%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU156+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:27:04 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU156+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 06:07:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(unordered_pair_type, type, (
% 0.20/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_C_15_type, type, (
% 0.20/0.40 tptp_fun_C_15: $i)).
% 0.20/0.40 tff(tptp_fun_A_17_type, type, (
% 0.20/0.40 tptp_fun_A_17: $i)).
% 0.20/0.40 tff(tptp_fun_B_16_type, type, (
% 0.20/0.40 tptp_fun_B_16: $i)).
% 0.20/0.40 tff(singleton_type, type, (
% 0.20/0.40 singleton: $i > $i)).
% 0.20/0.40 tff(tptp_fun_D_14_type, type, (
% 0.20/0.40 tptp_fun_D_14: $i)).
% 0.20/0.40 tff(ordered_pair_type, type, (
% 0.20/0.40 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[A: $i] : refl((unordered_pair(A, A) = singleton(A)) <=> (unordered_pair(A, A) = singleton(A)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![A: $i] : (unordered_pair(A, A) = singleton(A)) <=> ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![A: $i] : (unordered_pair(A, A) = singleton(A)) <=> ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(![A: $i] : (unordered_pair(A, A) = singleton(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t69_enumset1')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,(
% 0.20/0.40 ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.40 inference(skolemize,[status(sab)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) | (unordered_pair(C!15, C!15) = singleton(C!15))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (unordered_pair(C!15, C!15) = singleton(C!15)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.40 tff(15,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.40 inference(skolemize,[status(sab)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!17, B!16) = unordered_pair(B!16, A!17))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (unordered_pair(A!17, B!16) = unordered_pair(B!16, A!17)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (unordered_pair(B!16, A!17) = unordered_pair(A!17, B!16)),
% 0.20/0.40 inference(symmetry,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15)) <=> (unordered_pair(A!17, B!16) = singleton(C!15))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[19, 9])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((unordered_pair(A!17, B!16) = singleton(C!15)) <=> (unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))),
% 0.20/0.40 inference(symmetry,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 ((unordered_pair(B!16, A!17) = singleton(C!15)) <=> (unordered_pair(A!17, B!16) = singleton(C!15))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((unordered_pair(B!16, A!17) = singleton(C!15)) <=> (unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))),
% 0.20/0.40 inference(transitivity,[status(thm)],[22, 21])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((singleton(A!17) = unordered_pair(C!15, D!14)) <=> (unordered_pair(C!15, D!14) = singleton(A!17))),
% 0.20/0.40 inference(commutativity,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(C!15, D!14) = unordered_pair(D!14, C!15))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (unordered_pair(C!15, D!14) = unordered_pair(D!14, C!15)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[25, 16])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (unordered_pair(D!14, C!15) = unordered_pair(C!15, D!14)),
% 0.20/0.40 inference(symmetry,[status(thm)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 ((singleton(A!17) = unordered_pair(D!14, C!15)) <=> (singleton(A!17) = unordered_pair(C!15, D!14))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 ((singleton(A!17) = unordered_pair(D!14, C!15)) <=> (unordered_pair(C!15, D!14) = singleton(A!17))),
% 0.20/0.40 inference(transitivity,[status(thm)],[28, 24])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ((unordered_pair(C!15, D!14) = singleton(A!17)) <=> (singleton(A!17) = unordered_pair(D!14, C!15))),
% 0.20/0.40 inference(symmetry,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((singleton(A!17) = unordered_pair(C!15, D!14)) <=> (singleton(A!17) = unordered_pair(D!14, C!15))),
% 0.20/0.40 inference(transitivity,[status(thm)],[24, 30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~(singleton(A!17) = unordered_pair(C!15, D!14))) <=> (~(singleton(A!17) = unordered_pair(D!14, C!15)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.40 tff(33,assumption,(~(A!17 = C!15)), introduced(assumption)).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i] : refl(((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((singleton(A) = unordered_pair(B, C)) => (A = B)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.40 tff(39,axiom,(![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_zfmisc_1')).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.40 tff(42,plain,(
% 0.20/0.40 ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.40 inference(skolemize,[status(sab)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(A!17) = unordered_pair(C!15, D!14))) | (A!17 = C!15))) <=> ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(A!17) = unordered_pair(C!15, D!14))) | (A!17 = C!15))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(A!17) = unordered_pair(C!15, D!14))) | (A!17 = C!15))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(A!17) = unordered_pair(C!15, D!14))) | (A!17 = C!15)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~(singleton(A!17) = unordered_pair(C!15, D!14))) | (A!17 = C!15)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (~(singleton(A!17) = unordered_pair(C!15, D!14))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (~(singleton(A!17) = unordered_pair(D!14, C!15))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[48, 32])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 ((singleton(A!17) = singleton(C!15)) <=> (singleton(C!15) = singleton(A!17))),
% 0.20/0.40 inference(commutativity,[status(thm)],[])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 ((singleton(C!15) = singleton(A!17)) <=> (singleton(A!17) = singleton(C!15))),
% 0.20/0.40 inference(symmetry,[status(thm)],[50])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) | (unordered_pair(A!17, A!17) = singleton(A!17))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (unordered_pair(A!17, A!17) = singleton(A!17)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[52, 7])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ((unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15)) <=> (singleton(A!17) = singleton(C!15))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[53, 9])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15)) <=> (singleton(C!15) = singleton(A!17))),
% 0.20/0.40 inference(transitivity,[status(thm)],[54, 50])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15)) <=> (singleton(A!17) = singleton(C!15))),
% 0.20/0.40 inference(transitivity,[status(thm)],[55, 51])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ((~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))) <=> (~(singleton(A!17) = singleton(C!15)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i, D: $i] : refl(((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D)))) <=> ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite(((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))) <=> (~((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D)))))), ((~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D)))) <=> (~(~((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D)))))))), rewrite((~(~((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D)))))) <=> ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))), ((~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D)))) <=> ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((~(((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C))) & (~(A = D)))) <=> (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~(((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C))) & (~(A = D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.40 tff(65,axiom,(![A: $i, B: $i, C: $i, D: $i] : (~(((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C))) & (~(A = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_zfmisc_1')).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.40 tff(68,plain,(
% 0.20/0.40 ![A: $i, B: $i, C: $i, D: $i] : (~((unordered_pair(A, B) = unordered_pair(C, D)) & (~(A = C)) & (~(A = D))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[67])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (((A!17 = C!15) | (A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15)))) <=> ((A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((A!17 = C!15) | (A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((A!17 = C!15) | (A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((A!17 = C!15) | (A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 ((A!17 = C!15) | (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[76, 70])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (~(unordered_pair(A!17, A!17) = unordered_pair(C!15, C!15))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[77, 33])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (~(singleton(A!17) = singleton(C!15))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[78, 57])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ((unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(unordered_pair(D!14, C!15), singleton(C!15))) <=> (unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)))),
% 0.20/0.40 inference(commutativity,[status(thm)],[])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 ((unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17))) <=> (unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[80])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(singleton(A!17), unordered_pair(A!17, B!16))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (unordered_pair(singleton(A!17), unordered_pair(A!17, B!16)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17))),
% 0.20/0.40 inference(symmetry,[status(thm)],[82])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(unordered_pair(A!17, B!16), singleton(A!17)) = unordered_pair(singleton(A!17), unordered_pair(A!17, B!16)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (unordered_pair(unordered_pair(A!17, B!16), singleton(A!17)) = unordered_pair(singleton(A!17), unordered_pair(A!17, B!16))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 16])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl((ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A))) <=> ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(89,axiom,(![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_tarski')).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.41 tff(91,plain,(
% 0.20/0.41 ![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[90])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))) | (ordered_pair(A!17, B!16) = unordered_pair(unordered_pair(A!17, B!16), singleton(A!17)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (ordered_pair(A!17, B!16) = unordered_pair(unordered_pair(A!17, B!16), singleton(A!17))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((ordered_pair(A, B) = ordered_pair(C, D)) => ((A = C) & (B = D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(97,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((ordered_pair(A, B) = ordered_pair(C, D)) => ((A = C) & (B = D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t33_zfmisc_1')).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i, D: $i] : ((~(ordered_pair(A, B) = ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[100, 95])).
% 0.20/0.41 tff(102,plain,(
% 0.20/0.41 ~((~(ordered_pair(A!17, B!16) = ordered_pair(C!15, D!14))) | ((A!17 = C!15) & (B!16 = D!14)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[101])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (ordered_pair(A!17, B!16) = ordered_pair(C!15, D!14)),
% 0.20/0.41 inference(or_elim,[status(thm)],[102])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (ordered_pair(C!15, D!14) = ordered_pair(A!17, B!16)),
% 0.20/0.41 inference(symmetry,[status(thm)],[103])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (ordered_pair(A, B) = unordered_pair(unordered_pair(A, B), singleton(A)))) | (ordered_pair(C!15, D!14) = unordered_pair(unordered_pair(C!15, D!14), singleton(C!15)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (ordered_pair(C!15, D!14) = unordered_pair(unordered_pair(C!15, D!14), singleton(C!15))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[105, 92])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (unordered_pair(unordered_pair(C!15, D!14), singleton(C!15)) = ordered_pair(C!15, D!14)),
% 0.20/0.41 inference(symmetry,[status(thm)],[106])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(unordered_pair(C!15, D!14), singleton(C!15))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17))),
% 0.20/0.41 inference(transitivity,[status(thm)],[108, 107, 104, 94, 85, 83])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(unordered_pair(D!14, C!15), singleton(C!15))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[109, 81])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((singleton(A!17) = singleton(C!15)) | (singleton(A!17) = unordered_pair(D!14, C!15)) | (~(unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (singleton(A!17) = singleton(C!15)) | (singleton(A!17) = unordered_pair(D!14, C!15)) | (~(unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((singleton(A!17) = singleton(C!15)) | (singleton(A!17) = unordered_pair(D!14, C!15)) | (~(unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (singleton(A!17) = singleton(C!15)) | (singleton(A!17) = unordered_pair(D!14, C!15)) | (~(unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(unordered_pair(D!14, C!15), singleton(C!15))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 ((singleton(A!17) = singleton(C!15)) | (singleton(A!17) = unordered_pair(D!14, C!15)) | (~(unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)) = unordered_pair(unordered_pair(D!14, C!15), singleton(C!15))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[113, 70])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((singleton(A!17) = singleton(C!15)) | (singleton(A!17) = unordered_pair(D!14, C!15))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[115, 79, 49])).
% 0.20/0.41 tff(117,plain,(A!17 = C!15), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~(~((~(A!17 = C!15)) | (~(B!16 = D!14))))) <=> ((~(A!17 = C!15)) | (~(B!16 = D!14)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (((A!17 = C!15) & (B!16 = D!14)) <=> (~((~(A!17 = C!15)) | (~(B!16 = D!14))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 ((~((A!17 = C!15) & (B!16 = D!14))) <=> (~(~((~(A!17 = C!15)) | (~(B!16 = D!14)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 ((~((A!17 = C!15) & (B!16 = D!14))) <=> ((~(A!17 = C!15)) | (~(B!16 = D!14)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 (~((A!17 = C!15) & (B!16 = D!14))),
% 0.20/0.41 inference(or_elim,[status(thm)],[102])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ((~(A!17 = C!15)) | (~(B!16 = D!14))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (~(B!16 = D!14)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[123, 117])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 ((B!16 = C!15) <=> (C!15 = B!16)),
% 0.20/0.41 inference(commutativity,[status(thm)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 ((C!15 = B!16) <=> (B!16 = C!15)),
% 0.20/0.41 inference(symmetry,[status(thm)],[125])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 ((unordered_pair(D!14, C!15) = singleton(A!17)) <=> (unordered_pair(C!15, D!14) = singleton(A!17))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 ((unordered_pair(C!15, D!14) = singleton(A!17)) <=> (unordered_pair(D!14, C!15) = singleton(A!17))),
% 0.20/0.41 inference(symmetry,[status(thm)],[127])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 ((singleton(A!17) = unordered_pair(D!14, C!15)) <=> (unordered_pair(D!14, C!15) = singleton(A!17))),
% 0.20/0.41 inference(transitivity,[status(thm)],[29, 128])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 ((~(singleton(A!17) = unordered_pair(D!14, C!15))) <=> (~(unordered_pair(D!14, C!15) = singleton(A!17)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.41 tff(131,assumption,(~(singleton(A!17) = unordered_pair(D!14, C!15))), introduced(assumption)).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 (~(unordered_pair(D!14, C!15) = singleton(A!17))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)) | (unordered_pair(D!14, C!15) = singleton(A!17)) | (~(unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)) | (unordered_pair(D!14, C!15) = singleton(A!17)) | (~(unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)) | (unordered_pair(D!14, C!15) = singleton(A!17)) | (~(unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)) | (unordered_pair(D!14, C!15) = singleton(A!17)) | (~(unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 ((unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)) | (unordered_pair(D!14, C!15) = singleton(A!17)) | (~(unordered_pair(unordered_pair(D!14, C!15), singleton(C!15)) = unordered_pair(singleton(A!17), unordered_pair(B!16, A!17))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[135, 70])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 ((unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)) | (unordered_pair(D!14, C!15) = singleton(A!17))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[136, 109])).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 (unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[137, 132])).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 (unordered_pair(C!15, D!14) = unordered_pair(A!17, B!16)),
% 0.20/0.41 inference(transitivity,[status(thm)],[26, 138, 19])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 ((unordered_pair(C!15, D!14) = singleton(C!15)) <=> (unordered_pair(A!17, B!16) = singleton(C!15))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 ((unordered_pair(A!17, B!16) = singleton(C!15)) <=> (unordered_pair(C!15, D!14) = singleton(C!15))),
% 0.20/0.41 inference(symmetry,[status(thm)],[140])).
% 0.20/0.41 tff(142,plain,
% 0.20/0.41 ((D!14 = B!16) <=> (B!16 = D!14)),
% 0.20/0.41 inference(commutativity,[status(thm)],[])).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 ((B!16 = D!14) <=> (D!14 = B!16)),
% 0.20/0.41 inference(symmetry,[status(thm)],[142])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 ((~(B!16 = D!14)) <=> (~(D!14 = B!16))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[143])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 (~(D!14 = B!16)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[124, 144])).
% 0.20/0.41 tff(146,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((D!14 = A!17) | (D!14 = B!16) | (~(unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (D!14 = A!17) | (D!14 = B!16) | (~(unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((D!14 = A!17) | (D!14 = B!16) | (~(unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(148,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (D!14 = A!17) | (D!14 = B!16) | (~(unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.41 tff(149,plain,
% 0.20/0.41 ((D!14 = A!17) | (D!14 = B!16) | (~(unordered_pair(D!14, C!15) = unordered_pair(B!16, A!17)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[148, 70])).
% 0.20/0.41 tff(150,plain,
% 0.20/0.41 (D!14 = A!17),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[149, 138, 145])).
% 0.20/0.41 tff(151,plain,
% 0.20/0.41 (D!14 = C!15),
% 0.20/0.41 inference(transitivity,[status(thm)],[150, 117])).
% 0.20/0.41 tff(152,plain,
% 0.20/0.41 (unordered_pair(C!15, D!14) = unordered_pair(C!15, C!15)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.41 tff(153,plain,
% 0.20/0.41 (unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)),
% 0.20/0.41 inference(symmetry,[status(thm)],[138])).
% 0.20/0.41 tff(154,plain,
% 0.20/0.41 (unordered_pair(A!17, B!16) = singleton(C!15)),
% 0.20/0.41 inference(transitivity,[status(thm)],[18, 153, 27, 152, 9])).
% 0.20/0.41 tff(155,plain,
% 0.20/0.41 (unordered_pair(C!15, D!14) = singleton(C!15)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[154, 141])).
% 0.20/0.41 tff(156,plain,
% 0.20/0.41 (singleton(A!17) = singleton(C!15)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.41 tff(157,plain,
% 0.20/0.41 ((unordered_pair(C!15, D!14) = singleton(A!17)) <=> (unordered_pair(C!15, D!14) = singleton(C!15))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[156])).
% 0.20/0.41 tff(158,plain,
% 0.20/0.41 ((singleton(A!17) = unordered_pair(D!14, C!15)) <=> (unordered_pair(C!15, D!14) = singleton(C!15))),
% 0.20/0.41 inference(transitivity,[status(thm)],[29, 157])).
% 0.20/0.41 tff(159,plain,
% 0.20/0.41 ((~(singleton(A!17) = unordered_pair(D!14, C!15))) <=> (~(unordered_pair(C!15, D!14) = singleton(C!15)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.41 tff(160,plain,
% 0.20/0.41 (~(unordered_pair(C!15, D!14) = singleton(C!15))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[131, 159])).
% 0.20/0.41 tff(161,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[160, 155])).
% 0.20/0.41 tff(162,plain,(singleton(A!17) = unordered_pair(D!14, C!15)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(163,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : refl(((~(singleton(A) = unordered_pair(B, C))) | (B = C)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (B = C)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(164,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.41 tff(165,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(166,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((singleton(A) = unordered_pair(B, C)) => (B = C)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (B = C)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(167,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (B = C)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.42 tff(168,axiom,(![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (B = C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t9_zfmisc_1')).
% 0.20/0.42 tff(169,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.42 tff(170,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.20/0.42 tff(171,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.42 inference(skolemize,[status(sab)],[170])).
% 0.20/0.42 tff(172,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.20/0.42 tff(173,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))) | ((~(singleton(A!17) = unordered_pair(D!14, C!15))) | (D!14 = C!15))) <=> ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))) | (~(singleton(A!17) = unordered_pair(D!14, C!15))) | (D!14 = C!15))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(174,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))) | ((~(singleton(A!17) = unordered_pair(D!14, C!15))) | (D!14 = C!15))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(175,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))) | (~(singleton(A!17) = unordered_pair(D!14, C!15))) | (D!14 = C!15)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.42 tff(176,plain,
% 0.20/0.42 ((~(singleton(A!17) = unordered_pair(D!14, C!15))) | (D!14 = C!15)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.20/0.42 tff(177,plain,
% 0.20/0.42 (D!14 = C!15),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[176, 162])).
% 0.20/0.42 tff(178,plain,
% 0.20/0.42 ((B!16 = D!14) <=> (B!16 = C!15)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[177])).
% 0.20/0.42 tff(179,plain,
% 0.20/0.42 ((B!16 = D!14) <=> (C!15 = B!16)),
% 0.20/0.42 inference(transitivity,[status(thm)],[178, 125])).
% 0.20/0.42 tff(180,plain,
% 0.20/0.42 ((B!16 = D!14) <=> (B!16 = C!15)),
% 0.20/0.42 inference(transitivity,[status(thm)],[179, 126])).
% 0.20/0.42 tff(181,plain,
% 0.20/0.42 ((~(B!16 = D!14)) <=> (~(B!16 = C!15))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[180])).
% 0.20/0.42 tff(182,plain,
% 0.20/0.42 (~(B!16 = C!15)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[124, 181])).
% 0.20/0.42 tff(183,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = D!14) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (B!16 = D!14) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(184,plain,
% 0.20/0.42 (((B!16 = C!15) | (B!16 = D!14) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)))) <=> ((B!16 = D!14) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(185,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = C!15) | (B!16 = D!14) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = D!14) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[184])).
% 0.20/0.42 tff(186,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = C!15) | (B!16 = D!14) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (B!16 = D!14) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[185, 183])).
% 0.20/0.42 tff(187,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = C!15) | (B!16 = D!14) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(188,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (B!16 = D!14) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.42 tff(189,plain,
% 0.20/0.42 ((B!16 = D!14) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[188, 70])).
% 0.20/0.42 tff(190,plain,
% 0.20/0.42 (~(unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[189, 182, 124])).
% 0.20/0.42 tff(191,plain,
% 0.20/0.42 (unordered_pair(singleton(C!15), unordered_pair(D!14, C!15)) = unordered_pair(singleton(C!15), unordered_pair(C!15, D!14))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.42 tff(192,plain,
% 0.20/0.42 (unordered_pair(singleton(C!15), unordered_pair(C!15, D!14)) = unordered_pair(singleton(C!15), unordered_pair(D!14, C!15))),
% 0.20/0.42 inference(symmetry,[status(thm)],[191])).
% 0.20/0.42 tff(193,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(unordered_pair(C!15, D!14), singleton(C!15)) = unordered_pair(singleton(C!15), unordered_pair(C!15, D!14)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(194,plain,
% 0.20/0.42 (unordered_pair(unordered_pair(C!15, D!14), singleton(C!15)) = unordered_pair(singleton(C!15), unordered_pair(C!15, D!14))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[193, 16])).
% 0.20/0.42 tff(195,plain,
% 0.20/0.42 (unordered_pair(unordered_pair(A!17, B!16), singleton(A!17)) = ordered_pair(A!17, B!16)),
% 0.20/0.42 inference(symmetry,[status(thm)],[94])).
% 0.20/0.42 tff(196,plain,
% 0.20/0.42 (unordered_pair(unordered_pair(B!16, A!17), singleton(A!17)) = unordered_pair(unordered_pair(A!17, B!16), singleton(A!17))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.42 tff(197,plain,
% 0.20/0.42 (unordered_pair(unordered_pair(B!16, A!17), singleton(A!17)) = unordered_pair(singleton(C!15), unordered_pair(D!14, C!15))),
% 0.20/0.42 inference(transitivity,[status(thm)],[196, 195, 103, 106, 194, 192])).
% 0.20/0.42 tff(198,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)) | (unordered_pair(B!16, A!17) = singleton(C!15)) | (~(unordered_pair(unordered_pair(B!16, A!17), singleton(A!17)) = unordered_pair(singleton(C!15), unordered_pair(D!14, C!15)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)) | (unordered_pair(B!16, A!17) = singleton(C!15)) | (~(unordered_pair(unordered_pair(B!16, A!17), singleton(A!17)) = unordered_pair(singleton(C!15), unordered_pair(D!14, C!15)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(199,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)) | (unordered_pair(B!16, A!17) = singleton(C!15)) | (~(unordered_pair(unordered_pair(B!16, A!17), singleton(A!17)) = unordered_pair(singleton(C!15), unordered_pair(D!14, C!15)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(200,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)) | (unordered_pair(B!16, A!17) = singleton(C!15)) | (~(unordered_pair(unordered_pair(B!16, A!17), singleton(A!17)) = unordered_pair(singleton(C!15), unordered_pair(D!14, C!15))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.43 tff(201,plain,
% 0.20/0.43 ((unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)) | (unordered_pair(B!16, A!17) = singleton(C!15)) | (~(unordered_pair(unordered_pair(B!16, A!17), singleton(A!17)) = unordered_pair(singleton(C!15), unordered_pair(D!14, C!15))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[200, 70])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 ((unordered_pair(B!16, A!17) = unordered_pair(D!14, C!15)) | (unordered_pair(B!16, A!17) = singleton(C!15))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[201, 197])).
% 0.20/0.43 tff(203,plain,
% 0.20/0.43 (unordered_pair(B!16, A!17) = singleton(C!15)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[202, 190])).
% 0.20/0.43 tff(204,plain,
% 0.20/0.43 (unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[203, 23])).
% 0.20/0.43 tff(205,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(206,plain,
% 0.20/0.43 (((B!16 = C!15) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15)))) <=> ((B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(207,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = C!15) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[206])).
% 0.20/0.43 tff(208,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = C!15) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[207, 205])).
% 0.20/0.43 tff(209,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | ((B!16 = C!15) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(210,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : ((A = D) | (A = C) | (~(unordered_pair(A, B) = unordered_pair(C, D))))) | (B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.20/0.43 tff(211,plain,
% 0.20/0.43 ((B!16 = C!15) | (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[210, 70])).
% 0.20/0.43 tff(212,plain,
% 0.20/0.43 (~(unordered_pair(B!16, A!17) = unordered_pair(C!15, C!15))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[211, 182])).
% 0.20/0.43 tff(213,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[212, 204])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------