%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET062+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:25:02 AM UTC 2025
% Result : Theorem 0.23s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET062+4 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 04:10:26 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.40 % SZS status Theorem
% 0.23/0.40 % SZS output start Proof
% 0.23/0.40 tff(member_type, type, (
% 0.23/0.40 member: ( $i * $i ) > $o)).
% 0.23/0.40 tff(empty_set_type, type, (
% 0.23/0.40 empty_set: $i)).
% 0.23/0.40 tff(tptp_fun_X_0_type, type, (
% 0.23/0.40 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.23/0.40 tff(tptp_fun_A_3_type, type, (
% 0.23/0.40 tptp_fun_A_3: $i)).
% 0.23/0.40 tff(subset_type, type, (
% 0.23/0.40 subset: ( $i * $i ) > $o)).
% 0.23/0.40 tff(1,plain,
% 0.23/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(2,plain,
% 0.23/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.40 tff(3,plain,
% 0.23/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(4,plain,
% 0.23/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.40 tff(5,plain,
% 0.23/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.23/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.23/0.40 tff(6,plain,
% 0.23/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(7,plain,
% 0.23/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.23/0.40 tff(8,plain,
% 0.23/0.40 (![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)))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(9,plain,
% 0.23/0.40 (^[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))))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(10,plain,
% 0.23/0.40 (![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)))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.23/0.40 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')).
% 0.23/0.40 tff(12,plain,
% 0.23/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.23/0.40 tff(13,plain,
% 0.23/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.23/0.40 tff(14,plain,(
% 0.23/0.40 ![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)))))),
% 0.23/0.40 inference(skolemize,[status(sab)],[13])).
% 0.23/0.40 tff(15,plain,
% 0.23/0.40 (![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)))))))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.23/0.40 tff(16,plain,
% 0.23/0.40 (![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)))))))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.23/0.40 tff(17,plain,
% 0.23/0.40 ((~![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(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))))),
% 0.23/0.40 inference(quant_inst,[status(thm)],[])).
% 0.23/0.40 tff(18,plain,
% 0.23/0.40 (~((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))))),
% 0.23/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.23/0.40 tff(19,plain,
% 0.23/0.40 (((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))) | (subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))),
% 0.23/0.40 inference(tautology,[status(thm)],[])).
% 0.23/0.40 tff(20,plain,
% 0.23/0.40 (subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.23/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.23/0.40 tff(21,plain,
% 0.23/0.40 ((~![A: $i] : subset(empty_set, A)) <=> (~![A: $i] : subset(empty_set, A))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(22,axiom,(~![A: $i] : subset(empty_set, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI15')).
% 0.23/0.40 tff(23,plain,
% 0.23/0.40 (~![A: $i] : subset(empty_set, A)),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.40 tff(24,plain,
% 0.23/0.40 (~![A: $i] : subset(empty_set, A)),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.23/0.40 tff(25,plain,
% 0.23/0.40 (~![A: $i] : subset(empty_set, A)),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.23/0.40 tff(26,plain,
% 0.23/0.40 (~![A: $i] : subset(empty_set, A)),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.23/0.40 tff(27,plain,(
% 0.23/0.40 ~subset(empty_set, A!3)),
% 0.23/0.40 inference(skolemize,[status(sab)],[26])).
% 0.23/0.40 tff(28,plain,
% 0.23/0.40 ((~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))) | subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.23/0.40 inference(tautology,[status(thm)],[])).
% 0.23/0.40 tff(29,plain,
% 0.23/0.40 ((~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.23/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.23/0.40 tff(30,plain,
% 0.23/0.40 (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))),
% 0.23/0.40 inference(unit_resolution,[status(thm)],[29, 20])).
% 0.23/0.40 tff(31,plain,
% 0.23/0.40 (((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)) | member(tptp_fun_X_0(A!3, empty_set), empty_set)),
% 0.23/0.40 inference(tautology,[status(thm)],[])).
% 0.23/0.40 tff(32,plain,
% 0.23/0.40 (member(tptp_fun_X_0(A!3, empty_set), empty_set)),
% 0.23/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.23/0.40 tff(33,plain,
% 0.23/0.40 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.23/0.40 inference(bind,[status(th)],[])).
% 0.23/0.40 tff(34,plain,
% 0.23/0.40 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.23/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.23/0.40 tff(35,plain,
% 0.23/0.40 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.23/0.40 inference(rewrite,[status(thm)],[])).
% 0.23/0.40 tff(36,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.23/0.40 tff(37,plain,
% 0.23/0.40 (![X: $i] : (~member(X, empty_set))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.23/0.40 tff(38,plain,(
% 0.23/0.40 ![X: $i] : (~member(X, empty_set))),
% 0.23/0.40 inference(skolemize,[status(sab)],[37])).
% 0.23/0.40 tff(39,plain,
% 0.23/0.40 (![X: $i] : (~member(X, empty_set))),
% 0.23/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.23/0.40 tff(40,plain,
% 0.23/0.40 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(A!3, empty_set), empty_set))),
% 0.23/0.40 inference(quant_inst,[status(thm)],[])).
% 0.23/0.40 tff(41,plain,
% 0.23/0.40 ($false),
% 0.23/0.40 inference(unit_resolution,[status(thm)],[40, 39, 32])).
% 0.23/0.40 % SZS output end Proof
% 0.23/0.40 % E exiting
%------------------------------------------------------------------------------