%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET687+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:26:09 AM UTC 2025
% Result : Theorem 0.21s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET687+4 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 05:42:20 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % SZS output start Proof
% 0.21/0.37 tff(subset_type, type, (
% 0.21/0.37 subset: ( $i * $i ) > $o)).
% 0.21/0.37 tff(tptp_fun_A_3_type, type, (
% 0.21/0.37 tptp_fun_A_3: $i)).
% 0.21/0.37 tff(member_type, type, (
% 0.21/0.37 member: ( $i * $i ) > $o)).
% 0.21/0.37 tff(tptp_fun_X_0_type, type, (
% 0.21/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.21/0.37 tff(1,plain,
% 0.21/0.37 ((~![A: $i] : subset(A, A)) <=> (~![A: $i] : subset(A, A))),
% 0.21/0.37 inference(rewrite,[status(thm)],[])).
% 0.21/0.37 tff(2,axiom,(~![A: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI01')).
% 0.21/0.37 tff(3,plain,
% 0.21/0.37 (~![A: $i] : subset(A, A)),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.37 tff(4,plain,
% 0.21/0.37 (~![A: $i] : subset(A, A)),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.21/0.37 tff(5,plain,
% 0.21/0.37 (~![A: $i] : subset(A, A)),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.37 tff(6,plain,
% 0.21/0.37 (~![A: $i] : subset(A, A)),
% 0.21/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.37 tff(7,plain,(
% 0.21/0.37 ~subset(A!3, A!3)),
% 0.21/0.37 inference(skolemize,[status(sab)],[6])).
% 0.21/0.37 tff(8,plain,
% 0.21/0.37 (^[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))))))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(9,plain,
% 0.21/0.37 (![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)))))))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.37 tff(10,plain,
% 0.21/0.37 (^[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))))))))),
% 0.21/0.37 inference(bind,[status(th)],[])).
% 0.21/0.37 tff(11,plain,
% 0.21/0.37 (![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)))))))),
% 0.21/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.37 tff(12,plain,
% 0.21/0.37 (![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)))))))),
% 0.21/0.37 inference(transitivity,[status(thm)],[11, 9])).
% 0.21/0.37 tff(13,plain,
% 0.21/0.37 (^[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)))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (![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)))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.38 tff(18,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')).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.38 tff(21,plain,(
% 0.21/0.38 ![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)))))),
% 0.21/0.38 inference(skolemize,[status(sab)],[20])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (![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)))))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (![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)))))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (((~![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!3, A!3)) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(A!3, A!3))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 ((~(~subset(A!3, A!3))) <=> subset(A!3, A!3)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (($false | (~subset(A!3, A!3))) <=> (~subset(A!3, A!3))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 ((~(subset(A!3, A!3) | (~((~member(tptp_fun_X_0(A!3, A!3), A!3)) | member(tptp_fun_X_0(A!3, A!3), A!3))))) <=> (~subset(A!3, A!3))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(28,plain,
% 0.21/0.38 ((~$true) <=> $false),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (((~subset(A!3, A!3)) | $true) <=> $true),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 (![X: $i] : $true <=> $true),
% 0.21/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 (![X: $i] : $true <=> ![X: $i] : $true),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 (![X: $i] : $true <=> $true),
% 0.21/0.38 inference(transitivity,[status(thm)],[31, 30])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (^[X: $i] : rewrite(((~member(X, A!3)) | member(X, A!3)) <=> $true)),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (![X: $i] : ((~member(X, A!3)) | member(X, A!3)) <=> ![X: $i] : $true),
% 0.21/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 (![X: $i] : ((~member(X, A!3)) | member(X, A!3)) <=> $true),
% 0.21/0.38 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 (((~subset(A!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3))) <=> ((~subset(A!3, A!3)) | $true)),
% 0.21/0.38 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 (((~subset(A!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3))) <=> $true),
% 0.21/0.38 inference(transitivity,[status(thm)],[36, 29])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 ((~((~subset(A!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) <=> (~$true)),
% 0.21/0.38 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.38 tff(39,plain,
% 0.21/0.38 ((~((~subset(A!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) <=> $false),
% 0.21/0.38 inference(transitivity,[status(thm)],[38, 28])).
% 0.21/0.38 tff(40,plain,
% 0.21/0.38 (((~((~subset(A!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) | (~(subset(A!3, A!3) | (~((~member(tptp_fun_X_0(A!3, A!3), A!3)) | member(tptp_fun_X_0(A!3, A!3), A!3)))))) <=> ($false | (~subset(A!3, A!3)))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[39, 27])).
% 0.21/0.38 tff(41,plain,
% 0.21/0.38 (((~((~subset(A!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) | (~(subset(A!3, A!3) | (~((~member(tptp_fun_X_0(A!3, A!3), A!3)) | member(tptp_fun_X_0(A!3, A!3), A!3)))))) <=> (~subset(A!3, A!3))),
% 0.21/0.38 inference(transitivity,[status(thm)],[40, 26])).
% 0.21/0.38 tff(42,plain,
% 0.21/0.38 ((~((~((~subset(A!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) | (~(subset(A!3, A!3) | (~((~member(tptp_fun_X_0(A!3, A!3), A!3)) | member(tptp_fun_X_0(A!3, A!3), A!3))))))) <=> (~(~subset(A!3, A!3)))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.38 tff(43,plain,
% 0.21/0.38 ((~((~((~subset(A!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) | (~(subset(A!3, A!3) | (~((~member(tptp_fun_X_0(A!3, A!3), A!3)) | member(tptp_fun_X_0(A!3, A!3), A!3))))))) <=> subset(A!3, A!3)),
% 0.21/0.38 inference(transitivity,[status(thm)],[42, 25])).
% 0.21/0.38 tff(44,plain,
% 0.21/0.38 (((~![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!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) | (~(subset(A!3, A!3) | (~((~member(tptp_fun_X_0(A!3, A!3), A!3)) | member(tptp_fun_X_0(A!3, A!3), A!3)))))))) <=> ((~![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!3, A!3))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.38 tff(45,plain,
% 0.21/0.38 (((~![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!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) | (~(subset(A!3, A!3) | (~((~member(tptp_fun_X_0(A!3, A!3), A!3)) | member(tptp_fun_X_0(A!3, A!3), A!3)))))))) <=> ((~![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!3, A!3))),
% 0.21/0.38 inference(transitivity,[status(thm)],[44, 24])).
% 0.21/0.38 tff(46,plain,
% 0.21/0.38 ((~![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!3, A!3)) | ![X: $i] : ((~member(X, A!3)) | member(X, A!3)))) | (~(subset(A!3, A!3) | (~((~member(tptp_fun_X_0(A!3, A!3), A!3)) | member(tptp_fun_X_0(A!3, A!3), A!3)))))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | subset(A!3, A!3)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.38 tff(48,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[47, 23, 7])).
% 0.21/0.38 % SZS output end Proof
% 0.21/0.38 % E exiting
%------------------------------------------------------------------------------