%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET928+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 05:26:41 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET928+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 05:50:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(disjoint_type, type, (
% 0.20/0.37 disjoint: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_C_2_type, type, (
% 0.20/0.37 tptp_fun_C_2: $i)).
% 0.20/0.37 tff(unordered_pair_type, type, (
% 0.20/0.37 unordered_pair: ( $i * $i ) > $i)).
% 0.20/0.37 tff(tptp_fun_A_4_type, type, (
% 0.20/0.37 tptp_fun_A_4: $i)).
% 0.20/0.37 tff(tptp_fun_B_3_type, type, (
% 0.20/0.37 tptp_fun_B_3: $i)).
% 0.20/0.37 tff(set_difference_type, type, (
% 0.20/0.37 set_difference: ( $i * $i ) > $i)).
% 0.20/0.37 tff(in_type, type, (
% 0.20/0.37 in: ( $i * $i ) > $o)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.37 tff(6,plain,(
% 0.20/0.37 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.37 inference(skolemize,[status(sab)],[5])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.20/0.37 inference(symmetry,[status(thm)],[9])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (disjoint(unordered_pair(B!3, A!4), C!2) <=> disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.20/0.37 inference(monotonicity,[status(thm)],[10])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (disjoint(unordered_pair(A!4, B!3), C!2) <=> disjoint(unordered_pair(B!3, A!4), C!2)),
% 0.20/0.37 inference(symmetry,[status(thm)],[11])).
% 0.20/0.37 tff(13,assumption,(~(set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))), introduced(assumption)).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_difference(A, B) = A)) <=> (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(17,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t83_xboole_1')).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.37 tff(19,plain,(
% 0.20/0.37 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.20/0.37 inference(skolemize,[status(sab)],[18])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) | (disjoint(unordered_pair(A!4, B!3), C!2) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (disjoint(unordered_pair(A!4, B!3), C!2) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 ((~(disjoint(unordered_pair(A!4, B!3), C!2) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))) | (~disjoint(unordered_pair(A!4, B!3), C!2)) | (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 ((~disjoint(unordered_pair(A!4, B!3), C!2)) | (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (~disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[24, 13])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 ((~(~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))))) <=> ((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 ((~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))) <=> (~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> (~(in(A!4, C!2) | in(B!3, C!2)))) <=> (~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (((~in(A!4, C!2)) & (~in(B!3, C!2))) <=> (~(in(A!4, C!2) | in(B!3, C!2)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2)))) <=> ((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> (~(in(A!4, C!2) | in(B!3, C!2))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2)))) <=> (~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2)))) <=> (~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[31, 27])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 ((~((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2))))) <=> (~(~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 ((~((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2))))) <=> ((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))),
% 0.20/0.37 inference(transitivity,[status(thm)],[33, 26])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 ((~((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2))))) <=> (~((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 ((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))) <=> (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(37,axiom,(~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t72_zfmisc_1')).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.37 tff(42,plain,(
% 0.20/0.37 ~((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[41])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 (~((set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) <=> ((~in(A!4, C!2)) & (~in(B!3, C!2))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 ((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[43, 34])).
% 0.20/0.37 tff(45,plain,
% 0.20/0.37 ((~(in(A!4, C!2) | in(B!3, C!2))) | (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)) | (~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(46,plain,
% 0.20/0.37 ((~(in(A!4, C!2) | in(B!3, C!2))) | (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.37 tff(47,plain,
% 0.20/0.37 (~(in(A!4, C!2) | in(B!3, C!2))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[46, 13])).
% 0.20/0.37 tff(48,plain,
% 0.20/0.37 ((in(A!4, C!2) | in(B!3, C!2)) | (~in(A!4, C!2))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(49,plain,
% 0.20/0.37 (~in(A!4, C!2)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.37 tff(50,plain,
% 0.20/0.37 ((in(A!4, C!2) | in(B!3, C!2)) | (~in(B!3, C!2))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(51,plain,
% 0.20/0.37 (~in(B!3, C!2)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.20/0.37 tff(52,plain,
% 0.20/0.37 (^[A: $i, B: $i, C: $i] : refl((in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B)) <=> (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(53,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B)) <=> ![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.37 tff(54,plain,
% 0.20/0.37 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))) <=> (~(in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B)))), ((~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))) <=> (~(~(in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B)))))), rewrite((~(~(in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B)))) <=> (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))), ((~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))) <=> (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(55,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))) <=> ![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.37 tff(56,plain,
% 0.20/0.37 (![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))) <=> ![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(57,plain,
% 0.20/0.37 (^[A: $i, B: $i, C: $i] : rewrite((~(((~in(A, B)) & (~in(C, B))) & (~disjoint(unordered_pair(A, C), B)))) <=> (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (~(((~in(A, B)) & (~in(C, B))) & (~disjoint(unordered_pair(A, C), B)))) <=> ![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.38 tff(59,axiom,(![A: $i, B: $i, C: $i] : (~(((~in(A, B)) & (~in(C, B))) & (~disjoint(unordered_pair(A, C), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t57_zfmisc_1')).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.38 tff(62,plain,(
% 0.20/0.38 ![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[61])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (((~![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))) | (in(A!4, C!2) | in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2))) <=> ((~![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))) | in(A!4, C!2) | in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 ((in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2) | in(A!4, C!2)) <=> (in(A!4, C!2) | in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 (((~![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))) | (in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2) | in(A!4, C!2))) <=> ((~![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))) | (in(A!4, C!2) | in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 (((~![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))) | (in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2) | in(A!4, C!2))) <=> ((~![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))) | in(A!4, C!2) | in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2))),
% 0.20/0.38 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))) | (in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2) | in(A!4, C!2))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))) | in(A!4, C!2) | in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 (in(A!4, C!2) | in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[70, 64])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[71, 51, 49, 25])).
% 0.20/0.38 tff(73,plain,(set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 ((~(disjoint(unordered_pair(A!4, B!3), C!2) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))) | disjoint(unordered_pair(A!4, B!3), C!2) | (~(set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(75,plain,
% 0.20/0.38 (disjoint(unordered_pair(A!4, B!3), C!2) | (~(set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[74, 22])).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 (disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[75, 73])).
% 0.20/0.38 tff(77,plain,
% 0.20/0.38 (disjoint(unordered_pair(B!3, A!4), C!2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[76, 12])).
% 0.20/0.38 tff(78,plain,
% 0.20/0.38 ((in(A!4, C!2) | in(B!3, C!2)) | (~(set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))) | (~((in(A!4, C!2) | in(B!3, C!2)) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 ((in(A!4, C!2) | in(B!3, C!2)) | (~(set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[78, 44])).
% 0.20/0.38 tff(80,plain,
% 0.20/0.38 (in(A!4, C!2) | in(B!3, C!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[79, 73])).
% 0.20/0.38 tff(81,plain,
% 0.20/0.38 (^[A: $i, B: $i, C: $i] : refl(((~in(A, C)) | (~disjoint(unordered_pair(A, B), C))) <=> ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((disjoint(unordered_pair(A, B), C) & in(A, C)) <=> (~((~in(A, C)) | (~disjoint(unordered_pair(A, B), C))))), ((~(disjoint(unordered_pair(A, B), C) & in(A, C))) <=> (~(~((~in(A, C)) | (~disjoint(unordered_pair(A, B), C))))))), rewrite((~(~((~in(A, C)) | (~disjoint(unordered_pair(A, B), C))))) <=> ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))), ((~(disjoint(unordered_pair(A, B), C) & in(A, C))) <=> ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(84,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C))) <=> ![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C))) <=> ![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(86,axiom,(![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t55_zfmisc_1')).
% 0.20/0.38 tff(87,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.38 tff(88,plain,(
% 0.20/0.38 ![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[87])).
% 0.20/0.38 tff(89,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.38 tff(90,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.38 tff(91,plain,
% 0.20/0.38 (((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | ((~in(A!4, C!2)) | (~disjoint(unordered_pair(A!4, B!3), C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | (~in(A!4, C!2)) | (~disjoint(unordered_pair(A!4, B!3), C!2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(92,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | ((~in(A!4, C!2)) | (~disjoint(unordered_pair(A!4, B!3), C!2)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(93,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | (~in(A!4, C!2)) | (~disjoint(unordered_pair(A!4, B!3), C!2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.38 tff(94,plain,
% 0.20/0.38 ((~in(A!4, C!2)) | (~disjoint(unordered_pair(A!4, B!3), C!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.20/0.38 tff(95,plain,
% 0.20/0.38 (~in(A!4, C!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[94, 76])).
% 0.20/0.38 tff(96,plain,
% 0.20/0.38 ((~(in(A!4, C!2) | in(B!3, C!2))) | in(A!4, C!2) | in(B!3, C!2)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(97,plain,
% 0.20/0.38 (in(B!3, C!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[96, 95, 80])).
% 0.20/0.38 tff(98,plain,
% 0.20/0.38 (((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | ((~in(B!3, C!2)) | (~disjoint(unordered_pair(B!3, A!4), C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | (~in(B!3, C!2)) | (~disjoint(unordered_pair(B!3, A!4), C!2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(99,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | ((~in(B!3, C!2)) | (~disjoint(unordered_pair(B!3, A!4), C!2)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(100,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | (~in(B!3, C!2)) | (~disjoint(unordered_pair(B!3, A!4), C!2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.38 tff(101,plain,
% 0.20/0.38 ((~in(B!3, C!2)) | (~disjoint(unordered_pair(B!3, A!4), C!2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[100, 90])).
% 0.20/0.38 tff(102,plain,
% 0.20/0.38 (~disjoint(unordered_pair(B!3, A!4), C!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.20/0.38 tff(103,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[102, 77])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------