%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET699+4 : TPTP v9.0.0. Released v2.2.0.
% 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 05:26:10 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET699+4 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:37:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(member_type, type, (
% 0.19/0.42 member: ( $i * $i ) > $o)).
% 0.19/0.42 tff(difference_type, type, (
% 0.19/0.42 difference: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_A_5_type, type, (
% 0.19/0.42 tptp_fun_A_5: $i)).
% 0.19/0.42 tff(tptp_fun_E_3_type, type, (
% 0.19/0.42 tptp_fun_E_3: $i)).
% 0.19/0.42 tff(tptp_fun_X_0_type, type, (
% 0.19/0.42 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_B_4_type, type, (
% 0.19/0.42 tptp_fun_B_4: $i)).
% 0.19/0.42 tff(subset_type, type, (
% 0.19/0.42 subset: ( $i * $i ) > $o)).
% 0.19/0.42 tff(intersection_type, type, (
% 0.19/0.42 intersection: ( $i * $i ) > $i)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.42 tff(8,plain,(
% 0.19/0.42 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[7])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (~(((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.43 tff(13,assumption,(~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))), introduced(assumption)).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (^[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))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (^[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))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (^[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)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.43 tff(24,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')).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.43 tff(27,plain,(
% 0.19/0.43 ![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)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[26])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 ((~![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(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (~((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))))) | (subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 ((~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5)))))) | subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[35, 13])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 ((((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 ((((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[40, 12])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.43 tff(44,assumption,(((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))), introduced(assumption)).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (^[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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(50,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')).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.43 tff(52,plain,(
% 0.19/0.43 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[51])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[55, 54, 44])).
% 0.19/0.44 tff(57,plain,(~(((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[58, 41])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 ((((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[60, 59, 57])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(66,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI33')).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[69, 64])).
% 0.19/0.44 tff(71,plain,(
% 0.19/0.44 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[70])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (~(subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)))),
% 0.19/0.44 inference(or_elim,[status(thm)],[71])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 ((subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | subset(A!5, B!4) | subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (subset(A!5, B!4) | subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (subset(A!5, B!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[74, 13])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 ((~![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!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (~((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[76, 29])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 ((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[85, 82, 63, 43])).
% 0.19/0.44 tff(87,plain,(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 ((subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | (~subset(A!5, B!4)) | (~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 ((~subset(A!5, B!4)) | (~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[88, 72])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (~subset(A!5, B!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[89, 87])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[91, 77])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 ((~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[94, 90])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), A!5))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.44 tff(100,assumption,(~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))), introduced(assumption)).
% 0.19/0.44 tff(101,assumption,(((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))), introduced(assumption)).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[102, 10, 101])).
% 0.19/0.44 tff(104,plain,(~(((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(105,assumption,(((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))), introduced(assumption)).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[106, 54, 105])).
% 0.19/0.44 tff(108,plain,(~(((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(109,plain,
% 0.19/0.45 ((~![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!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (~((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[109, 29])).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 (((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))) | ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (subset(A!5, E!3) & subset(B!4, E!3)),
% 0.19/0.45 inference(or_elim,[status(thm)],[71])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 (subset(A!5, E!3)),
% 0.19/0.45 inference(and_elim,[status(thm)],[113])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[116, 112])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 (((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[120, 117, 97])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | (~member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[122, 95])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 ((~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))) | (~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[124, 123, 121])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 ((((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 ((((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 (member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[127, 108])).
% 0.19/0.45 tff(129,plain,
% 0.19/0.45 ((~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[129, 97, 128])).
% 0.19/0.45 tff(131,plain,
% 0.19/0.45 ((((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(132,plain,
% 0.19/0.45 ((((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 (member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[132, 104])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 (((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))))) | ((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(135,plain,
% 0.19/0.45 ((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[134, 31])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 ((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 ((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 (![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[137, 87])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 (((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))) | ((~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))) <=> ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))) | (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))) | ((~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))) | (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[141, 138, 133, 100])).
% 0.19/0.45 tff(143,plain,(member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 ((((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 (((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[144, 143, 99])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[146, 54, 145])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------