TSTP Solution File: SET872+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 05:08:28 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 08:48:07 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(in_type, type, (
% 0.13/0.39 in: ( $i * $i ) > $o)).
% 0.13/0.39 tff(unordered_pair_type, type, (
% 0.13/0.39 unordered_pair: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_A_6_type, type, (
% 0.13/0.39 tptp_fun_A_6: $i)).
% 0.13/0.39 tff(tptp_fun_B_5_type, type, (
% 0.13/0.39 tptp_fun_B_5: $i)).
% 0.13/0.39 tff(tptp_fun_C_2_type, type, (
% 0.13/0.39 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.13/0.39 tff(singleton_type, type, (
% 0.13/0.39 singleton: $i > $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_D_1_type, type, (
% 0.13/0.39 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_C_0_type, type, (
% 0.13/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.39 inference(skolemize,[status(sab)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!6, B!5) = unordered_pair(B!5, A!6))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (unordered_pair(A!6, B!5) = unordered_pair(B!5, A!6)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (unordered_pair(B!5, A!6) = unordered_pair(A!6, B!5)),
% 0.13/0.39 inference(symmetry,[status(thm)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)) <=> in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))),
% 0.13/0.39 inference(symmetry,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))) <=> (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[17, 15])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.39 tff(24,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.13/0.39 tff(27,plain,(
% 0.13/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[26])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(singleton(A!6), unordered_pair(A!6, B!5))) | ![C: $i] : ((~in(C, singleton(A!6))) | in(C, unordered_pair(A!6, B!5))))) | (~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (~((~((~subset(singleton(A!6), unordered_pair(A!6, B!5))) | ![C: $i] : ((~in(C, singleton(A!6))) | in(C, unordered_pair(A!6, B!5))))) | (~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (((~((~subset(singleton(A!6), unordered_pair(A!6, B!5))) | ![C: $i] : ((~in(C, singleton(A!6))) | in(C, unordered_pair(A!6, B!5))))) | (~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))))) | (subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))) <=> (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(35,axiom,(~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_zfmisc_1')).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (~![A: $i, B: $i] : subset(singleton(A), unordered_pair(A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.39 tff(43,plain,(
% 0.21/0.39 ~subset(singleton(A!6), unordered_pair(A!6, B!5))),
% 0.21/0.39 inference(skolemize,[status(sab)],[42])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))))) | subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 ((~(subset(singleton(A!6), unordered_pair(A!6, B!5)) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))))) | (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[45, 33])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[48, 13])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(pull_quant,[status(thm)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[55, 51])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[58, 56])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.40 tff(67,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.21/0.40 tff(70,plain,(
% 0.21/0.40 ![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[69])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[72, 59])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))) | $false) <=> ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 ((~$true) <=> $false),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (($true | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 ((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))) <=> ($true | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))) <=> $true),
% 0.21/0.41 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ((~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 ((~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[82, 77])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 (($false | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 ((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[86, 77])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> ($false | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[88, 85])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 ((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 ((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) <=> ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[90, 84])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))) <=> (((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[91, 83])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))) <=> ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[92, 76])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ((~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))) <=> (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 ((~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5))))))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[94, 75])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[95])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))) <=> ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[96, 74])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))))) | (~((unordered_pair(B!5, A!6) = unordered_pair(B!5, A!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5), unordered_pair(B!5, A!6))) <=> ((tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = A!6) | (tptp_fun_D_1(unordered_pair(B!5, A!6), A!6, B!5) = B!5)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 73])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(pull_quant,[status(thm)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[106, 102])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(116,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.42 tff(118,plain,(
% 0.21/0.42 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[117])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 ((~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ((((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)) | $false) <=> ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (($true | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))) <=> $true),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ((singleton(A!6) = singleton(A!6)) <=> $true),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))) <=> $true),
% 0.21/0.42 inference(transitivity,[status(thm)],[127, 125])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 ((~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> (~$true)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 ((~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> $false),
% 0.21/0.42 inference(transitivity,[status(thm)],[129, 77])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (($false | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 ((~(singleton(A!6) = singleton(A!6))) <=> (~$true)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 ((~(singleton(A!6) = singleton(A!6))) <=> $false),
% 0.21/0.43 inference(transitivity,[status(thm)],[133, 77])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 (((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> ($false | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[134])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.43 inference(transitivity,[status(thm)],[135, 132])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 ((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) <=> (~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 ((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) <=> ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.43 inference(transitivity,[status(thm)],[137, 131])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))) <=> (((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)) | $false)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[138, 130])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))) <=> ((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.43 inference(transitivity,[status(thm)],[139, 124])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 ((~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))) <=> (~((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 ((~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))) <=> (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.43 inference(transitivity,[status(thm)],[141, 123])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[142])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[143, 122])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[146, 121])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (((~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(A!6, B!5))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[148, 46])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) | (~in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6))) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[151, 147])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)) | (~(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 ((~(in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) <=> ((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))) | in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6)) | (~((tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = A!6) | (tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)) = B!5)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 (in(tptp_fun_C_2(unordered_pair(A!6, B!5), singleton(A!6)), unordered_pair(B!5, A!6))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[155, 154, 100])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[156, 49])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------