%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET159+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:22 AM UTC 2025
% Result : Theorem 0.19s 0.35s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET159+4 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 04:27:54 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.35 % SZS status Theorem
% 0.19/0.35 % SZS output start Proof
% 0.19/0.35 tff(member_type, type, (
% 0.19/0.35 member: ( $i * $i ) > $o)).
% 0.19/0.35 tff(tptp_fun_B_4_type, type, (
% 0.19/0.35 tptp_fun_B_4: $i)).
% 0.19/0.35 tff(tptp_fun_X_0_type, type, (
% 0.19/0.35 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.35 tff(union_type, type, (
% 0.19/0.35 union: ( $i * $i ) > $i)).
% 0.19/0.35 tff(tptp_fun_C_3_type, type, (
% 0.19/0.35 tptp_fun_C_3: $i)).
% 0.19/0.35 tff(tptp_fun_A_5_type, type, (
% 0.19/0.35 tptp_fun_A_5: $i)).
% 0.19/0.35 tff(subset_type, type, (
% 0.19/0.35 subset: ( $i * $i ) > $o)).
% 0.19/0.35 tff(equal_set_type, type, (
% 0.19/0.35 equal_set: ( $i * $i ) > $o)).
% 0.19/0.35 tff(1,plain,
% 0.19/0.35 (^[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))))),
% 0.19/0.35 inference(bind,[status(th)],[])).
% 0.19/0.35 tff(2,plain,
% 0.19/0.35 (![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)))),
% 0.19/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.35 tff(3,plain,
% 0.19/0.35 (![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)))),
% 0.19/0.35 inference(rewrite,[status(thm)],[])).
% 0.19/0.35 tff(4,plain,
% 0.19/0.35 (^[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))))),
% 0.19/0.35 inference(bind,[status(th)],[])).
% 0.19/0.35 tff(5,plain,
% 0.19/0.35 (![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)))),
% 0.19/0.35 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.35 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.19/0.35 tff(7,plain,
% 0.19/0.35 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.35 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.35 tff(8,plain,
% 0.19/0.35 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.35 tff(9,plain,(
% 0.19/0.35 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.35 inference(skolemize,[status(sab)],[8])).
% 0.19/0.35 tff(10,plain,
% 0.19/0.35 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.35 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.35 tff(11,plain,
% 0.19/0.35 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))))),
% 0.19/0.35 inference(rewrite,[status(thm)],[])).
% 0.19/0.35 tff(12,plain,
% 0.19/0.35 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.19/0.35 inference(rewrite,[status(thm)],[])).
% 0.19/0.35 tff(13,plain,
% 0.19/0.35 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))))),
% 0.19/0.36 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))))),
% 0.19/0.36 inference(transitivity,[status(thm)],[13, 11])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[18, 10])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 (^[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))))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 (![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)))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 (^[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))))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (![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)))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 (![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)))))))),
% 0.19/0.36 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 (^[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)))))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(26,plain,
% 0.19/0.36 (![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)))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.36 tff(27,plain,
% 0.19/0.36 (![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)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(28,plain,
% 0.19/0.36 (^[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))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(29,plain,
% 0.19/0.36 (![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)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.36 tff(30,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.36 tff(31,plain,
% 0.19/0.36 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.36 tff(32,plain,
% 0.19/0.36 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.36 tff(33,plain,(
% 0.19/0.36 ![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)))))),
% 0.19/0.36 inference(skolemize,[status(sab)],[32])).
% 0.19/0.36 tff(34,plain,
% 0.19/0.36 (![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)))))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.36 tff(35,plain,
% 0.19/0.36 (![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)))))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.19/0.36 tff(36,plain,
% 0.19/0.36 ((~![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(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, union(A!5, union(B!4, C!3)))) | member(X, union(union(A!5, B!4), C!3))))) | (~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(37,plain,
% 0.19/0.36 (~((~((~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, union(A!5, union(B!4, C!3)))) | member(X, union(union(A!5, B!4), C!3))))) | (~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))))))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.36 tff(38,plain,
% 0.19/0.36 (((~((~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, union(A!5, union(B!4, C!3)))) | member(X, union(union(A!5, B!4), C!3))))) | (~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))))) | (subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(39,plain,
% 0.19/0.36 (subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.36 tff(40,assumption,((~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(union(A!5, B!4), C!3))) | member(X, union(A!5, union(B!4, C!3)))))) | (~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))))), introduced(assumption)).
% 0.19/0.36 tff(41,plain,
% 0.19/0.36 ((~![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(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(union(A!5, B!4), C!3))) | member(X, union(A!5, union(B!4, C!3)))))) | (~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(42,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[41, 35, 40])).
% 0.19/0.36 tff(43,plain,(~((~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(union(A!5, B!4), C!3))) | member(X, union(A!5, union(B!4, C!3)))))) | (~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.36 tff(44,plain,
% 0.19/0.36 (((~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(union(A!5, B!4), C!3))) | member(X, union(A!5, union(B!4, C!3)))))) | (~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))))) | (subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(45,plain,
% 0.19/0.36 (subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.36 tff(46,plain,
% 0.19/0.36 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(47,plain,
% 0.19/0.36 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[46, 10])).
% 0.19/0.36 tff(48,assumption,(~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))), introduced(assumption)).
% 0.19/0.36 tff(49,plain,
% 0.19/0.36 (((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(50,plain,
% 0.19/0.36 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.36 tff(51,plain,
% 0.19/0.36 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))))) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(52,plain,
% 0.19/0.36 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.36 tff(53,plain,
% 0.19/0.36 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.19/0.36 tff(54,plain,
% 0.19/0.36 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(55,plain,
% 0.19/0.36 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[54, 10])).
% 0.19/0.36 tff(56,plain,
% 0.19/0.36 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(57,plain,
% 0.19/0.36 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[56, 10])).
% 0.19/0.36 tff(58,plain,
% 0.19/0.36 (((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(59,plain,
% 0.19/0.36 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[58, 48])).
% 0.19/0.36 tff(60,plain,
% 0.19/0.36 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) | (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(61,plain,
% 0.19/0.37 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))) | (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.37 tff(62,plain,
% 0.19/0.37 (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[61, 57])).
% 0.19/0.37 tff(63,plain,
% 0.19/0.37 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(64,plain,
% 0.19/0.37 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.37 tff(65,plain,
% 0.19/0.37 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(66,plain,
% 0.19/0.37 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))) | (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.37 tff(67,plain,
% 0.19/0.37 (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[66, 55])).
% 0.19/0.37 tff(68,plain,
% 0.19/0.37 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(69,plain,
% 0.19/0.37 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.37 tff(70,plain,
% 0.19/0.37 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(71,plain,
% 0.19/0.37 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[70, 69, 53])).
% 0.19/0.37 tff(72,plain,
% 0.19/0.37 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(73,plain,
% 0.19/0.37 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[72, 62])).
% 0.19/0.37 tff(74,plain,
% 0.19/0.37 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(75,plain,
% 0.19/0.37 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[74, 67])).
% 0.19/0.37 tff(76,plain,
% 0.19/0.37 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(77,plain,
% 0.19/0.37 (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[76, 75, 73])).
% 0.19/0.37 tff(78,assumption,(~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))), introduced(assumption)).
% 0.19/0.37 tff(79,plain,
% 0.19/0.37 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(80,plain,
% 0.19/0.37 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(81,plain,
% 0.19/0.37 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.37 tff(82,plain,
% 0.19/0.37 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.37 tff(83,plain,
% 0.19/0.37 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(84,plain,
% 0.19/0.37 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.37 tff(85,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[84, 10, 78])).
% 0.19/0.37 tff(86,plain,(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(87,plain,
% 0.19/0.37 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(88,plain,
% 0.19/0.37 ((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.37 tff(89,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[88, 77, 71])).
% 0.19/0.37 tff(90,plain,((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(91,plain,
% 0.19/0.37 ((~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))))) | subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(92,plain,
% 0.19/0.38 ((~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))))) | subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.38 tff(93,plain,
% 0.19/0.38 (subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[92, 45])).
% 0.19/0.38 tff(94,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(95,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.38 tff(96,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(97,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.38 tff(98,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(99,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.38 tff(100,plain,
% 0.19/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.38 tff(101,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[100])).
% 0.19/0.38 tff(102,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.38 tff(103,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.19/0.38 tff(104,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))) <=> equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(105,plain,
% 0.19/0.38 (~(((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))) <=> equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.38 tff(106,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))) <=> (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(107,axiom,(~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI09')).
% 0.19/0.38 tff(108,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.38 tff(109,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[108, 106])).
% 0.19/0.38 tff(110,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[109, 106])).
% 0.19/0.38 tff(111,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.19/0.38 tff(112,plain,(
% 0.19/0.38 ~equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[111])).
% 0.19/0.38 tff(113,plain,
% 0.19/0.38 ((((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))) <=> equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))) | equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(114,plain,
% 0.19/0.38 ((((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))) <=> equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.38 tff(115,plain,
% 0.19/0.38 ((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[114, 105])).
% 0.19/0.38 tff(116,plain,
% 0.19/0.38 ((~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))))) | (~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(117,plain,
% 0.19/0.38 ((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.19/0.38 tff(118,plain,
% 0.19/0.38 (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[117, 93])).
% 0.19/0.38 tff(119,plain,
% 0.19/0.38 ((~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))))) | subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(120,plain,
% 0.19/0.38 ((~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))))) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.38 tff(121,plain,
% 0.19/0.38 (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[120, 39])).
% 0.19/0.38 tff(122,plain,
% 0.19/0.38 (((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(123,plain,
% 0.19/0.38 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.38 tff(124,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) | (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(125,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))) | (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.19/0.38 tff(126,plain,
% 0.19/0.38 (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[125, 19])).
% 0.19/0.38 tff(127,plain,
% 0.19/0.38 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(128,plain,
% 0.19/0.38 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.38 tff(129,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) | (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(130,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))) | (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.19/0.38 tff(131,plain,
% 0.19/0.38 (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[130, 17])).
% 0.19/0.38 tff(132,plain,
% 0.19/0.38 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(133,plain,
% 0.19/0.38 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.19/0.38 tff(134,plain,
% 0.19/0.38 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(135,plain,
% 0.19/0.38 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[134, 126])).
% 0.19/0.38 tff(136,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(137,plain,
% 0.19/0.38 (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[136, 135, 133])).
% 0.19/0.38 tff(138,plain,
% 0.19/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(139,plain,
% 0.19/0.38 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[138, 10])).
% 0.19/0.38 tff(140,plain,
% 0.19/0.38 (((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(141,plain,
% 0.19/0.38 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[140, 121])).
% 0.19/0.38 tff(142,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(143,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.39 tff(144,plain,
% 0.19/0.39 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[143, 139])).
% 0.19/0.39 tff(145,plain,
% 0.19/0.39 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(146,plain,
% 0.19/0.39 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[145, 131])).
% 0.19/0.39 tff(147,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(148,plain,
% 0.19/0.39 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[147, 146, 144])).
% 0.19/0.39 tff(149,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(150,plain,
% 0.19/0.39 (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[149, 148, 137])).
% 0.19/0.39 tff(151,plain,
% 0.19/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(152,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[151, 10, 150])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------