%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET923+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:26:40 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET923+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 05:51:02 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(singleton_type, type, (
% 0.12/0.37 singleton: $i > $i)).
% 0.12/0.37 tff(tptp_fun_B_2_type, type, (
% 0.12/0.37 tptp_fun_B_2: $i)).
% 0.12/0.37 tff(tptp_fun_A_3_type, type, (
% 0.12/0.37 tptp_fun_A_3: $i)).
% 0.12/0.37 tff(empty_set_type, type, (
% 0.12/0.37 empty_set: $i)).
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(set_difference_type, type, (
% 0.12/0.37 set_difference: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))) <=> (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : (~(((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set))) & (~(A = singleton(B)))))) <=> (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,axiom,(~![A: $i, B: $i] : (~(((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set))) & (~(A = singleton(B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t66_zfmisc_1')).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![A: $i, B: $i] : (~((set_difference(A, singleton(B)) = empty_set) & (~(A = empty_set)) & (~(A = singleton(B)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.37 tff(8,plain,(
% 0.12/0.37 (set_difference(A!3, singleton(B!2)) = empty_set) & (~(A!3 = empty_set)) & (~(A!3 = singleton(B!2)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~(A!3 = singleton(B!2))),
% 0.12/0.37 inference(and_elim,[status(thm)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~(A!3 = empty_set)),
% 0.12/0.37 inference(and_elim,[status(thm)],[8])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~((A!3 = empty_set) | (A!3 = singleton(B!2)))) | (A!3 = empty_set) | (A!3 = singleton(B!2))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (~((A!3 = empty_set) | (A!3 = singleton(B!2)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[11, 10, 9])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_xboole_1')).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,(
% 0.12/0.37 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.37 inference(skolemize,[status(sab)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(A!3, singleton(B!2)) = empty_set) <=> subset(A!3, singleton(B!2)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((set_difference(A!3, singleton(B!2)) = empty_set) <=> subset(A!3, singleton(B!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (set_difference(A!3, singleton(B!2)) = empty_set),
% 0.12/0.37 inference(and_elim,[status(thm)],[8])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~((set_difference(A!3, singleton(B!2)) = empty_set) <=> subset(A!3, singleton(B!2)))) | (~(set_difference(A!3, singleton(B!2)) = empty_set)) | subset(A!3, singleton(B!2))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~((set_difference(A!3, singleton(B!2)) = empty_set) <=> subset(A!3, singleton(B!2)))) | subset(A!3, singleton(B!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (subset(A!3, singleton(B!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 ((~(subset(A!3, singleton(B!2)) <=> ((A!3 = empty_set) | (A!3 = singleton(B!2))))) | (~subset(A!3, singleton(B!2))) | ((A!3 = empty_set) | (A!3 = singleton(B!2)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (~(subset(A!3, singleton(B!2)) <=> ((A!3 = empty_set) | (A!3 = singleton(B!2))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[26, 25, 12])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (^[A: $i, B: $i] : refl((subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(31,axiom,(![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l4_zfmisc_1')).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.37 tff(33,plain,(
% 0.12/0.37 ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))) | (subset(A!3, singleton(B!2)) <=> ((A!3 = empty_set) | (A!3 = singleton(B!2))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[35, 34, 27])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------