%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET886+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:26:36 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET886+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:51:41 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(singleton_type, type, (
% 0.13/0.38 singleton: $i > $i)).
% 0.13/0.38 tff(tptp_fun_C_2_type, type, (
% 0.13/0.38 tptp_fun_C_2: $i)).
% 0.13/0.38 tff(unordered_pair_type, type, (
% 0.13/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.13/0.38 tff(tptp_fun_B_3_type, type, (
% 0.13/0.38 tptp_fun_B_3: $i)).
% 0.13/0.38 tff(tptp_fun_A_4_type, type, (
% 0.13/0.38 tptp_fun_A_4: $i)).
% 0.13/0.38 tff(subset_type, type, (
% 0.13/0.38 subset: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 (^[A: $i] : refl((unordered_pair(A, A) = singleton(A)) <=> (unordered_pair(A, A) = singleton(A)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (![A: $i] : (unordered_pair(A, A) = singleton(A)) <=> ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![A: $i] : (unordered_pair(A, A) = singleton(A)) <=> ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(4,axiom,(![A: $i] : (unordered_pair(A, A) = singleton(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t69_enumset1')).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.38 tff(6,plain,(
% 0.13/0.38 ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.13/0.38 inference(skolemize,[status(sab)],[5])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) | (unordered_pair(C!2, C!2) = singleton(C!2))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (unordered_pair(C!2, C!2) = singleton(C!2)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(13,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.38 tff(15,plain,(
% 0.13/0.38 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.38 inference(skolemize,[status(sab)],[14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.13/0.38 inference(symmetry,[status(thm)],[18])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 ((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (unordered_pair(A, B) = singleton(C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (unordered_pair(A, B) = singleton(C))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), singleton(C)) => (unordered_pair(A, B) = singleton(C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (unordered_pair(A, B) = singleton(C))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(22,axiom,(~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), singleton(C)) => (unordered_pair(A, B) = singleton(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_zfmisc_1')).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (unordered_pair(A, B) = singleton(C)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (unordered_pair(A, B) = singleton(C)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (unordered_pair(A, B) = singleton(C)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (unordered_pair(A, B) = singleton(C)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.13/0.38 tff(27,plain,(
% 0.13/0.38 ~((~subset(unordered_pair(A!4, B!3), singleton(C!2))) | (unordered_pair(A!4, B!3) = singleton(C!2)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[26])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (subset(unordered_pair(A!4, B!3), singleton(C!2))),
% 0.13/0.38 inference(or_elim,[status(thm)],[27])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (^[A: $i, B: $i, C: $i] : refl(((~subset(unordered_pair(A, B), singleton(C))) | (A = C)) <=> ((~subset(unordered_pair(A, B), singleton(C))) | (A = C)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C)) <=> ![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C)) <=> ![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (^[A: $i, B: $i, C: $i] : rewrite((subset(unordered_pair(A, B), singleton(C)) => (A = C)) <=> ((~subset(unordered_pair(A, B), singleton(C))) | (A = C)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), singleton(C)) => (A = C)) <=> ![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.38 tff(34,axiom,(![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), singleton(C)) => (A = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t26_zfmisc_1')).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.13/0.38 tff(37,plain,(
% 0.13/0.38 ![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 0.13/0.38 inference(skolemize,[status(sab)],[36])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) | ((~subset(unordered_pair(A!4, B!3), singleton(C!2))) | (A!4 = C!2))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) | (~subset(unordered_pair(A!4, B!3), singleton(C!2))) | (A!4 = C!2))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 ((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) | ((~subset(unordered_pair(A!4, B!3), singleton(C!2))) | (A!4 = C!2))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 ((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) | (~subset(unordered_pair(A!4, B!3), singleton(C!2))) | (A!4 = C!2)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 (A!4 = C!2),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 (C!2 = A!4),
% 0.13/0.38 inference(symmetry,[status(thm)],[42])).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 (unordered_pair(B!3, C!2) = unordered_pair(B!3, A!4)),
% 0.13/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.13/0.38 tff(45,plain,
% 0.13/0.38 (unordered_pair(B!3, C!2) = unordered_pair(A!4, B!3)),
% 0.13/0.38 inference(transitivity,[status(thm)],[44, 19])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 (subset(unordered_pair(B!3, C!2), singleton(C!2)) <=> subset(unordered_pair(A!4, B!3), singleton(C!2))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 (subset(unordered_pair(A!4, B!3), singleton(C!2)) <=> subset(unordered_pair(B!3, C!2), singleton(C!2))),
% 0.13/0.38 inference(symmetry,[status(thm)],[46])).
% 0.13/0.38 tff(48,plain,
% 0.13/0.38 (subset(unordered_pair(B!3, C!2), singleton(C!2))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[28, 47])).
% 0.13/0.38 tff(49,plain,
% 0.13/0.38 (((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) | ((~subset(unordered_pair(B!3, C!2), singleton(C!2))) | (B!3 = C!2))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) | (~subset(unordered_pair(B!3, C!2), singleton(C!2))) | (B!3 = C!2))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(50,plain,
% 0.13/0.38 ((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) | ((~subset(unordered_pair(B!3, C!2), singleton(C!2))) | (B!3 = C!2))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(51,plain,
% 0.13/0.38 ((~![A: $i, B: $i, C: $i] : ((~subset(unordered_pair(A, B), singleton(C))) | (A = C))) | (~subset(unordered_pair(B!3, C!2), singleton(C!2))) | (B!3 = C!2)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.13/0.38 tff(52,plain,
% 0.13/0.38 ((~subset(unordered_pair(B!3, C!2), singleton(C!2))) | (B!3 = C!2)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[51, 38])).
% 0.13/0.38 tff(53,plain,
% 0.13/0.38 (B!3 = C!2),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[52, 48])).
% 0.13/0.38 tff(54,plain,
% 0.13/0.38 (C!2 = B!3),
% 0.13/0.38 inference(symmetry,[status(thm)],[53])).
% 0.13/0.38 tff(55,plain,
% 0.13/0.38 (unordered_pair(C!2, C!2) = unordered_pair(A!4, B!3)),
% 0.13/0.38 inference(monotonicity,[status(thm)],[43, 54])).
% 0.13/0.38 tff(56,plain,
% 0.13/0.38 (unordered_pair(A!4, B!3) = unordered_pair(C!2, C!2)),
% 0.13/0.38 inference(symmetry,[status(thm)],[55])).
% 0.13/0.38 tff(57,plain,
% 0.13/0.38 (unordered_pair(A!4, B!3) = singleton(C!2)),
% 0.13/0.38 inference(transitivity,[status(thm)],[56, 9])).
% 0.13/0.38 tff(58,plain,
% 0.13/0.38 (~(unordered_pair(A!4, B!3) = singleton(C!2))),
% 0.13/0.38 inference(or_elim,[status(thm)],[27])).
% 0.13/0.38 tff(59,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------