%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU230+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:27:19 AM UTC 2025
% Result : Theorem 0.90s 1.13s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU230+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 06:23:35 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.90/1.13 % SZS status Theorem
% 0.90/1.13 % SZS output start Proof
% 0.90/1.13 tff(subset_type, type, (
% 0.90/1.13 subset: ( $i * $i ) > $o)).
% 0.90/1.13 tff(set_union2_type, type, (
% 0.90/1.13 set_union2: ( $i * $i ) > $i)).
% 0.90/1.13 tff(tptp_fun_A_73_type, type, (
% 0.90/1.13 tptp_fun_A_73: $i)).
% 0.90/1.13 tff(singleton_type, type, (
% 0.90/1.13 singleton: $i > $i)).
% 0.90/1.13 tff(succ_type, type, (
% 0.90/1.13 succ: $i > $i)).
% 0.90/1.13 tff(in_type, type, (
% 0.90/1.13 in: ( $i * $i ) > $o)).
% 0.90/1.13 tff(1,plain,
% 0.90/1.13 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(2,plain,
% 0.90/1.13 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[1])).
% 0.90/1.13 tff(3,plain,
% 0.90/1.13 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(4,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.90/1.13 tff(5,plain,
% 0.90/1.13 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.90/1.13 tff(6,plain,(
% 0.90/1.13 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.90/1.13 inference(skolemize,[status(sab)],[5])).
% 0.90/1.13 tff(7,plain,
% 0.90/1.13 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.90/1.13 tff(8,plain,
% 0.90/1.13 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(A!73) = set_union2(A!73, singleton(A!73)))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(9,plain,
% 0.90/1.13 (succ(A!73) = set_union2(A!73, singleton(A!73))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.90/1.13 tff(10,plain,
% 0.90/1.13 (set_union2(A!73, singleton(A!73)) = succ(A!73)),
% 0.90/1.13 inference(symmetry,[status(thm)],[9])).
% 0.90/1.13 tff(11,plain,
% 0.90/1.13 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(12,plain,
% 0.90/1.13 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[11])).
% 0.90/1.13 tff(13,plain,
% 0.90/1.13 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(14,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.90/1.13 tff(15,plain,
% 0.90/1.13 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.90/1.13 tff(16,plain,(
% 0.90/1.13 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.90/1.13 inference(skolemize,[status(sab)],[15])).
% 0.90/1.13 tff(17,plain,
% 0.90/1.13 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.90/1.13 tff(18,plain,
% 0.90/1.13 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!73, singleton(A!73)) = set_union2(singleton(A!73), A!73))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(19,plain,
% 0.90/1.13 (set_union2(A!73, singleton(A!73)) = set_union2(singleton(A!73), A!73)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.90/1.13 tff(20,plain,
% 0.90/1.13 (set_union2(singleton(A!73), A!73) = set_union2(A!73, singleton(A!73))),
% 0.90/1.13 inference(symmetry,[status(thm)],[19])).
% 0.90/1.13 tff(21,plain,
% 0.90/1.13 (set_union2(singleton(A!73), A!73) = succ(A!73)),
% 0.90/1.13 inference(transitivity,[status(thm)],[20, 10])).
% 0.90/1.13 tff(22,plain,
% 0.90/1.13 (subset(singleton(A!73), set_union2(singleton(A!73), A!73)) <=> subset(singleton(A!73), succ(A!73))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[21])).
% 0.90/1.13 tff(23,plain,
% 0.90/1.13 (subset(singleton(A!73), succ(A!73)) <=> subset(singleton(A!73), set_union2(singleton(A!73), A!73))),
% 0.90/1.13 inference(symmetry,[status(thm)],[22])).
% 0.90/1.13 tff(24,plain,
% 0.90/1.13 ((~subset(singleton(A!73), succ(A!73))) <=> (~subset(singleton(A!73), set_union2(singleton(A!73), A!73)))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[23])).
% 0.90/1.13 tff(25,plain,
% 0.90/1.13 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.14 tff(26,plain,
% 0.90/1.14 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.90/1.14 inference(quant_intro,[status(thm)],[25])).
% 0.90/1.14 tff(27,plain,
% 0.90/1.14 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(28,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.90/1.14 tff(29,plain,
% 0.90/1.14 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.90/1.14 tff(30,plain,(
% 0.90/1.14 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.90/1.14 inference(skolemize,[status(sab)],[29])).
% 0.90/1.14 tff(31,plain,
% 0.90/1.14 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.90/1.14 tff(32,plain,
% 0.90/1.14 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(A!73), succ(A!73)) <=> in(A!73, succ(A!73)))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(33,plain,
% 0.90/1.14 (subset(singleton(A!73), succ(A!73)) <=> in(A!73, succ(A!73))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.90/1.14 tff(34,plain,
% 0.90/1.14 ((~![A: $i] : in(A, succ(A))) <=> (~![A: $i] : in(A, succ(A)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(35,axiom,(~![A: $i] : in(A, succ(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_ordinal1')).
% 0.90/1.14 tff(36,plain,
% 0.90/1.14 (~![A: $i] : in(A, succ(A))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.90/1.14 tff(37,plain,
% 0.90/1.14 (~![A: $i] : in(A, succ(A))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.90/1.14 tff(38,plain,
% 0.90/1.14 (~![A: $i] : in(A, succ(A))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.90/1.14 tff(39,plain,
% 0.90/1.14 (~![A: $i] : in(A, succ(A))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.90/1.14 tff(40,plain,(
% 0.90/1.14 ~in(A!73, succ(A!73))),
% 0.90/1.14 inference(skolemize,[status(sab)],[39])).
% 0.90/1.14 tff(41,plain,
% 0.90/1.14 ((~(subset(singleton(A!73), succ(A!73)) <=> in(A!73, succ(A!73)))) | (~subset(singleton(A!73), succ(A!73))) | in(A!73, succ(A!73))),
% 0.90/1.14 inference(tautology,[status(thm)],[])).
% 0.90/1.14 tff(42,plain,
% 0.90/1.14 ((~(subset(singleton(A!73), succ(A!73)) <=> in(A!73, succ(A!73)))) | (~subset(singleton(A!73), succ(A!73)))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.90/1.14 tff(43,plain,
% 0.90/1.14 (~subset(singleton(A!73), succ(A!73))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[42, 33])).
% 0.90/1.14 tff(44,plain,
% 0.90/1.14 (~subset(singleton(A!73), set_union2(singleton(A!73), A!73))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[43, 24])).
% 0.90/1.14 tff(45,plain,
% 0.90/1.14 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 0.90/1.14 inference(bind,[status(th)],[])).
% 0.90/1.14 tff(46,plain,
% 0.90/1.14 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.90/1.14 inference(quant_intro,[status(thm)],[45])).
% 0.90/1.14 tff(47,plain,
% 0.90/1.14 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(48,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.90/1.14 tff(49,plain,
% 0.90/1.14 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.90/1.14 tff(50,plain,(
% 0.90/1.14 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.90/1.14 inference(skolemize,[status(sab)],[49])).
% 0.90/1.14 tff(51,plain,
% 0.90/1.14 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.90/1.14 tff(52,plain,
% 0.90/1.14 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(singleton(A!73), set_union2(singleton(A!73), A!73))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(53,plain,
% 0.90/1.14 (subset(singleton(A!73), set_union2(singleton(A!73), A!73))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.90/1.14 tff(54,plain,
% 0.90/1.14 ($false),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[53, 44])).
% 0.90/1.14 % SZS output end Proof
% 0.90/1.15 % E exiting
%------------------------------------------------------------------------------