TSTP Solution File: SET881+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 05:08:30 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 08:48:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(in_type, type, (
% 0.19/0.39 in: ( $i * $i ) > $o)).
% 0.19/0.39 tff(unordered_pair_type, type, (
% 0.19/0.39 unordered_pair: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_A_4_type, type, (
% 0.19/0.39 tptp_fun_A_4: $i)).
% 0.19/0.39 tff(tptp_fun_B_3_type, type, (
% 0.19/0.39 tptp_fun_B_3: $i)).
% 0.19/0.39 tff(empty_set_type, type, (
% 0.19/0.39 empty_set: $i)).
% 0.19/0.39 tff(set_difference_type, type, (
% 0.19/0.39 set_difference: ( $i * $i ) > $i)).
% 0.19/0.39 tff(singleton_type, type, (
% 0.19/0.39 singleton: $i > $i)).
% 0.19/0.39 tff(tptp_fun_D_0_type, type, (
% 0.19/0.39 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.19/0.39 inference(symmetry,[status(thm)],[9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (in(A!4, unordered_pair(B!3, A!4)) <=> in(A!4, unordered_pair(A!4, B!3))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (in(A!4, unordered_pair(A!4, B!3)) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.19/0.39 inference(symmetry,[status(thm)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((~in(A!4, unordered_pair(A!4, B!3))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl(((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B)) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,axiom,(![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l36_zfmisc_1')).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,(
% 0.19/0.39 ![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.19/0.39 inference(skolemize,[status(sab)],[18])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((set_difference(singleton(A), B) = empty_set) <=> in(A, B))) | ((set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) <=> in(A!4, unordered_pair(A!4, B!3)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) <=> in(A!4, unordered_pair(A!4, B!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)) <=> (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(24,axiom,(~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_zfmisc_1')).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (~![A: $i, B: $i] : (set_difference(singleton(A), unordered_pair(A, B)) = empty_set)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.39 tff(32,plain,(
% 0.19/0.39 ~(set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set)),
% 0.19/0.39 inference(skolemize,[status(sab)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~((set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) <=> in(A!4, unordered_pair(A!4, B!3)))) | (set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) | (~in(A!4, unordered_pair(A!4, B!3)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~((set_difference(singleton(A!4), unordered_pair(A!4, B!3)) = empty_set) <=> in(A!4, unordered_pair(A!4, B!3)))) | (~in(A!4, unordered_pair(A!4, B!3)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (~in(A!4, unordered_pair(A!4, B!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 22])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (~in(A!4, unordered_pair(B!3, A!4))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 13])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (^[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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.39 inference(pull_quant,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (^[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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[42, 38])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (^[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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[45, 43])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (^[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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (^[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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.40 tff(54,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')).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.40 tff(57,plain,(
% 0.19/0.40 ![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_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[56])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 46])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | in(A!4, unordered_pair(B!3, A!4))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | in(A!4, unordered_pair(B!3, A!4)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~(~in(A!4, unordered_pair(B!3, A!4)))) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (((~in(A!4, unordered_pair(B!3, A!4))) | $false) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ((~$true) <=> $false),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (($true | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))) <=> ($true | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))) <=> $true),
% 0.19/0.40 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[69, 64])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))) <=> ((~in(A!4, unordered_pair(B!3, A!4))) | $false)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[71, 70])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[72, 63])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))) <=> (~(~in(A!4, unordered_pair(B!3, A!4))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.19/0.40 inference(transitivity,[status(thm)],[74, 62])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | in(A!4, unordered_pair(B!3, A!4)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))) <=> ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | in(A!4, unordered_pair(B!3, A!4)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[76, 61])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((~![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_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | in(A!4, unordered_pair(B!3, A!4))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (in(A!4, unordered_pair(B!3, A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[79, 60])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[80, 36])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------