ((~![A: $i, E: $i] : (subset(A, E) => equal_set(union(difference(E, A), A), E))) <=> (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(union(difference(E, A), A), E)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(76,axiom,(~![A: $i, E: $i] : (subset(A, E) => equal_set(union(difference(E, A), A), E))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI27')).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(union(difference(E, A), A), E))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(union(difference(E, A), A), E))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[77, 74])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(union(difference(E, A), A), E))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.13/0.40 tff(80,plain,
% 0.13/0.40 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(union(difference(E, A), A), E))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[79, 74])).
% 0.13/0.40 tff(81,plain,(
% 0.13/0.40 ~((~subset(A!4, E!3)) | equal_set(union(difference(E!3, A!4), A!4), E!3))),
% 0.13/0.40 inference(skolemize,[status(sab)],[80])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 (subset(A!4, E!3)),
% 0.13/0.40 inference(or_elim,[status(thm)],[81])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 ((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 ((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[84, 73])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 (((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3))) <=> ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(87,plain,
% 0.22/0.41 ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(88,plain,
% 0.22/0.41 ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), A!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.22/0.41 tff(89,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[88, 85, 58, 69])).
% 0.22/0.41 tff(90,plain,((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.41 tff(91,assumption,((~((~subset(union(difference(E!3, A!4), A!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!4), A!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)))))), introduced(assumption)).
% 0.22/0.41 tff(92,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(difference(E!3, A!4), A!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!4), A!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(93,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[92, 42, 91])).
% 0.22/0.41 tff(94,plain,(~((~((~subset(union(difference(E!3, A!4), A!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!4), A!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.41 tff(95,plain,
% 0.22/0.41 (((~((~subset(union(difference(E!3, A!4), A!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!4), A!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)))))) | (subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(96,plain,
% 0.22/0.41 (subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.22/0.41 tff(97,plain,
% 0.22/0.41 ((~(subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3))))) | subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(98,plain,
% 0.22/0.41 (subset(union(difference(E!3, A!4), A!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!4), A!4)), E!3)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.22/0.41 tff(99,plain,
% 0.22/0.41 (subset(union(difference(E!3, A!4), A!4), E!3)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[98, 90])).
% 0.22/0.41 tff(100,plain,
% 0.22/0.41 (^[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))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(101,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[100])).
% 0.22/0.41 tff(102,plain,
% 0.22/0.41 (^[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)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(103,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[102])).
% 0.22/0.41 tff(104,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(105,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.22/0.41 tff(106,plain,
% 0.22/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.22/0.41 tff(107,plain,(
% 0.22/0.41 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[106])).
% 0.22/0.41 tff(108,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.22/0.41 tff(109,plain,
% 0.22/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.22/0.41 tff(110,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4)))) <=> equal_set(union(difference(E!3, A!4), A!4), E!3)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(111,plain,
% 0.22/0.41 (~(((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4)))) <=> equal_set(union(difference(E!3, A!4), A!4), E!3))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.22/0.41 tff(112,plain,
% 0.22/0.41 (~equal_set(union(difference(E!3, A!4), A!4), E!3)),
% 0.22/0.41 inference(or_elim,[status(thm)],[81])).
% 0.22/0.41 tff(113,plain,
% 0.22/0.41 ((((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4)))) <=> equal_set(union(difference(E!3, A!4), A!4), E!3)) | ((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4)))) | equal_set(union(difference(E!3, A!4), A!4), E!3)),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(114,plain,
% 0.22/0.41 ((((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4)))) <=> equal_set(union(difference(E!3, A!4), A!4), E!3)) | ((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.22/0.41 tff(115,plain,
% 0.22/0.41 ((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.22/0.41 tff(116,plain,
% 0.22/0.41 ((~((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4))))) | (~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(117,plain,
% 0.22/0.41 ((~subset(union(difference(E!3, A!4), A!4), E!3)) | (~subset(E!3, union(difference(E!3, A!4), A!4)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.22/0.41 tff(118,plain,
% 0.22/0.41 (~subset(E!3, union(difference(E!3, A!4), A!4))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[117, 99])).
% 0.22/0.41 tff(119,plain,
% 0.22/0.41 ((~(subset(E!3, union(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)))))) | subset(E!3, union(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(120,plain,
% 0.22/0.41 ((~(subset(E!3, union(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)))))) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.22/0.41 tff(121,plain,
% 0.22/0.41 (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[120, 46])).
% 0.22/0.41 tff(122,plain,
% 0.22/0.41 (((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(123,plain,
% 0.22/0.41 (~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.22/0.41 tff(124,plain,
% 0.22/0.41 ((~(member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))))) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)) | (~(member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(125,plain,
% 0.22/0.41 ((~(member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))))) | (~(member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.22/0.41 tff(126,plain,
% 0.22/0.41 (~(member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[125, 26])).
% 0.22/0.41 tff(127,plain,
% 0.22/0.41 ((member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(128,plain,
% 0.22/0.42 (~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.22/0.42 tff(129,plain,
% 0.22/0.42 (((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), union(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(130,plain,
% 0.22/0.42 (member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[129, 121])).
% 0.22/0.42 tff(131,plain,
% 0.22/0.42 ((member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(132,plain,
% 0.22/0.42 (~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[131, 126])).
% 0.22/0.42 tff(133,plain,
% 0.22/0.42 ((~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(134,plain,
% 0.22/0.42 (~((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[133, 132, 130])).
% 0.22/0.42 tff(135,plain,
% 0.22/0.42 ((((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4)) <=> member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))) | ((~member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), A!4)) | member(tptp_fun_X_0(union(difference(E!3, A!4), A!4), E!3), difference(E!3, A!4))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(136,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[135, 134, 128, 14])).
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------