%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET987+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:26:45 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET987+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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 05:56:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(tptp_fun_B_2_type, type, (
% 0.19/0.37 tptp_fun_B_2: $i)).
% 0.19/0.37 tff(set_difference_type, type, (
% 0.19/0.37 set_difference: ( $i * $i ) > $i)).
% 0.19/0.37 tff(singleton_type, type, (
% 0.19/0.37 singleton: $i > $i)).
% 0.19/0.37 tff(tptp_fun_A_3_type, type, (
% 0.19/0.37 tptp_fun_A_3: $i)).
% 0.19/0.37 tff(set_union2_type, type, (
% 0.19/0.37 set_union2: ( $i * $i ) > $i)).
% 0.19/0.37 tff(in_type, type, (
% 0.19/0.37 in: ( $i * $i ) > $o)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[A: $i, B: $i] : refl((set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,axiom,(![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t40_xboole_1')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,(
% 0.19/0.37 ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.19/0.37 inference(skolemize,[status(sab)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) | (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = set_difference(B!2, singleton(A!3)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = set_difference(B!2, singleton(A!3))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ((set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2) <=> (set_difference(B!2, singleton(A!3)) = B!2)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ((set_difference(B!2, singleton(A!3)) = B!2) <=> (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2)),
% 0.19/0.37 inference(symmetry,[status(thm)],[10])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (^[A: $i, B: $i] : refl((~(in(B, A) <=> (set_difference(A, singleton(B)) = A))) <=> (~(in(B, A) <=> (set_difference(A, singleton(B)) = A))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A))) <=> ![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A))) <=> ![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (^[A: $i, B: $i] : trans(rewrite(((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))), rewrite((~(in(B, A) <=> (set_difference(A, singleton(B)) = A))) <=> (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))), (((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A))) <=> ![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.37 tff(17,axiom,(![A: $i, B: $i] : ((set_difference(A, singleton(B)) = A) <=> (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_zfmisc_1')).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.37 tff(20,plain,(
% 0.19/0.37 ![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[19])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (~(in(B, A) <=> (set_difference(A, singleton(B)) = A)))) | (~(in(A!3, B!2) <=> (set_difference(B!2, singleton(A!3)) = B!2)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (~(in(A!3, B!2) <=> (set_difference(B!2, singleton(A!3)) = B!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))) <=> (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : ((~in(A, B)) => (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))) <=> (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(26,axiom,(~![A: $i, B: $i] : ((~in(A, B)) => (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t141_zfmisc_1')).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (~![A: $i, B: $i] : (in(A, B) | (set_difference(set_union2(B, singleton(A)), singleton(A)) = B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.19/0.37 tff(31,plain,(
% 0.19/0.37 ~(in(A!3, B!2) | (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2))),
% 0.19/0.37 inference(skolemize,[status(sab)],[30])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (~in(A!3, B!2)),
% 0.19/0.37 inference(or_elim,[status(thm)],[31])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 ((in(A!3, B!2) <=> (set_difference(B!2, singleton(A!3)) = B!2)) | in(A!3, B!2) | (set_difference(B!2, singleton(A!3)) = B!2)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((in(A!3, B!2) <=> (set_difference(B!2, singleton(A!3)) = B!2)) | (set_difference(B!2, singleton(A!3)) = B!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (set_difference(B!2, singleton(A!3)) = B!2),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[34, 23])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[35, 11])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (~(set_difference(set_union2(B!2, singleton(A!3)), singleton(A!3)) = B!2)),
% 0.19/0.37 inference(or_elim,[status(thm)],[31])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------