%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU354+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:41 AM UTC 2025
% Result : Theorem 1.83s 2.00s
% Output : Proof 1.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU354+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 06:50:25 EDT 2025
% 0.13/0.33 % CPUTime :
% 1.83/2.00 % SZS status Theorem
% 1.83/2.00 % SZS output start Proof
% 1.83/2.00 tff(union_type, type, (
% 1.83/2.00 union: $i > $i)).
% 1.83/2.00 tff(powerset_type, type, (
% 1.83/2.00 powerset: $i > $i)).
% 1.83/2.00 tff(tptp_fun_A_6_type, type, (
% 1.83/2.00 tptp_fun_A_6: $i)).
% 1.83/2.00 tff(tptp_fun_B_5_type, type, (
% 1.83/2.00 tptp_fun_B_5: $i)).
% 1.83/2.00 tff(proper_element_type, type, (
% 1.83/2.00 proper_element: ( $i * $i ) > $o)).
% 1.83/2.00 tff(element_type, type, (
% 1.83/2.00 element: ( $i * $i ) > $o)).
% 1.83/2.00 tff(1,plain,
% 1.83/2.00 (![A: $i] : (union(powerset(A)) = A) <=> ![A: $i] : (union(powerset(A)) = A)),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(2,plain,
% 1.83/2.00 (![A: $i] : (union(powerset(A)) = A) <=> ![A: $i] : (union(powerset(A)) = A)),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(3,axiom,(![A: $i] : (union(powerset(A)) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t99_zfmisc_1')).
% 1.83/2.00 tff(4,plain,
% 1.83/2.00 (![A: $i] : (union(powerset(A)) = A)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[3, 2])).
% 1.83/2.00 tff(5,plain,(
% 1.83/2.00 ![A: $i] : (union(powerset(A)) = A)),
% 1.83/2.00 inference(skolemize,[status(sab)],[4])).
% 1.83/2.00 tff(6,plain,
% 1.83/2.00 (![A: $i] : (union(powerset(A)) = A)),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[5, 1])).
% 1.83/2.00 tff(7,plain,
% 1.83/2.00 ((~![A: $i] : (union(powerset(A)) = A)) | (union(powerset(A!6)) = A!6)),
% 1.83/2.00 inference(quant_inst,[status(thm)],[])).
% 1.83/2.00 tff(8,plain,
% 1.83/2.00 (union(powerset(A!6)) = A!6),
% 1.83/2.00 inference(unit_resolution,[status(thm)],[7, 6])).
% 1.83/2.00 tff(9,plain,
% 1.83/2.00 ((B!5 = union(powerset(A!6))) <=> (B!5 = A!6)),
% 1.83/2.00 inference(monotonicity,[status(thm)],[8])).
% 1.83/2.00 tff(10,plain,
% 1.83/2.00 ((B!5 = A!6) <=> (B!5 = union(powerset(A!6)))),
% 1.83/2.00 inference(symmetry,[status(thm)],[9])).
% 1.83/2.00 tff(11,plain,
% 1.83/2.00 ((~(B!5 = A!6)) <=> (~(B!5 = union(powerset(A!6))))),
% 1.83/2.00 inference(monotonicity,[status(thm)],[10])).
% 1.83/2.00 tff(12,assumption,(~proper_element(B!5, powerset(A!6))), introduced(assumption)).
% 1.83/2.00 tff(13,plain,
% 1.83/2.00 (((~element(B!5, powerset(A!6))) | (~((B!5 = A!6) <=> proper_element(B!5, powerset(A!6))))) <=> ((~element(B!5, powerset(A!6))) | (~((B!5 = A!6) <=> proper_element(B!5, powerset(A!6)))))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(14,plain,
% 1.83/2.00 ((~((~element(B!5, powerset(A!6))) | (~((B!5 = A!6) <=> proper_element(B!5, powerset(A!6)))))) <=> (~((~element(B!5, powerset(A!6))) | (~((B!5 = A!6) <=> proper_element(B!5, powerset(A!6))))))),
% 1.83/2.00 inference(monotonicity,[status(thm)],[13])).
% 1.83/2.00 tff(15,plain,
% 1.83/2.00 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (~((B = A) <=> proper_element(B, powerset(A)))))) <=> (~![A: $i, B: $i] : ((~element(B, powerset(A))) | (~((B = A) <=> proper_element(B, powerset(A))))))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(16,plain,
% 1.83/2.00 ((~![A: $i, B: $i] : (element(B, powerset(A)) => (proper_element(B, powerset(A)) <=> (~(B = A))))) <=> (~![A: $i, B: $i] : ((~element(B, powerset(A))) | (~((B = A) <=> proper_element(B, powerset(A))))))),
% 1.83/2.00 inference(rewrite,[status(thm)],[])).
% 1.83/2.00 tff(17,axiom,(~![A: $i, B: $i] : (element(B, powerset(A)) => (proper_element(B, powerset(A)) <=> (~(B = A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_tex_2')).
% 1.83/2.00 tff(18,plain,
% 1.83/2.00 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | (~((B = A) <=> proper_element(B, powerset(A)))))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.83/2.00 tff(19,plain,
% 1.83/2.00 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | (~((B = A) <=> proper_element(B, powerset(A)))))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[18, 15])).
% 1.83/2.00 tff(20,plain,
% 1.83/2.00 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | (~((B = A) <=> proper_element(B, powerset(A)))))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.83/2.00 tff(21,plain,
% 1.83/2.00 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | (~((B = A) <=> proper_element(B, powerset(A)))))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[20, 15])).
% 1.83/2.00 tff(22,plain,(
% 1.83/2.00 ~((~element(B!5, powerset(A!6))) | (~((B!5 = A!6) <=> proper_element(B!5, powerset(A!6)))))),
% 1.83/2.00 inference(skolemize,[status(sab)],[21])).
% 1.83/2.00 tff(23,plain,
% 1.83/2.00 (~((~element(B!5, powerset(A!6))) | (~((B!5 = A!6) <=> proper_element(B!5, powerset(A!6)))))),
% 1.83/2.00 inference(modus_ponens,[status(thm)],[22, 14])).
% 1.83/2.00 tff(24,plain,
% 1.83/2.00 ((B!5 = A!6) <=> proper_element(B!5, powerset(A!6))),
% 1.83/2.00 inference(or_elim,[status(thm)],[23])).
% 1.83/2.01 tff(25,plain,
% 1.83/2.01 ((~(B!5 = A!6)) | proper_element(B!5, powerset(A!6)) | (~((B!5 = A!6) <=> proper_element(B!5, powerset(A!6))))),
% 1.83/2.01 inference(tautology,[status(thm)],[])).
% 1.83/2.01 tff(26,plain,
% 1.83/2.01 ((~(B!5 = A!6)) | proper_element(B!5, powerset(A!6))),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[25, 24])).
% 1.83/2.01 tff(27,plain,
% 1.83/2.01 (~(B!5 = A!6)),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[26, 12])).
% 1.83/2.01 tff(28,plain,
% 1.83/2.01 (~(B!5 = union(powerset(A!6)))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[27, 11])).
% 1.83/2.01 tff(29,plain,
% 1.83/2.01 (element(B!5, powerset(A!6))),
% 1.83/2.01 inference(or_elim,[status(thm)],[23])).
% 1.83/2.01 tff(30,plain,
% 1.83/2.01 (^[A: $i, B: $i] : refl(((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A)))) <=> ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A)))))),
% 1.83/2.01 inference(bind,[status(th)],[])).
% 1.83/2.01 tff(31,plain,
% 1.83/2.01 (![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A)))) <=> ![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))),
% 1.83/2.01 inference(quant_intro,[status(thm)],[30])).
% 1.83/2.01 tff(32,plain,
% 1.83/2.01 (![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A)))) <=> ![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(33,plain,
% 1.83/2.01 (^[A: $i, B: $i] : trans(monotonicity(trans(rewrite((proper_element(B, A) <=> (~(B = union(A)))) <=> (~((B = union(A)) <=> proper_element(B, A)))), rewrite((~((B = union(A)) <=> proper_element(B, A))) <=> (~((B = union(A)) <=> proper_element(B, A)))), ((proper_element(B, A) <=> (~(B = union(A)))) <=> (~((B = union(A)) <=> proper_element(B, A))))), ((element(B, A) => (proper_element(B, A) <=> (~(B = union(A))))) <=> (element(B, A) => (~((B = union(A)) <=> proper_element(B, A)))))), rewrite((element(B, A) => (~((B = union(A)) <=> proper_element(B, A)))) <=> ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))), ((element(B, A) => (proper_element(B, A) <=> (~(B = union(A))))) <=> ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))))),
% 1.83/2.01 inference(bind,[status(th)],[])).
% 1.83/2.01 tff(34,plain,
% 1.83/2.01 (![A: $i, B: $i] : (element(B, A) => (proper_element(B, A) <=> (~(B = union(A))))) <=> ![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))),
% 1.83/2.01 inference(quant_intro,[status(thm)],[33])).
% 1.83/2.01 tff(35,axiom,(![A: $i, B: $i] : (element(B, A) => (proper_element(B, A) <=> (~(B = union(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tex_2')).
% 1.83/2.01 tff(36,plain,
% 1.83/2.01 (![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.83/2.01 tff(37,plain,
% 1.83/2.01 (![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[36, 32])).
% 1.83/2.01 tff(38,plain,(
% 1.83/2.01 ![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))),
% 1.83/2.01 inference(skolemize,[status(sab)],[37])).
% 1.83/2.01 tff(39,plain,
% 1.83/2.01 (![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[38, 31])).
% 1.83/2.01 tff(40,plain,
% 1.83/2.01 (((~![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))) | ((~element(B!5, powerset(A!6))) | (~((B!5 = union(powerset(A!6))) <=> proper_element(B!5, powerset(A!6)))))) <=> ((~![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))) | (~element(B!5, powerset(A!6))) | (~((B!5 = union(powerset(A!6))) <=> proper_element(B!5, powerset(A!6)))))),
% 1.83/2.01 inference(rewrite,[status(thm)],[])).
% 1.83/2.01 tff(41,plain,
% 1.83/2.01 ((~![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))) | ((~element(B!5, powerset(A!6))) | (~((B!5 = union(powerset(A!6))) <=> proper_element(B!5, powerset(A!6)))))),
% 1.83/2.01 inference(quant_inst,[status(thm)],[])).
% 1.83/2.01 tff(42,plain,
% 1.83/2.01 ((~![A: $i, B: $i] : ((~element(B, A)) | (~((B = union(A)) <=> proper_element(B, A))))) | (~element(B!5, powerset(A!6))) | (~((B!5 = union(powerset(A!6))) <=> proper_element(B!5, powerset(A!6))))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.83/2.01 tff(43,plain,
% 1.83/2.01 (~((B!5 = union(powerset(A!6))) <=> proper_element(B!5, powerset(A!6)))),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[42, 39, 29])).
% 1.83/2.01 tff(44,plain,
% 1.83/2.01 (((B!5 = union(powerset(A!6))) <=> proper_element(B!5, powerset(A!6))) | (B!5 = union(powerset(A!6))) | proper_element(B!5, powerset(A!6))),
% 1.83/2.01 inference(tautology,[status(thm)],[])).
% 1.83/2.01 tff(45,plain,
% 1.83/2.01 ((B!5 = union(powerset(A!6))) | proper_element(B!5, powerset(A!6))),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[44, 43])).
% 1.83/2.01 tff(46,plain,
% 1.83/2.01 (B!5 = union(powerset(A!6))),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[45, 12])).
% 1.83/2.01 tff(47,plain,
% 1.83/2.01 ($false),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[46, 28])).
% 1.83/2.01 tff(48,plain,(proper_element(B!5, powerset(A!6))), inference(lemma,lemma(discharge,[]))).
% 1.83/2.01 tff(49,plain,
% 1.83/2.01 ((B!5 = A!6) | (~proper_element(B!5, powerset(A!6))) | (~((B!5 = A!6) <=> proper_element(B!5, powerset(A!6))))),
% 1.83/2.01 inference(tautology,[status(thm)],[])).
% 1.83/2.01 tff(50,plain,
% 1.83/2.01 ((B!5 = A!6) | (~proper_element(B!5, powerset(A!6)))),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[49, 24])).
% 1.83/2.01 tff(51,plain,
% 1.83/2.01 (B!5 = A!6),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[50, 48])).
% 1.83/2.01 tff(52,plain,
% 1.83/2.01 (B!5 = union(powerset(A!6))),
% 1.83/2.01 inference(modus_ponens,[status(thm)],[51, 10])).
% 1.83/2.01 tff(53,plain,
% 1.83/2.01 (((B!5 = union(powerset(A!6))) <=> proper_element(B!5, powerset(A!6))) | (~(B!5 = union(powerset(A!6)))) | (~proper_element(B!5, powerset(A!6)))),
% 1.83/2.01 inference(tautology,[status(thm)],[])).
% 1.83/2.01 tff(54,plain,
% 1.83/2.01 ((~(B!5 = union(powerset(A!6)))) | (~proper_element(B!5, powerset(A!6)))),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[53, 43])).
% 1.83/2.01 tff(55,plain,
% 1.83/2.01 (~(B!5 = union(powerset(A!6)))),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[54, 48])).
% 1.83/2.01 tff(56,plain,
% 1.83/2.01 ($false),
% 1.83/2.01 inference(unit_resolution,[status(thm)],[55, 52])).
% 1.83/2.01 % SZS output end Proof
% 1.83/2.02 % E exiting
%------------------------------------------------------------------------------