TSTP Solution File: SET928+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 : Tue Sep 20 05:08:40 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 07:59:39 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(disjoint_type, type, (
% 0.14/0.39 disjoint: ( $i * $i ) > $o)).
% 0.14/0.39 tff(tptp_fun_C_2_type, type, (
% 0.14/0.39 tptp_fun_C_2: $i)).
% 0.14/0.39 tff(unordered_pair_type, type, (
% 0.14/0.39 unordered_pair: ( $i * $i ) > $i)).
% 0.14/0.39 tff(tptp_fun_A_4_type, type, (
% 0.14/0.39 tptp_fun_A_4: $i)).
% 0.14/0.39 tff(tptp_fun_B_3_type, type, (
% 0.14/0.39 tptp_fun_B_3: $i)).
% 0.14/0.39 tff(set_difference_type, type, (
% 0.14/0.39 set_difference: ( $i * $i ) > $i)).
% 0.14/0.39 tff(in_type, type, (
% 0.14/0.39 in: ( $i * $i ) > $o)).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.39 tff(6,plain,(
% 0.14/0.39 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.39 inference(skolemize,[status(sab)],[5])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.14/0.39 inference(symmetry,[status(thm)],[9])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (disjoint(unordered_pair(B!3, A!4), C!2) <=> disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.14/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (disjoint(unordered_pair(A!4, B!3), C!2) <=> disjoint(unordered_pair(B!3, A!4), C!2)),
% 0.14/0.39 inference(symmetry,[status(thm)],[11])).
% 0.14/0.39 tff(13,assumption,(~(in(A!4, C!2) | in(B!3, C!2))), introduced(assumption)).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 (((~(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)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (((~in(A!4, C!2)) & (~in(B!3, C!2))) <=> (~(in(A!4, C!2) | in(B!3, C!2)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (((~(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))))),
% 0.14/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 (((~(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)))),
% 0.14/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 ((~((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))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 ((~![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)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(20,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/sandbox2/benchmark/theBenchmark.p','t72_zfmisc_1')).
% 0.14/0.39 tff(21,plain,
% 0.14/0.39 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.14/0.39 tff(22,plain,
% 0.14/0.39 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.14/0.39 tff(23,plain,
% 0.14/0.39 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.14/0.39 tff(27,plain,
% 0.14/0.39 (~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = unordered_pair(A, B)) <=> ((~in(A, C)) & (~in(B, C))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.14/0.39 tff(28,plain,(
% 0.14/0.39 ~((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))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[27])).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 ((~(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)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 ((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))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 ((~(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))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 ((~(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))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (~(set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[32, 13])).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 ((in(A!4, C!2) | in(B!3, C!2)) | (~in(A!4, C!2))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (~in(A!4, C!2)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[34, 13])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 ((in(A!4, C!2) | in(B!3, C!2)) | (~in(B!3, C!2))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 (~in(B!3, C!2)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[36, 13])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 (^[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)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (![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))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 (^[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))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (![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))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (^[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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.14/0.40 tff(45,axiom,(![A: $i, B: $i, C: $i] : (~(((~in(A, B)) & (~in(C, B))) & (~disjoint(unordered_pair(A, C), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t57_zfmisc_1')).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.14/0.40 tff(48,plain,(
% 0.14/0.40 ![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[47])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (in(C, B) | disjoint(unordered_pair(A, C), B) | in(A, B))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (((~![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))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 ((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))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (((~![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)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[52])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 (((~![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))),
% 0.14/0.40 inference(transitivity,[status(thm)],[53, 51])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 ((~![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))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(56,plain,
% 0.14/0.40 ((~![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)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 (in(A!4, C!2) | in(B!3, C!2) | disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[56, 50])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 (disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[57, 37, 35])).
% 0.14/0.40 tff(59,plain,
% 0.14/0.40 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_difference(A, B) = A)) <=> (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(62,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t83_xboole_1')).
% 0.14/0.40 tff(63,plain,
% 0.14/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.14/0.40 tff(64,plain,(
% 0.14/0.40 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.14/0.40 inference(skolemize,[status(sab)],[63])).
% 0.14/0.40 tff(65,plain,
% 0.14/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.14/0.40 tff(66,plain,
% 0.14/0.40 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) | (disjoint(unordered_pair(A!4, B!3), C!2) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(67,plain,
% 0.14/0.40 (disjoint(unordered_pair(A!4, B!3), C!2) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.14/0.40 tff(68,plain,
% 0.14/0.40 ((~(disjoint(unordered_pair(A!4, B!3), C!2) <=> (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)))) | (~disjoint(unordered_pair(A!4, B!3), C!2)) | (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(69,plain,
% 0.14/0.40 ((~disjoint(unordered_pair(A!4, B!3), C!2)) | (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.14/0.40 tff(70,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[69, 58, 33])).
% 0.14/0.40 tff(71,plain,(in(A!4, C!2) | in(B!3, C!2)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(72,plain,
% 0.14/0.40 ((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))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(73,plain,
% 0.14/0.40 ((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)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[72, 30])).
% 0.14/0.40 tff(74,plain,
% 0.14/0.40 (set_difference(unordered_pair(A!4, B!3), C!2) = unordered_pair(A!4, B!3)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[73, 71])).
% 0.14/0.40 tff(75,plain,
% 0.14/0.40 ((~(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)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(76,plain,
% 0.14/0.40 (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)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[75, 67])).
% 0.14/0.40 tff(77,plain,
% 0.14/0.40 (disjoint(unordered_pair(A!4, B!3), C!2)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[76, 74])).
% 0.14/0.40 tff(78,plain,
% 0.14/0.40 (disjoint(unordered_pair(B!3, A!4), C!2)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[77, 12])).
% 0.14/0.40 tff(79,plain,
% 0.14/0.40 (^[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))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(80,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.14/0.40 tff(81,plain,
% 0.14/0.40 (^[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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(82,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.14/0.40 tff(83,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(84,axiom,(![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t55_zfmisc_1')).
% 0.14/0.40 tff(85,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.14/0.40 tff(86,plain,(
% 0.14/0.40 ![A: $i, B: $i, C: $i] : (~(disjoint(unordered_pair(A, B), C) & in(A, C)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[85])).
% 0.14/0.40 tff(87,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.14/0.40 tff(88,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.14/0.40 tff(89,plain,
% 0.14/0.40 (((~![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)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(90,plain,
% 0.14/0.40 ((~![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)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(91,plain,
% 0.14/0.40 ((~![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))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.14/0.40 tff(92,plain,
% 0.14/0.40 ((~in(A!4, C!2)) | (~disjoint(unordered_pair(A!4, B!3), C!2))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.14/0.40 tff(93,plain,
% 0.14/0.40 (~in(A!4, C!2)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[92, 77])).
% 0.14/0.40 tff(94,plain,
% 0.14/0.40 ((~(in(A!4, C!2) | in(B!3, C!2))) | in(A!4, C!2) | in(B!3, C!2)),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(95,plain,
% 0.14/0.40 (in(B!3, C!2)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[94, 93, 71])).
% 0.14/0.40 tff(96,plain,
% 0.14/0.40 (((~![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)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(97,plain,
% 0.14/0.40 ((~![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)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(98,plain,
% 0.14/0.40 ((~![A: $i, B: $i, C: $i] : ((~in(A, C)) | (~disjoint(unordered_pair(A, B), C)))) | (~in(B!3, C!2)) | (~disjoint(unordered_pair(B!3, A!4), C!2))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.14/0.40 tff(99,plain,
% 0.14/0.40 ((~in(B!3, C!2)) | (~disjoint(unordered_pair(B!3, A!4), C!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[98, 88])).
% 0.14/0.41 tff(100,plain,
% 0.14/0.41 (~disjoint(unordered_pair(B!3, A!4), C!2)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.14/0.41 tff(101,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[100, 78])).
% 0.14/0.41 % SZS output end Proof
%------------------------------------------------------------------------------