%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET358+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:25:39 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 : SET358+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.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 04:55:18 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_A_4_type, type, (
% 0.12/0.38 tptp_fun_A_4: $i)).
% 0.12/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.38 tptp_fun_Y_1: ( $i * $i ) > $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(sum_type, type, (
% 0.12/0.38 sum: $i > $i)).
% 0.12/0.38 tff(union_type, type, (
% 0.12/0.38 union: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_3_type, type, (
% 0.12/0.38 tptp_fun_B_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 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.38 tff(6,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')).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,(
% 0.12/0.38 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[X: $i, A: $i] : refl((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[X: $i, A: $i] : rewrite((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (^[X: $i, A: $i] : trans(monotonicity(rewrite(((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) <=> ((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))), rewrite((member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))) <=> (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))), rewrite((((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y))) <=> ![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,axiom,(![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','sum')).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.39 tff(23,plain,(
% 0.20/0.39 ![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[22])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ((~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))))) <=> (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (^[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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(36,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))))))) <=> ![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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (^[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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(38,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))))))) <=> ![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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.40 tff(39,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))))))) <=> ![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)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (^[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)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(41,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))))) <=> ![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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.40 tff(45,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')).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.40 tff(48,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)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[47])).
% 0.20/0.40 tff(49,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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.40 tff(50,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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.20/0.40 tff(51,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(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))) | ![X: $i] : ((~member(X, sum(union(A!4, B!3)))) | member(X, union(sum(A!4), sum(B!3)))))) | (~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (~((~((~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))) | ![X: $i] : ((~member(X, sum(union(A!4, B!3)))) | member(X, union(sum(A!4), sum(B!3)))))) | (~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (((~((~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))) | ![X: $i] : ((~member(X, sum(union(A!4, B!3)))) | member(X, union(sum(A!4), sum(B!3)))))) | (~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))))) | (subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.40 tff(55,assumption,((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(sum(A!4), sum(B!3)))) | member(X, sum(union(A!4, B!3)))))) | (~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))))), introduced(assumption)).
% 0.20/0.40 tff(56,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(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(sum(A!4), sum(B!3)))) | member(X, sum(union(A!4, B!3)))))) | (~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[56, 50, 55])).
% 0.20/0.40 tff(58,plain,(~((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(sum(A!4), sum(B!3)))) | member(X, sum(union(A!4, B!3)))))) | (~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(sum(A!4), sum(B!3)))) | member(X, sum(union(A!4, B!3)))))) | (~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))))) | (subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))))) <=> (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[66, 25])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))))))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 10])).
% 0.20/0.41 tff(72,assumption,(~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))), introduced(assumption)).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))))) | (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[76, 71])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))))) <=> (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[83, 25])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))))))) | (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[87, 72])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[90, 86])).
% 0.20/0.43 tff(92,assumption,(![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))), introduced(assumption)).
% 0.20/0.43 tff(93,assumption,(~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))), introduced(assumption)).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.43 tff(100,assumption,(~(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))), introduced(assumption)).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[101, 10, 100])).
% 0.20/0.43 tff(103,plain,(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ((~(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) <=> ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[109, 107])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[112, 106, 95, 92])).
% 0.20/0.44 tff(114,plain,(((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))) | (~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[114, 91])).
% 0.20/0.44 tff(116,assumption,((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))))), introduced(assumption)).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 ((~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))))) <=> (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.45 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[119, 117])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[122, 25, 116])).
% 0.20/0.45 tff(124,plain,(~((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 ((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[128, 115])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[130, 129, 77])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 ((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[133, 69])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.45 tff(141,assumption,(~(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))), introduced(assumption)).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 ((member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[143])).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[144, 142])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[147, 10, 141])).
% 0.20/0.46 tff(149,plain,(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 ((~(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[151, 140])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) <=> ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[155, 153])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[158, 152, 91, 136])).
% 0.20/0.46 tff(160,plain,((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 ((~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))))) | subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 ((~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))))) | subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 (subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[162, 60])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(169,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')).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.46 tff(171,plain,(
% 0.20/0.46 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[170])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))) <=> equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (~(((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))) <=> equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))) <=> (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(177,axiom,(~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI37')).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[178, 176])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[179, 176])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.20/0.46 tff(182,plain,(
% 0.20/0.46 ~equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[181])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 ((((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))) <=> equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))) | equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 ((((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))) <=> equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 ((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[184, 175])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 ((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 ((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[187, 163])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 ((~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))))) | subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 ((~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[190, 54])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.20/0.46 tff(194,plain,
% 0.20/0.46 ((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 ((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.20/0.46 tff(196,plain,
% 0.20/0.46 (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[195, 34])).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 (((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 ((~(member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 ((~(member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))) | (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[200, 12])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 ((~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))))) <=> (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[203])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[204, 202])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[207, 25])).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 (((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))))))) | (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(212,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[211, 10])).
% 0.20/0.47 tff(213,plain,
% 0.20/0.47 (((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(214,plain,
% 0.20/0.47 (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[213, 191])).
% 0.20/0.47 tff(215,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.20/0.47 tff(217,plain,
% 0.20/0.47 (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[216, 212])).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 ((member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.20/0.47 tff(220,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[221, 210])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 (((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[223, 196])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 (((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))) <=> ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))))))) <=> ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[226])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 (((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[227, 225])).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[230, 224, 222])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 ((~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))))) <=> (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[233])).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[234, 232])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[237, 25])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 (((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3))))))) | (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 ((member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[241, 217])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 (![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[244, 240])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))) <=> ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))))))) <=> ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 (((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[247])).
% 0.20/0.49 tff(249,plain,
% 0.20/0.49 (((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[248, 246])).
% 0.20/0.49 tff(250,plain,
% 0.20/0.49 ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(251,plain,
% 0.20/0.49 ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[251, 224, 245])).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 ((~(member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[253, 252, 231, 201])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------