%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET012+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:24:46 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET012+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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 04:00:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(difference_type, type, (
% 0.12/0.38 difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_A_4_type, type, (
% 0.12/0.38 tptp_fun_A_4: $i)).
% 0.12/0.38 tff(tptp_fun_E_3_type, type, (
% 0.12/0.38 tptp_fun_E_3: $i)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(equal_set_type, type, (
% 0.12/0.38 equal_set: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.38 tff(11,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')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.38 tff(14,plain,(
% 0.12/0.38 ![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)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![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)))))))) | (~((~((~subset(A!4, difference(E!3, difference(E!3, A!4)))) | ![X: $i] : ((~member(X, A!4)) | member(X, difference(E!3, difference(E!3, A!4)))))) | (~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~((~((~subset(A!4, difference(E!3, difference(E!3, A!4)))) | ![X: $i] : ((~member(X, A!4)) | member(X, difference(E!3, difference(E!3, A!4)))))) | (~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((~((~subset(A!4, difference(E!3, difference(E!3, A!4)))) | ![X: $i] : ((~member(X, A!4)) | member(X, difference(E!3, difference(E!3, A!4)))))) | (~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))))) | (subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,assumption,((~((~subset(difference(E!3, difference(E!3, A!4)), A!4)) | ![X: $i] : ((~member(X, difference(E!3, difference(E!3, A!4)))) | member(X, A!4)))) | (~(subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))))), introduced(assumption)).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![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)))))))) | (~((~((~subset(difference(E!3, difference(E!3, A!4)), A!4)) | ![X: $i] : ((~member(X, difference(E!3, difference(E!3, A!4)))) | member(X, A!4)))) | (~(subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.12/0.38 tff(24,plain,(~((~((~subset(difference(E!3, difference(E!3, A!4)), A!4)) | ![X: $i] : ((~member(X, difference(E!3, difference(E!3, A!4)))) | member(X, A!4)))) | (~(subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (((~((~subset(difference(E!3, difference(E!3, A!4)), A!4)) | ![X: $i] : ((~member(X, difference(E!3, difference(E!3, A!4)))) | member(X, A!4)))) | (~(subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))))) | (subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[B: $i, A: $i, E: $i] : refl((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (^[B: $i, A: $i, E: $i] : trans(trans(monotonicity(rewrite((member(B, E) & (~member(B, A))) <=> (~((~member(B, E)) | member(B, A)))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))), rewrite((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))), rewrite((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(32,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.39 tff(34,plain,(
% 0.12/0.39 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[33])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
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% 0.12/0.39 inference(tautology,[status(thm)],[])).
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% 0.12/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
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% 0.12/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
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% 0.12/0.39 inference(unit_resolution,[status(thm)],[62, 26])).
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% 0.12/0.39 inference(bind,[status(th)],[])).
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% 0.12/0.39 inference(bind,[status(th)],[])).
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% 0.12/0.39 inference(quant_intro,[status(thm)],[66])).
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% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(69,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')).
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% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(75,plain,
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% 0.12/0.39 inference(unit_resolution,[status(thm)],[74, 73])).
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% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(78,axiom,(~![A: $i, E: $i] : (subset(A, E) => equal_set(difference(E, difference(E, A)), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI23')).
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% 0.12/0.39 inference(modus_ponens,[status(thm)],[79, 76])).
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% 0.12/0.39 inference(or_elim,[status(thm)],[83])).
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% 0.12/0.39 inference(tautology,[status(thm)],[])).
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% 0.12/0.39 inference(unit_resolution,[status(thm)],[89, 63])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 ((~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))))) | subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 20])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))) <=> member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (~(((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))) <=> member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 36])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 93])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))) <=> member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))) | ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 ((((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))) <=> member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))) | ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[103, 99])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~![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(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (~((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[105, 16])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3)))))) | ((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (subset(A!4, E!3)),
% 0.19/0.40 inference(or_elim,[status(thm)],[83])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 ((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3))) <=> ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[115, 112, 95])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 ((~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[117, 116, 104])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 ((((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) <=> member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) <=> member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[119, 118, 97])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) <=> member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[121, 36, 120])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------