%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET014+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:24:47 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET014+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 04:01:18 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(member_type, type, (
% 0.13/0.39 member: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_X_4_type, type, (
% 0.13/0.39 tptp_fun_X_4: $i)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.39 tptp_fun_Y_3: $i)).
% 0.13/0.39 tff(tptp_fun_A_5_type, type, (
% 0.13/0.39 tptp_fun_A_5: $i)).
% 0.13/0.39 tff(union_type, type, (
% 0.13/0.39 union: ( $i * $i ) > $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (^[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)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.40 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.13/0.40 tff(14,plain,(
% 0.13/0.40 ![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)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~![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(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5)))) | (~(subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (~((~((~subset(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5)))) | (~(subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (((~((~subset(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5)))) | (~(subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5)))))) | (subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.40 tff(21,assumption,((~((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))) | (~(subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)))))), introduced(assumption)).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((~![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(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))) | (~(subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.13/0.40 tff(24,plain,(~((~((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))) | (~(subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5))))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (((~((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))) | (~(subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)))))) | (subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.40 tff(27,assumption,(~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5))), introduced(assumption)).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)) | (~member(tptp_fun_X_0(A!5, X!4), A!5))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (~member(tptp_fun_X_0(A!5, X!4), A!5)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)) | member(tptp_fun_X_0(A!5, X!4), X!4)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (member(tptp_fun_X_0(A!5, X!4), X!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((member(tptp_fun_X_0(A!5, X!4), Y!3) | member(tptp_fun_X_0(A!5, X!4), X!4)) | (~member(tptp_fun_X_0(A!5, X!4), X!4))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (member(tptp_fun_X_0(A!5, X!4), Y!3) | member(tptp_fun_X_0(A!5, X!4), X!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.40 tff(34,assumption,(~(member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, X!4), Y!3) | member(tptp_fun_X_0(A!5, X!4), X!4)))), introduced(assumption)).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.13/0.40 tff(40,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.13/0.40 tff(43,plain,(
% 0.13/0.40 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[42])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, X!4), Y!3) | member(tptp_fun_X_0(A!5, X!4), X!4)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[45, 44, 34])).
% 0.13/0.40 tff(47,plain,(member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, X!4), Y!3) | member(tptp_fun_X_0(A!5, X!4), X!4))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 ((~(member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, X!4), Y!3) | member(tptp_fun_X_0(A!5, X!4), X!4)))) | member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3)) | (~(member(tptp_fun_X_0(A!5, X!4), Y!3) | member(tptp_fun_X_0(A!5, X!4), X!4)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3)) | (~(member(tptp_fun_X_0(A!5, X!4), Y!3) | member(tptp_fun_X_0(A!5, X!4), X!4)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[49, 33])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[51, 44])).
% 0.13/0.40 tff(53,assumption,(~subset(union(X!4, Y!3), A!5)), introduced(assumption)).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 ((~![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(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5)))) | (~(subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (~((~((~subset(union(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5)))) | (~(subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 16])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (((~((~subset(union(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5)))) | (~(subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)))))) | (subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 ((~(subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))))) | subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[59, 53])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 ((~(member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)))) | (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 ((~(member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)))) | (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[64, 52])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (((~((~subset(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5)))) | (~(subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5)))))) | ((~subset(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 ((~subset(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[66, 18])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 ((~(~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5)))) <=> (((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 ((~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5))) <=> (~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (((~((~subset(X!4, A!5)) | (~subset(Y!3, A!5)))) <=> subset(union(X!4, Y!3), A!5)) <=> (~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 ((subset(X!4, A!5) & subset(Y!3, A!5)) <=> (~((~subset(X!4, A!5)) | (~subset(Y!3, A!5))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5)) <=> ((~((~subset(X!4, A!5)) | (~subset(Y!3, A!5)))) <=> subset(union(X!4, Y!3), A!5))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[71])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5)) <=> (~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[72, 70])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5)) <=> (~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[73, 69])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 ((~((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5))) <=> (~(~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[74])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 ((~((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5))) <=> (((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5))),
% 0.13/0.41 inference(transitivity,[status(thm)],[75, 68])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 ((~((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5))) <=> (~((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(78,plain,
% 0.13/0.41 ((~![A: $i, X: $i, Y: $i] : ((subset(X, A) & subset(Y, A)) <=> subset(union(X, Y), A))) <=> (~![A: $i, X: $i, Y: $i] : ((subset(X, A) & subset(Y, A)) <=> subset(union(X, Y), A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(79,axiom,(~![A: $i, X: $i, Y: $i] : ((subset(X, A) & subset(Y, A)) <=> subset(union(X, Y), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI45')).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (~![A: $i, X: $i, Y: $i] : ((subset(X, A) & subset(Y, A)) <=> subset(union(X, Y), A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (~![A: $i, X: $i, Y: $i] : ((subset(X, A) & subset(Y, A)) <=> subset(union(X, Y), A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[80, 78])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (~![A: $i, X: $i, Y: $i] : ((subset(X, A) & subset(Y, A)) <=> subset(union(X, Y), A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (~![A: $i, X: $i, Y: $i] : ((subset(X, A) & subset(Y, A)) <=> subset(union(X, Y), A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.21/0.41 tff(84,plain,(
% 0.21/0.41 ~((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5))),
% 0.21/0.41 inference(skolemize,[status(sab)],[83])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 (~((subset(X!4, A!5) & subset(Y!3, A!5)) <=> subset(union(X!4, Y!3), A!5))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[85, 76])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((~((~subset(X!4, A!5)) | (~subset(Y!3, A!5)))) | subset(union(X!4, Y!3), A!5) | (~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~((~subset(X!4, A!5)) | (~subset(Y!3, A!5)))) | subset(union(X!4, Y!3), A!5)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (~((~subset(X!4, A!5)) | (~subset(Y!3, A!5)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[88, 53])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) | subset(Y!3, A!5)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (subset(Y!3, A!5)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 ((~((~subset(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5)))) | (~subset(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 ((~((~subset(Y!3, A!5)) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5)))) | ![X: $i] : ((~member(X, Y!3)) | member(X, A!5))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 (![X: $i] : ((~member(X, Y!3)) | member(X, A!5))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[93, 67])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)) | (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[95, 60])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (((~![X: $i] : ((~member(X, Y!3)) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))) <=> ((~![X: $i] : ((~member(X, Y!3)) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 ((~![X: $i] : ((~member(X, Y!3)) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 ((~![X: $i] : ((~member(X, Y!3)) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[99, 96, 94])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 (~((~((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))) | (~(subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (((~((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))) | (~(subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)))))) | ((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 ((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) | subset(X!4, A!5)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (subset(X!4, A!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 89])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 ((~((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))) | (~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~((~subset(X!4, A!5)) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5)))) | ![X: $i] : ((~member(X, X!4)) | member(X, A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (![X: $i] : ((~member(X, X!4)) | member(X, A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[107, 103])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (((~![X: $i] : ((~member(X, X!4)) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))) <=> ((~![X: $i] : ((~member(X, X!4)) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 ((~![X: $i] : ((~member(X, X!4)) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 ((~![X: $i] : ((~member(X, X!4)) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[111, 96, 108])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 ((~(member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), Y!3) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), X!4)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[113, 112, 100, 65])).
% 0.21/0.42 tff(115,plain,(subset(union(X!4, Y!3), A!5)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (((~((~subset(union(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5)))) | (~(subset(union(X!4, Y!3), A!5) | (~((~member(tptp_fun_X_0(A!5, union(X!4, Y!3)), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, union(X!4, Y!3)), A!5)))))) | ((~subset(union(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 ((~subset(union(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[116, 55])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 ((~((~subset(union(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5)))) | (~subset(union(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 ((~subset(union(X!4, Y!3), A!5)) | ![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (((~![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, X!4), A!5))) <=> ((~![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, X!4), A!5))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 ((~![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, X!4), A!5))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 ((~![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, X!4), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, X!4), A!5)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[123, 120, 50, 29])).
% 0.21/0.42 tff(125,plain,((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ((~(subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5))))) | subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 ((~(subset(X!4, A!5) | (~((~member(tptp_fun_X_0(A!5, X!4), X!4)) | member(tptp_fun_X_0(A!5, X!4), A!5))))) | subset(X!4, A!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (subset(X!4, A!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[127, 26])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) | (~subset(union(X!4, Y!3), A!5)) | (~(((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) <=> subset(union(X!4, Y!3), A!5)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 (((~subset(X!4, A!5)) | (~subset(Y!3, A!5))) | (~subset(union(X!4, Y!3), A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[129, 86])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 ((~subset(X!4, A!5)) | (~subset(Y!3, A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[130, 115])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 ((~((~subset(X!4, A!5)) | (~subset(Y!3, A!5)))) | (~subset(X!4, A!5)) | (~subset(Y!3, A!5))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 ((~subset(X!4, A!5)) | (~subset(Y!3, A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 (~subset(Y!3, A!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[133, 128])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 ((~(subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5))))) | subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 ((~(subset(Y!3, A!5) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5))))) | (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 (~((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[136, 20])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5)) | member(tptp_fun_X_0(A!5, Y!3), Y!3)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 (member(tptp_fun_X_0(A!5, Y!3), Y!3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 ((member(tptp_fun_X_0(A!5, Y!3), Y!3) | member(tptp_fun_X_0(A!5, Y!3), X!4)) | (~member(tptp_fun_X_0(A!5, Y!3), Y!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 (member(tptp_fun_X_0(A!5, Y!3), Y!3) | member(tptp_fun_X_0(A!5, Y!3), X!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(A!5, Y!3), Y!3)) | member(tptp_fun_X_0(A!5, Y!3), A!5)) | (~member(tptp_fun_X_0(A!5, Y!3), A!5))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 (~member(tptp_fun_X_0(A!5, Y!3), A!5)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[142, 137])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 (((~![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, Y!3), A!5))) <=> ((~![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, Y!3), A!5))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(145,plain,
% 0.21/0.42 ((~![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, Y!3), A!5))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(146,plain,
% 0.21/0.42 ((~![X: $i] : ((~member(X, union(X!4, Y!3))) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3))) | member(tptp_fun_X_0(A!5, Y!3), A!5)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 (~member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[146, 120, 143])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 ((~(member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, Y!3), Y!3) | member(tptp_fun_X_0(A!5, Y!3), X!4)))) | member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3)) | (~(member(tptp_fun_X_0(A!5, Y!3), Y!3) | member(tptp_fun_X_0(A!5, Y!3), X!4)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 (~(member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, Y!3), Y!3) | member(tptp_fun_X_0(A!5, Y!3), X!4)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[148, 147, 141])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!5, Y!3), union(X!4, Y!3)) <=> (member(tptp_fun_X_0(A!5, Y!3), Y!3) | member(tptp_fun_X_0(A!5, Y!3), X!4)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[150, 44, 149])).
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------