TSTP Solution File: SEU148+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU148+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 07:27:46 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SEU148+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 10:02:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(in_type, type, (
% 0.19/0.40 in: ( $i * $i ) > $o)).
% 0.19/0.40 tff(set_union2_type, type, (
% 0.19/0.40 set_union2: ( $i * $i ) > $i)).
% 0.19/0.40 tff(set_difference_type, type, (
% 0.19/0.40 set_difference: ( $i * $i ) > $i)).
% 0.19/0.40 tff(singleton_type, type, (
% 0.19/0.40 singleton: $i > $i)).
% 0.19/0.40 tff(tptp_fun_A_14_type, type, (
% 0.19/0.40 tptp_fun_A_14: $i)).
% 0.19/0.40 tff(tptp_fun_B_13_type, type, (
% 0.19/0.40 tptp_fun_B_13: $i)).
% 0.19/0.40 tff(subset_type, type, (
% 0.19/0.40 subset: ( $i * $i ) > $o)).
% 0.19/0.40 tff(unordered_pair_type, type, (
% 0.19/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_D_3_type, type, (
% 0.19/0.40 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))) <=> (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (subset(singleton(A), singleton(B)) => (A = B))) <=> (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,axiom,(~![A: $i, B: $i] : (subset(singleton(A), singleton(B)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_zfmisc_1')).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ~((~subset(singleton(A!14), singleton(B!13))) | (A!14 = B!13))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (subset(singleton(A!14), singleton(B!13))),
% 0.19/0.40 inference(or_elim,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.40 tff(18,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_xboole_1')).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.40 tff(21,plain,(
% 0.19/0.40 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[20])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!14), singleton(B!13))) | (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!14), singleton(B!13))) | (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!14), singleton(B!13))) | (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!14), singleton(B!13))) | (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (singleton(B!13) = set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = singleton(B!13)),
% 0.19/0.41 inference(symmetry,[status(thm)],[26])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> in(A!14, singleton(B!13))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (in(A!14, singleton(B!13)) <=> in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(33,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.41 tff(35,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[34])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(A!14), singleton(B!13)) <=> in(A!14, singleton(B!13)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (subset(singleton(A!14), singleton(B!13)) <=> in(A!14, singleton(B!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~(subset(singleton(A!14), singleton(B!13)) <=> in(A!14, singleton(B!13)))) | (~subset(singleton(A!14), singleton(B!13))) | in(A!14, singleton(B!13))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~(subset(singleton(A!14), singleton(B!13)) <=> in(A!14, singleton(B!13)))) | in(A!14, singleton(B!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[39, 12])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (in(A!14, singleton(B!13))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[40, 38])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 29])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(pull_quant,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[48, 44])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.41 tff(60,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.41 tff(63,plain,(
% 0.19/0.41 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((A!14 = B!13) | (A!14 = B!13))))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> ((tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13) | (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))) <=> (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((A!14 = B!13) | (A!14 = B!13))))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> ((tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13) | (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((A!14 = B!13) | (A!14 = B!13))))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> ((tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13) | (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> ((A!14 = B!13) | (A!14 = B!13))))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> ((tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13) | (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) | (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (~((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 66])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~((set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)) | ((~in(tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13), set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) <=> (tptp_fun_D_3(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))), B!13, B!13) = B!13))))) | ((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (^[A: $i] : refl((unordered_pair(A, A) = singleton(A)) <=> (unordered_pair(A, A) = singleton(A)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (![A: $i] : (unordered_pair(A, A) = singleton(A)) <=> ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (![A: $i] : (unordered_pair(A, A) = singleton(A)) <=> ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(79,axiom,(![A: $i] : (unordered_pair(A, A) = singleton(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t69_enumset1')).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.42 tff(81,plain,(
% 0.19/0.42 ![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.42 inference(skolemize,[status(sab)],[80])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) | (unordered_pair(B!13, B!13) = singleton(B!13))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (unordered_pair(B!13, B!13) = singleton(B!13)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (singleton(B!13) = unordered_pair(B!13, B!13)),
% 0.19/0.42 inference(symmetry,[status(thm)],[84])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13)),
% 0.19/0.42 inference(transitivity,[status(thm)],[27, 85])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 ((~((~(set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))) = unordered_pair(B!13, B!13))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)))) | (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[88, 75])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (~(A!14 = B!13)),
% 0.19/0.43 inference(or_elim,[status(thm)],[11])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 ((~(in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))) | (~in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))) | (A!14 = B!13)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 ((~(in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))) <=> (A!14 = B!13))) | (~in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (~in(A!14, set_union2(singleton(A!14), set_difference(singleton(B!13), singleton(A!14))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[93, 42])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------