%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET706+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:26:11 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET706+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:38:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_B_4_type, type, (
% 0.12/0.38 tptp_fun_B_4: $i)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(union_type, type, (
% 0.12/0.38 union: ( $i * $i ) > $i)).
% 0.12/0.38 tff(difference_type, type, (
% 0.12/0.38 difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_A_5_type, type, (
% 0.12/0.38 tptp_fun_A_5: $i)).
% 0.12/0.38 tff(tptp_fun_C_3_type, type, (
% 0.12/0.38 tptp_fun_C_3: $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(equal_set_type, type, (
% 0.12/0.38 equal_set: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,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')).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,(
% 0.12/0.38 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~(((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,assumption,(((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4))), introduced(assumption)).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[14, 10, 13])).
% 0.12/0.39 tff(16,plain,(~(((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(17,assumption,(~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4))), introduced(assumption)).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[20, 17])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (~(((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[22, 10])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (^[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)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.39 tff(34,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')).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.39 tff(37,plain,(
% 0.20/0.39 ![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)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[36])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 ((~![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)))))))) | (~((~((~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3))) | ![X: $i] : ((~member(X, union(difference(B!4, C!3), difference(A!5, B!4)))) | member(X, difference(A!5, C!3))))) | (~(subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (~((~((~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3))) | ![X: $i] : ((~member(X, union(difference(B!4, C!3), difference(A!5, B!4)))) | member(X, difference(A!5, C!3))))) | (~(subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3)))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (((~((~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3))) | ![X: $i] : ((~member(X, union(difference(B!4, C!3), difference(A!5, B!4)))) | member(X, difference(A!5, C!3))))) | (~(subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))))))) | (subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.40 tff(44,assumption,((~((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | ![X: $i] : ((~member(X, difference(A!5, C!3))) | member(X, union(difference(B!4, C!3), difference(A!5, B!4)))))) | (~(subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))))))), introduced(assumption)).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ((~![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(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | ![X: $i] : ((~member(X, difference(A!5, C!3))) | member(X, union(difference(B!4, C!3), difference(A!5, B!4)))))) | (~(subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[45, 39, 44])).
% 0.20/0.40 tff(47,plain,(~((~((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | ![X: $i] : ((~member(X, difference(A!5, C!3))) | member(X, union(difference(B!4, C!3), difference(A!5, B!4)))))) | (~(subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (((~((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | ![X: $i] : ((~member(X, difference(A!5, C!3))) | member(X, union(difference(B!4, C!3), difference(A!5, B!4)))))) | (~(subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))))))) | (subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (~(((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[50, 10])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.40 tff(57,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')).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.40 tff(60,plain,(
% 0.20/0.40 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[59])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))) <=> (member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))) <=> (member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.40 tff(64,assumption,(~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))))), introduced(assumption)).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))) <=> (member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))) | (~(member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))) <=> (member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))))) | (~(member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (~(member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 63])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4))) | ((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4))) | ((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 ((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 51])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (~(((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[75, 10])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 ((member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[77, 69])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))) | ((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 ((((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(B!4, C!3))) | ((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 ((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[80, 76])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (~(((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[82, 10])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[84, 64])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 ((((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3))) | (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) <=> member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[87, 83])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) | (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 ((~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3))) | (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 ((~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3))) | (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[92, 81])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), C!3)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[94, 88])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4))) | (~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), A!5)) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), B!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 93, 74])).
% 0.20/0.41 tff(99,plain,((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~(subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))))))) | subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~(subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), difference(A!5, C!3))) | member(tptp_fun_X_0(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)), union(difference(B!4, C!3), difference(A!5, B!4))))))) | subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 49])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(108,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')).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.42 tff(110,plain,(
% 0.20/0.42 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[109])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)))) <=> equal_set(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (~(((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)))) <=> equal_set(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~(subset(C, B) & subset(B, A))) | equal_set(difference(A, C), union(difference(B, C), difference(A, B))))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(C, B) & subset(B, A))) | equal_set(difference(A, C), union(difference(B, C), difference(A, B)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((subset(C, B) & subset(B, A)) => equal_set(difference(A, C), union(difference(B, C), difference(A, B))))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(C, B) & subset(B, A))) | equal_set(difference(A, C), union(difference(B, C), difference(A, B)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(117,axiom,(~![A: $i, B: $i, C: $i] : ((subset(C, B) & subset(B, A)) => equal_set(difference(A, C), union(difference(B, C), difference(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI49')).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~(subset(C, B) & subset(B, A))) | equal_set(difference(A, C), union(difference(B, C), difference(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~(subset(C, B) & subset(B, A))) | equal_set(difference(A, C), union(difference(B, C), difference(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[118, 115])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~(subset(C, B) & subset(B, A))) | equal_set(difference(A, C), union(difference(B, C), difference(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (~![A: $i, B: $i, C: $i] : ((~(subset(C, B) & subset(B, A))) | equal_set(difference(A, C), union(difference(B, C), difference(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[120, 115])).
% 0.20/0.42 tff(122,plain,(
% 0.20/0.42 ~((~(subset(C!3, B!4) & subset(B!4, A!5))) | equal_set(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[121])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (~equal_set(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))),
% 0.20/0.42 inference(or_elim,[status(thm)],[122])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 ((((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)))) <=> equal_set(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | ((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)))) | equal_set(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)))) <=> equal_set(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | ((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 ((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[125, 114])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 ((~((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3))))) | (~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 ((~subset(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4)))) | (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (~subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[128, 102])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 ((~(subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3)))))) | subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 ((~(subset(union(difference(B!4, C!3), difference(A!5, B!4)), difference(A!5, C!3)) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3)))))) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[131, 43])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))) | ((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))) | ((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 ((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 23])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 ((~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 ((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[139, 21])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 ((~![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(C!3, B!4)) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4)))) | (~(subset(C!3, B!4) | (~((~member(tptp_fun_X_0(B!4, C!3), C!3)) | member(tptp_fun_X_0(B!4, C!3), B!4)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (~((~((~subset(C!3, B!4)) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4)))) | (~(subset(C!3, B!4) | (~((~member(tptp_fun_X_0(B!4, C!3), C!3)) | member(tptp_fun_X_0(B!4, C!3), B!4))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[141, 39])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (((~((~subset(C!3, B!4)) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4)))) | (~(subset(C!3, B!4) | (~((~member(tptp_fun_X_0(B!4, C!3), C!3)) | member(tptp_fun_X_0(B!4, C!3), B!4)))))) | ((~subset(C!3, B!4)) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 ((~subset(C!3, B!4)) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (subset(C!3, B!4) & subset(B!4, A!5)),
% 0.20/0.43 inference(or_elim,[status(thm)],[122])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (subset(C!3, B!4)),
% 0.20/0.43 inference(and_elim,[status(thm)],[145])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 ((~((~subset(C!3, B!4)) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4)))) | (~subset(C!3, B!4)) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 ((~((~subset(C!3, B!4)) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4)))) | ![X: $i] : ((~member(X, C!3)) | member(X, B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (![X: $i] : ((~member(X, C!3)) | member(X, B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[148, 144])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 (((~![X: $i] : ((~member(X, C!3)) | member(X, B!4))) | ((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4))) <=> ((~![X: $i] : ((~member(X, C!3)) | member(X, B!4))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, C!3)) | member(X, B!4))) | ((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, C!3)) | member(X, B!4))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[152, 149, 140, 19])).
% 0.20/0.43 tff(154,plain,((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 ((((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 ((((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[156, 16])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4))) <=> (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4))) <=> (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[158, 61])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, C!3))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[160, 132])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4))) <=> (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4)))) | (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), union(difference(B!4, C!3), difference(A!5, B!4))) <=> (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))))) | (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[163, 159])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3)))) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(A!5, B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[166, 157])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 ((((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 ((((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) <=> member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), difference(B!4, C!3))) | (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (~((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[169, 12])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 (member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 (((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), C!3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[173, 170])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[139, 174])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 ((~![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(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))) | (~(subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 (~((~((~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))) | (~(subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[176, 39])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 (((~((~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))) | (~(subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)))))) | ((~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 ((~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 (subset(B!4, A!5)),
% 0.20/0.44 inference(and_elim,[status(thm)],[145])).
% 0.20/0.44 tff(181,plain,
% 0.20/0.44 ((~((~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))) | (~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(182,plain,
% 0.20/0.44 ((~((~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.20/0.44 tff(183,plain,
% 0.20/0.44 (![X: $i] : ((~member(X, B!4)) | member(X, A!5))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.20/0.44 tff(184,plain,
% 0.20/0.44 (((~![X: $i] : ((~member(X, B!4)) | member(X, A!5))) | ((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5))) <=> ((~![X: $i] : ((~member(X, B!4)) | member(X, A!5))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(185,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, B!4)) | member(X, A!5))) | ((~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(186,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, B!4)) | member(X, A!5))) | (~member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), B!4)) | member(tptp_fun_X_0(difference(A!5, C!3), union(difference(B!4, C!3), difference(A!5, B!4))), A!5)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.44 tff(187,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[186, 183, 175, 172])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------