%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET352+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET352+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:54:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(member_type, type, (
% 0.12/0.37 member: ( $i * $i ) > $o)).
% 0.12/0.37 tff(unordered_pair_type, type, (
% 0.12/0.37 unordered_pair: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_B_3_type, type, (
% 0.12/0.37 tptp_fun_B_3: $i)).
% 0.12/0.37 tff(tptp_fun_A_4_type, type, (
% 0.12/0.37 tptp_fun_A_4: $i)).
% 0.12/0.37 tff(tptp_fun_X_0_type, type, (
% 0.12/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(union_type, type, (
% 0.12/0.37 union: ( $i * $i ) > $i)).
% 0.12/0.37 tff(sum_type, type, (
% 0.12/0.37 sum: $i > $i)).
% 0.12/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.37 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(equal_set_type, type, (
% 0.12/0.37 equal_set: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,assumption,(~member(A!4, unordered_pair(A!4, B!3))), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[X: $i, A: $i, B: $i] : refl((member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))) <=> (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))) <=> ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))) <=> ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (^[X: $i, A: $i, B: $i] : rewrite((member(X, unordered_pair(A, B)) <=> ((X = A) | (X = B))) <=> (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = A) | (X = B))) <=> ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.37 tff(7,axiom,(![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = A) | (X = B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','unordered_pair')).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.37 tff(10,plain,(
% 0.12/0.37 ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!4, unordered_pair(A!4, B!3))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!4, unordered_pair(A!4, B!3)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 ((member(A!4, unordered_pair(A!4, B!3)) <=> $true) <=> member(A!4, unordered_pair(A!4, B!3))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (((A!4 = B!3) | $true) <=> $true),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((A!4 = A!4) <=> $true),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (((A!4 = B!3) | (A!4 = A!4)) <=> ((A!4 = B!3) | $true)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (((A!4 = B!3) | (A!4 = A!4)) <=> $true),
% 0.12/0.37 inference(transitivity,[status(thm)],[16, 14])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((member(A!4, unordered_pair(A!4, B!3)) <=> ((A!4 = B!3) | (A!4 = A!4))) <=> (member(A!4, unordered_pair(A!4, B!3)) <=> $true)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ((member(A!4, unordered_pair(A!4, B!3)) <=> ((A!4 = B!3) | (A!4 = A!4))) <=> member(A!4, unordered_pair(A!4, B!3))),
% 0.12/0.37 inference(transitivity,[status(thm)],[18, 13])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!4, unordered_pair(A!4, B!3)) <=> ((A!4 = B!3) | (A!4 = A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!4, unordered_pair(A!4, B!3)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!4, unordered_pair(A!4, B!3)) <=> ((A!4 = B!3) | (A!4 = A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!4, unordered_pair(A!4, B!3)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[20, 12])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!4, unordered_pair(A!4, B!3)) <=> ((A!4 = B!3) | (A!4 = A!4)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!4, unordered_pair(A!4, B!3))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[23, 11, 1])).
% 0.12/0.37 tff(25,plain,(member(A!4, unordered_pair(A!4, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (^[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))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (^[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))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[29, 27])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (^[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)))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(34,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')).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.37 tff(36,plain,(
% 0.12/0.37 ![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)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[35])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (((~![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(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(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(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3))))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((~((~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))))))) | (~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))))) <=> (~((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3)))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(41,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)))))))) | (~((~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))))))) | (~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), 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(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3))))))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[40])).
% 0.12/0.38 tff(42,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)))))))) | (~((~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))))))) | (~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), 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(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3))))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[41, 39])).
% 0.12/0.38 tff(43,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)))))))) | (~((~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))))))) | (~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(44,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)))))))) | (~((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3)))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (~((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3))))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 38])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))), unordered_pair(A!4, B!3)))))))) | (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.39 tff(58,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.39 tff(61,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, sum(unordered_pair(A!4, B!3)))))) | (~(subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (~((~((~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, sum(unordered_pair(A!4, B!3)))))) | (~(subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (((~((~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, sum(unordered_pair(A!4, B!3)))))) | (~(subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))))))) | (subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.39 tff(68,assumption,((~((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | ![X: $i] : ((~member(X, sum(unordered_pair(A!4, B!3)))) | member(X, union(A!4, B!3))))) | (~(subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))))))), introduced(assumption)).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | ![X: $i] : ((~member(X, sum(unordered_pair(A!4, B!3)))) | member(X, union(A!4, B!3))))) | (~(subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[69, 63, 68])).
% 0.19/0.39 tff(71,plain,(~((~((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | ![X: $i] : ((~member(X, sum(unordered_pair(A!4, B!3)))) | member(X, union(A!4, B!3))))) | (~(subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (((~((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | ![X: $i] : ((~member(X, sum(unordered_pair(A!4, B!3)))) | member(X, union(A!4, B!3))))) | (~(subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))))))) | (subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)) <=> ((tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)) <=> ((tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 11])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (((~![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(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(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(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~((~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))))) <=> (~((~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (((~![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(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(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(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (((~![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(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(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(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((~![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(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~![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(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (~((~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 38])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (((~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)))))))) | ((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.40 tff(85,assumption,(~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)))), introduced(assumption)).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 ((~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))))))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[89, 84])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)))) | member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ((~(member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)) <=> ((tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4)))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3))) | ((tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~(member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)) <=> ((tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4)))) | ((tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[94, 75])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.41 tff(101,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')).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.19/0.41 tff(104,plain,(
% 0.19/0.41 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[103])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[108, 85])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)) | (~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)))) | (~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (~(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[111, 107])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~member(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))), unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[115, 90])).
% 0.19/0.41 tff(117,assumption,(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4), introduced(assumption)).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))) <=> member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4) <=> member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[118])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 ((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)) <=> (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[119])).
% 0.19/0.41 tff(121,assumption,(~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)), introduced(assumption)).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.41 tff(123,assumption,(member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))), introduced(assumption)).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.19/0.42 tff(125,plain,((~(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (~(tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[125, 116, 114])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 ((~((tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4))) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3) | (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = A!4)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))) = B!3),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[127, 126, 95])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))) <=> member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) <=> member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.42 inference(symmetry,[status(thm)],[129])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 ((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3)) <=> (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 ((member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), B!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[132, 112])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), tptp_fun_Y_1(unordered_pair(A!4, B!3), tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[133, 131])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[116, 134])).
% 0.19/0.42 tff(136,plain,((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 ((~(subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)))))) | subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((~(subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), sum(unordered_pair(A!4, B!3))), union(A!4, B!3)))))) | subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 73])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[142])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(145,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')).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.42 tff(147,plain,(
% 0.19/0.42 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[146])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))) <=> equal_set(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (~(((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))) <=> equal_set(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : equal_set(sum(unordered_pair(A, B)), union(A, B))) <=> (~![A: $i, B: $i] : equal_set(sum(unordered_pair(A, B)), union(A, B)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(153,axiom,(~![A: $i, B: $i] : equal_set(sum(unordered_pair(A, B)), union(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI40')).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (~![A: $i, B: $i] : equal_set(sum(unordered_pair(A, B)), union(A, B))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (~![A: $i, B: $i] : equal_set(sum(unordered_pair(A, B)), union(A, B))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[154, 152])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (~![A: $i, B: $i] : equal_set(sum(unordered_pair(A, B)), union(A, B))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[155, 152])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (~![A: $i, B: $i] : equal_set(sum(unordered_pair(A, B)), union(A, B))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.19/0.42 tff(158,plain,(
% 0.19/0.42 ~equal_set(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))),
% 0.19/0.42 inference(skolemize,[status(sab)],[157])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 ((((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))) <=> equal_set(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | ((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))) | equal_set(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 ((((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))) <=> equal_set(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | ((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 ((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[160, 151])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 ((~((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))))) | (~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 ((~subset(sum(unordered_pair(A!4, B!3)), union(A!4, B!3))) | (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (~subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[163, 139])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 ((~(subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))))))) | subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 ((~(subset(union(A!4, B!3), sum(unordered_pair(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))))))) | (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (~((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[166, 67])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y))))) | ![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[171, 47])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (((~![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))) | ((~member(A!4, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)))) <=> ((~![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))) | (~member(A!4, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 ((~![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))) | ((~member(A!4, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 ((~![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))) | (~member(A!4, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[175, 172, 25])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[177, 105])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), sum(unordered_pair(A!4, B!3)))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[179, 167])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3))) | (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)))) | (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[182, 178])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4))) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), A!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 (member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[185, 176])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (((~![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))) | ((~member(B!3, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3)))) <=> ((~![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))) | (~member(B!3, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 ((~![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))) | ((~member(B!3, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 ((~![Y: $i] : ((~member(Y, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), Y)))) | (~member(B!3, unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(sum(unordered_pair(A!4, B!3)), union(A!4, B!3)), B!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (~member(B!3, unordered_pair(A!4, B!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[189, 172, 186])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!3, unordered_pair(A!4, B!3))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!3, unordered_pair(A!4, B!3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 ((member(B!3, unordered_pair(A!4, B!3)) <=> $true) <=> member(B!3, unordered_pair(A!4, B!3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 (($true | (B!3 = A!4)) <=> $true),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 ((B!3 = B!3) <=> $true),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (((B!3 = B!3) | (B!3 = A!4)) <=> ($true | (B!3 = A!4))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[194])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (((B!3 = B!3) | (B!3 = A!4)) <=> $true),
% 0.19/0.43 inference(transitivity,[status(thm)],[195, 193])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 ((member(B!3, unordered_pair(A!4, B!3)) <=> ((B!3 = B!3) | (B!3 = A!4))) <=> (member(B!3, unordered_pair(A!4, B!3)) <=> $true)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[196])).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 ((member(B!3, unordered_pair(A!4, B!3)) <=> ((B!3 = B!3) | (B!3 = A!4))) <=> member(B!3, unordered_pair(A!4, B!3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[197, 192])).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(B!3, unordered_pair(A!4, B!3)) <=> ((B!3 = B!3) | (B!3 = A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!3, unordered_pair(A!4, B!3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[198])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(B!3, unordered_pair(A!4, B!3)) <=> ((B!3 = B!3) | (B!3 = A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!3, unordered_pair(A!4, B!3)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[199, 191])).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(B!3, unordered_pair(A!4, B!3)) <=> ((B!3 = B!3) | (B!3 = A!4)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!3, unordered_pair(A!4, B!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[202, 11, 190])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------