TSTP Solution File: SET918+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 05:08:37 EDT 2022
% Result : Theorem 7.70s 5.11s
% Output : Proof 7.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET918+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 : n020.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 08:35:14 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.
% 7.70/5.11 % SZS status Theorem
% 7.70/5.11 % SZS output start Proof
% 7.70/5.11 tff(tptp_fun_B_6_type, type, (
% 7.70/5.11 tptp_fun_B_6: $i)).
% 7.70/5.11 tff(tptp_fun_D_1_type, type, (
% 7.70/5.11 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 7.70/5.11 tff(tptp_fun_A_7_type, type, (
% 7.70/5.11 tptp_fun_A_7: $i)).
% 7.70/5.11 tff(singleton_type, type, (
% 7.70/5.11 singleton: $i > $i)).
% 7.70/5.11 tff(in_type, type, (
% 7.70/5.11 in: ( $i * $i ) > $o)).
% 7.70/5.11 tff(tptp_fun_C_0_type, type, (
% 7.70/5.11 tptp_fun_C_0: ( $i * $i ) > $i)).
% 7.70/5.11 tff(unordered_pair_type, type, (
% 7.70/5.11 unordered_pair: ( $i * $i ) > $i)).
% 7.70/5.11 tff(set_intersection2_type, type, (
% 7.70/5.11 set_intersection2: ( $i * $i ) > $i)).
% 7.70/5.11 tff(tptp_fun_C_5_type, type, (
% 7.70/5.11 tptp_fun_C_5: $i)).
% 7.70/5.11 tff(tptp_fun_D_2_type, type, (
% 7.70/5.11 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 7.70/5.11 tff(1,assumption,(~(tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)), introduced(assumption)).
% 7.70/5.11 tff(2,assumption,(~(in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))), introduced(assumption)).
% 7.70/5.11 tff(3,plain,
% 7.70/5.11 (^[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)))))))),
% 7.70/5.11 inference(bind,[status(th)],[])).
% 7.70/5.11 tff(4,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(quant_intro,[status(thm)],[3])).
% 7.70/5.11 tff(5,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(pull_quant,[status(thm)],[])).
% 7.70/5.11 tff(6,plain,
% 7.70/5.11 (^[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))))))))),
% 7.70/5.11 inference(bind,[status(th)],[])).
% 7.70/5.11 tff(7,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(quant_intro,[status(thm)],[6])).
% 7.70/5.11 tff(8,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(transitivity,[status(thm)],[7, 5])).
% 7.70/5.11 tff(9,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(transitivity,[status(thm)],[8, 4])).
% 7.70/5.11 tff(10,plain,
% 7.70/5.11 (^[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)))))))),
% 7.70/5.11 inference(bind,[status(th)],[])).
% 7.70/5.11 tff(11,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(quant_intro,[status(thm)],[10])).
% 7.70/5.11 tff(12,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(transitivity,[status(thm)],[11, 9])).
% 7.70/5.11 tff(13,plain,
% 7.70/5.11 (^[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))))))))),
% 7.70/5.11 inference(bind,[status(th)],[])).
% 7.70/5.11 tff(14,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(quant_intro,[status(thm)],[13])).
% 7.70/5.11 tff(15,plain,
% 7.70/5.11 (^[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)))))),
% 7.70/5.11 inference(bind,[status(th)],[])).
% 7.70/5.11 tff(16,plain,
% 7.70/5.11 (![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))))),
% 7.70/5.11 inference(quant_intro,[status(thm)],[15])).
% 7.70/5.11 tff(17,plain,
% 7.70/5.11 (![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)))),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(18,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 7.70/5.11 tff(19,plain,
% 7.70/5.11 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 7.70/5.11 inference(modus_ponens,[status(thm)],[18, 17])).
% 7.70/5.11 tff(20,plain,(
% 7.70/5.11 ![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)))))),
% 7.70/5.11 inference(skolemize,[status(sab)],[19])).
% 7.70/5.11 tff(21,plain,
% 7.70/5.11 (![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))))),
% 7.70/5.11 inference(modus_ponens,[status(thm)],[20, 16])).
% 7.70/5.11 tff(22,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(modus_ponens,[status(thm)],[21, 14])).
% 7.70/5.11 tff(23,plain,
% 7.70/5.11 (![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))))))),
% 7.70/5.11 inference(modus_ponens,[status(thm)],[22, 12])).
% 7.70/5.11 tff(24,plain,
% 7.70/5.11 (((~![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_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))) <=> ((~![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_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(25,plain,
% 7.70/5.11 ((~((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))) <=> (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(26,plain,
% 7.70/5.11 ((((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)) | $false) <=> ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(27,plain,
% 7.70/5.11 ((~$true) <=> $false),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(28,plain,
% 7.70/5.11 (($true | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> $true),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(29,plain,
% 7.70/5.11 ((singleton(A!7) = singleton(A!7)) <=> $true),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(30,plain,
% 7.70/5.11 (((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))),
% 7.70/5.11 inference(monotonicity,[status(thm)],[29])).
% 7.70/5.11 tff(31,plain,
% 7.70/5.11 (((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> $true),
% 7.70/5.11 inference(transitivity,[status(thm)],[30, 28])).
% 7.70/5.11 tff(32,plain,
% 7.70/5.11 ((~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> (~$true)),
% 7.70/5.11 inference(monotonicity,[status(thm)],[31])).
% 7.70/5.11 tff(33,plain,
% 7.70/5.11 ((~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $false),
% 7.70/5.11 inference(transitivity,[status(thm)],[32, 27])).
% 7.70/5.11 tff(34,plain,
% 7.70/5.11 ((~(in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))) <=> ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(35,plain,
% 7.70/5.11 (($false | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))) <=> (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(rewrite,[status(thm)],[])).
% 7.70/5.11 tff(36,plain,
% 7.70/5.11 ((~(singleton(A!7) = singleton(A!7))) <=> (~$true)),
% 7.70/5.11 inference(monotonicity,[status(thm)],[29])).
% 7.70/5.11 tff(37,plain,
% 7.70/5.11 ((~(singleton(A!7) = singleton(A!7))) <=> $false),
% 7.70/5.11 inference(transitivity,[status(thm)],[36, 27])).
% 7.70/5.11 tff(38,plain,
% 7.70/5.11 (((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))) <=> ($false | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))),
% 7.70/5.11 inference(monotonicity,[status(thm)],[37])).
% 7.70/5.11 tff(39,plain,
% 7.70/5.11 (((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))) <=> (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(transitivity,[status(thm)],[38, 35])).
% 7.70/5.11 tff(40,plain,
% 7.70/5.11 ((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) <=> (~(in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))),
% 7.70/5.11 inference(monotonicity,[status(thm)],[39])).
% 7.70/5.11 tff(41,plain,
% 7.70/5.11 ((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) <=> ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(transitivity,[status(thm)],[40, 34])).
% 7.70/5.11 tff(42,plain,
% 7.70/5.11 (((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> (((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)) | $false)),
% 7.70/5.11 inference(monotonicity,[status(thm)],[41, 33])).
% 7.70/5.11 tff(43,plain,
% 7.70/5.11 (((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(transitivity,[status(thm)],[42, 26])).
% 7.70/5.11 tff(44,plain,
% 7.70/5.11 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))),
% 7.70/5.11 inference(monotonicity,[status(thm)],[43])).
% 7.70/5.11 tff(45,plain,
% 7.70/5.11 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(transitivity,[status(thm)],[44, 25])).
% 7.70/5.11 tff(46,plain,
% 7.70/5.11 (((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> ((~![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_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))),
% 7.70/5.11 inference(monotonicity,[status(thm)],[45])).
% 7.70/5.11 tff(47,plain,
% 7.70/5.11 (((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> ((~![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_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))),
% 7.70/5.11 inference(transitivity,[status(thm)],[46, 24])).
% 7.70/5.11 tff(48,plain,
% 7.70/5.11 ((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))),
% 7.70/5.11 inference(quant_inst,[status(thm)],[])).
% 7.70/5.11 tff(49,plain,
% 7.70/5.11 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.70/5.11 inference(modus_ponens,[status(thm)],[48, 47])).
% 7.70/5.11 tff(50,plain,
% 7.70/5.11 ($false),
% 7.70/5.11 inference(unit_resolution,[status(thm)],[49, 23, 2])).
% 7.70/5.11 tff(51,plain,(in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)), inference(lemma,lemma(discharge,[]))).
% 7.70/5.11 tff(52,plain,
% 7.70/5.11 ((~(in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))) | (~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)),
% 7.70/5.11 inference(tautology,[status(thm)],[])).
% 7.70/5.11 tff(53,plain,
% 7.70/5.11 ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)),
% 7.70/5.11 inference(unit_resolution,[status(thm)],[52, 51])).
% 7.70/5.11 tff(54,plain,
% 7.70/5.11 (~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))),
% 7.70/5.11 inference(unit_resolution,[status(thm)],[53, 1])).
% 7.70/5.11 tff(55,assumption,((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))))), introduced(assumption)).
% 7.70/5.11 tff(56,plain,
% 7.70/5.11 (^[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))))))))),
% 7.70/5.11 inference(bind,[status(th)],[])).
% 7.70/5.11 tff(57,plain,
% 7.70/5.11 (![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)))))))),
% 7.70/5.11 inference(quant_intro,[status(thm)],[56])).
% 7.70/5.11 tff(58,plain,
% 7.70/5.11 (![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)))))))),
% 7.70/5.11 inference(pull_quant,[status(thm)],[])).
% 7.70/5.11 tff(59,plain,
% 7.70/5.11 (^[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)))))))))),
% 7.70/5.12 inference(bind,[status(th)],[])).
% 7.70/5.12 tff(60,plain,
% 7.70/5.12 (![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)))))))),
% 7.70/5.12 inference(quant_intro,[status(thm)],[59])).
% 7.70/5.12 tff(61,plain,
% 7.70/5.12 (![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)))))))),
% 7.70/5.12 inference(transitivity,[status(thm)],[60, 58])).
% 7.70/5.12 tff(62,plain,
% 7.70/5.12 (![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)))))))),
% 7.70/5.12 inference(transitivity,[status(thm)],[61, 57])).
% 7.70/5.12 tff(63,plain,
% 7.70/5.12 (^[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))))))))),
% 7.70/5.12 inference(bind,[status(th)],[])).
% 7.70/5.12 tff(64,plain,
% 7.70/5.12 (![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)))))))),
% 7.70/5.12 inference(quant_intro,[status(thm)],[63])).
% 7.70/5.12 tff(65,plain,
% 7.70/5.12 (![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)))))))),
% 7.70/5.12 inference(transitivity,[status(thm)],[64, 62])).
% 7.70/5.12 tff(66,plain,
% 7.70/5.12 (^[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)))))))))),
% 7.70/5.12 inference(bind,[status(th)],[])).
% 7.70/5.12 tff(67,plain,
% 7.70/5.12 (![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)))))))),
% 7.70/5.12 inference(quant_intro,[status(thm)],[66])).
% 7.70/5.12 tff(68,plain,
% 7.70/5.12 (^[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))))))),
% 7.70/5.12 inference(bind,[status(th)],[])).
% 7.70/5.12 tff(69,plain,
% 7.70/5.12 (![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)))))),
% 7.70/5.12 inference(quant_intro,[status(thm)],[68])).
% 7.70/5.12 tff(70,plain,
% 7.70/5.12 (![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))))),
% 7.70/5.12 inference(rewrite,[status(thm)],[])).
% 7.70/5.12 tff(71,plain,
% 7.70/5.12 (^[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)))))),
% 7.70/5.12 inference(bind,[status(th)],[])).
% 7.70/5.12 tff(72,plain,
% 7.70/5.12 (![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))))),
% 7.70/5.12 inference(quant_intro,[status(thm)],[71])).
% 7.70/5.12 tff(73,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')).
% 7.70/5.12 tff(74,plain,
% 7.70/5.12 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[73, 72])).
% 7.70/5.12 tff(75,plain,
% 7.70/5.12 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[74, 70])).
% 7.70/5.12 tff(76,plain,(
% 7.70/5.12 ![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))))))),
% 7.70/5.12 inference(skolemize,[status(sab)],[75])).
% 7.70/5.12 tff(77,plain,
% 7.70/5.12 (![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)))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[76, 69])).
% 7.70/5.12 tff(78,plain,
% 7.70/5.12 (![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)))))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[77, 67])).
% 7.70/5.12 tff(79,plain,
% 7.70/5.12 (![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)))))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[78, 65])).
% 7.70/5.12 tff(80,plain,
% 7.70/5.12 (((~![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)))))))) | (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))))))) <=> ((~![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)))))))) | (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))))))),
% 7.70/5.12 inference(rewrite,[status(thm)],[])).
% 7.70/5.12 tff(81,plain,
% 7.70/5.12 ((~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))))))) <=> (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))))))),
% 7.70/5.12 inference(rewrite,[status(thm)],[])).
% 7.70/5.12 tff(82,plain,
% 7.70/5.12 (((~![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)))))))) | (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))))))) <=> ((~![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)))))))) | (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))))))),
% 7.70/5.12 inference(monotonicity,[status(thm)],[81])).
% 7.70/5.12 tff(83,plain,
% 7.70/5.12 (((~![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)))))))) | (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))))))) <=> ((~![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)))))))) | (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))))))),
% 7.70/5.12 inference(transitivity,[status(thm)],[82, 80])).
% 7.70/5.12 tff(84,plain,
% 7.70/5.12 ((~![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)))))))) | (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7)))))))),
% 7.70/5.12 inference(quant_inst,[status(thm)],[])).
% 7.70/5.12 tff(85,plain,
% 7.70/5.12 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[84, 83])).
% 7.70/5.12 tff(86,plain,
% 7.70/5.12 ($false),
% 7.70/5.12 inference(unit_resolution,[status(thm)],[85, 79, 55])).
% 7.70/5.12 tff(87,plain,(~((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))))), inference(lemma,lemma(discharge,[]))).
% 7.70/5.12 tff(88,plain,
% 7.70/5.12 (((~((~(singleton(A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))))) | ((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))),
% 7.70/5.12 inference(tautology,[status(thm)],[])).
% 7.70/5.12 tff(89,plain,
% 7.70/5.12 ((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))),
% 7.70/5.12 inference(unit_resolution,[status(thm)],[88, 87])).
% 7.70/5.12 tff(90,plain,
% 7.70/5.12 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 7.70/5.12 inference(bind,[status(th)],[])).
% 7.70/5.12 tff(91,plain,
% 7.70/5.12 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 7.70/5.12 inference(quant_intro,[status(thm)],[90])).
% 7.70/5.12 tff(92,plain,
% 7.70/5.12 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 7.70/5.12 inference(rewrite,[status(thm)],[])).
% 7.70/5.12 tff(93,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 7.70/5.12 tff(94,plain,
% 7.70/5.12 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[93, 92])).
% 7.70/5.12 tff(95,plain,(
% 7.70/5.12 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 7.70/5.12 inference(skolemize,[status(sab)],[94])).
% 7.70/5.12 tff(96,plain,
% 7.70/5.12 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[95, 91])).
% 7.70/5.12 tff(97,plain,
% 7.70/5.12 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7))),
% 7.70/5.12 inference(quant_inst,[status(thm)],[])).
% 7.70/5.12 tff(98,plain,
% 7.70/5.12 (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7)),
% 7.70/5.12 inference(unit_resolution,[status(thm)],[97, 96])).
% 7.70/5.12 tff(99,plain,
% 7.70/5.12 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 7.70/5.12 inference(symmetry,[status(thm)],[98])).
% 7.70/5.12 tff(100,plain,
% 7.70/5.12 (set_intersection2(unordered_pair(B!6, A!7), C!5) = set_intersection2(unordered_pair(A!7, B!6), C!5)),
% 7.70/5.12 inference(monotonicity,[status(thm)],[99])).
% 7.70/5.12 tff(101,plain,
% 7.70/5.12 (set_intersection2(unordered_pair(A!7, B!6), C!5) = set_intersection2(unordered_pair(B!6, A!7), C!5)),
% 7.70/5.12 inference(symmetry,[status(thm)],[100])).
% 7.70/5.12 tff(102,plain,
% 7.70/5.12 ((~(~((set_intersection2(unordered_pair(A!7, B!6), C!5) = singleton(A!7)) & in(B!6, C!5) & (~(A!7 = B!6))))) <=> ((set_intersection2(unordered_pair(A!7, B!6), C!5) = singleton(A!7)) & in(B!6, C!5) & (~(A!7 = B!6)))),
% 7.70/5.12 inference(rewrite,[status(thm)],[])).
% 7.70/5.12 tff(103,plain,
% 7.70/5.12 ((~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))) <=> (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B)))))),
% 7.70/5.12 inference(rewrite,[status(thm)],[])).
% 7.70/5.12 tff(104,plain,
% 7.70/5.12 ((~![A: $i, B: $i, C: $i] : (~(((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C)) & (~(A = B))))) <=> (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B)))))),
% 7.70/5.12 inference(rewrite,[status(thm)],[])).
% 7.70/5.12 tff(105,axiom,(~![A: $i, B: $i, C: $i] : (~(((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C)) & (~(A = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t59_zfmisc_1')).
% 7.70/5.12 tff(106,plain,
% 7.70/5.12 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[105, 104])).
% 7.70/5.12 tff(107,plain,
% 7.70/5.12 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[106, 103])).
% 7.70/5.12 tff(108,plain,
% 7.70/5.12 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[107, 103])).
% 7.70/5.12 tff(109,plain,
% 7.70/5.12 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[108, 103])).
% 7.70/5.12 tff(110,plain,
% 7.70/5.12 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[109, 103])).
% 7.70/5.12 tff(111,plain,
% 7.70/5.12 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[110, 103])).
% 7.70/5.12 tff(112,plain,
% 7.70/5.12 (~![A: $i, B: $i, C: $i] : (~((set_intersection2(unordered_pair(A, B), C) = singleton(A)) & in(B, C) & (~(A = B))))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[111, 103])).
% 7.70/5.12 tff(113,plain,(
% 7.70/5.12 ~(~((set_intersection2(unordered_pair(A!7, B!6), C!5) = singleton(A!7)) & in(B!6, C!5) & (~(A!7 = B!6))))),
% 7.70/5.12 inference(skolemize,[status(sab)],[112])).
% 7.70/5.12 tff(114,plain,
% 7.70/5.12 ((set_intersection2(unordered_pair(A!7, B!6), C!5) = singleton(A!7)) & in(B!6, C!5) & (~(A!7 = B!6))),
% 7.70/5.12 inference(modus_ponens,[status(thm)],[113, 102])).
% 7.70/5.12 tff(115,plain,
% 7.70/5.12 (set_intersection2(unordered_pair(A!7, B!6), C!5) = singleton(A!7)),
% 7.70/5.12 inference(and_elim,[status(thm)],[114])).
% 7.70/5.12 tff(116,plain,
% 7.70/5.12 (singleton(A!7) = set_intersection2(unordered_pair(A!7, B!6), C!5)),
% 7.70/5.12 inference(symmetry,[status(thm)],[115])).
% 7.70/5.12 tff(117,assumption,(singleton(A!7) = unordered_pair(A!7, B!6)), introduced(assumption)).
% 7.70/5.12 tff(118,plain,
% 7.70/5.12 (unordered_pair(A!7, B!6) = singleton(A!7)),
% 7.70/5.12 inference(symmetry,[status(thm)],[117])).
% 7.70/5.12 tff(119,plain,
% 7.70/5.12 (unordered_pair(B!6, A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)),
% 7.70/5.12 inference(transitivity,[status(thm)],[99, 118, 116, 101])).
% 7.70/5.12 tff(120,plain,
% 7.70/5.12 (singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)),
% 7.70/5.12 inference(transitivity,[status(thm)],[116, 101])).
% 7.70/5.12 tff(121,plain,
% 7.70/5.12 ((unordered_pair(B!6, A!7) = singleton(A!7)) <=> (unordered_pair(B!6, A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))),
% 7.70/5.12 inference(monotonicity,[status(thm)],[120])).
% 7.70/5.12 tff(122,plain,
% 7.70/5.12 ((~(unordered_pair(B!6, A!7) = singleton(A!7))) <=> (~(unordered_pair(B!6, A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)))),
% 7.70/5.12 inference(monotonicity,[status(thm)],[121])).
% 7.70/5.12 tff(123,plain,
% 7.70/5.12 ((~![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))))))) | (~((~((~(unordered_pair(B!6, A!7) = singleton(A!7))) | (in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7)))) | (~((unordered_pair(B!6, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(B!6, A!7), A!7), unordered_pair(B!6, A!7))) <=> (tptp_fun_C_0(unordered_pair(B!6, A!7), A!7) = A!7))))))),
% 7.70/5.12 inference(quant_inst,[status(thm)],[])).
% 7.70/5.12 tff(124,plain,
% 7.70/5.12 (~((~((~(unordered_pair(B!6, A!7) = singleton(A!7))) | (in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7)))) | (~((unordered_pair(B!6, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(B!6, A!7), A!7), unordered_pair(B!6, A!7))) <=> (tptp_fun_C_0(unordered_pair(B!6, A!7), A!7) = A!7)))))),
% 7.70/5.12 inference(unit_resolution,[status(thm)],[123, 23])).
% 7.70/5.12 tff(125,plain,
% 7.70/5.12 (((~((~(unordered_pair(B!6, A!7) = singleton(A!7))) | (in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7)))) | (~((unordered_pair(B!6, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(B!6, A!7), A!7), unordered_pair(B!6, A!7))) <=> (tptp_fun_C_0(unordered_pair(B!6, A!7), A!7) = A!7))))) | ((~(unordered_pair(B!6, A!7) = singleton(A!7))) | (in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7)))),
% 7.70/5.12 inference(tautology,[status(thm)],[])).
% 7.70/5.12 tff(126,plain,
% 7.70/5.12 ((~(unordered_pair(B!6, A!7) = singleton(A!7))) | (in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7))),
% 7.70/5.12 inference(unit_resolution,[status(thm)],[125, 124])).
% 7.70/5.12 tff(127,assumption,((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))), introduced(assumption)).
% 7.70/5.12 tff(128,plain,
% 7.70/5.12 (((~![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!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![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!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 7.70/5.13 inference(rewrite,[status(thm)],[])).
% 7.70/5.13 tff(129,plain,
% 7.70/5.13 ((~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(B!6, unordered_pair(B!6, A!7)) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))) <=> (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 7.70/5.13 inference(rewrite,[status(thm)],[])).
% 7.70/5.13 tff(130,plain,
% 7.70/5.13 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(B!6, unordered_pair(B!6, A!7)) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![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!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 7.70/5.13 inference(monotonicity,[status(thm)],[129])).
% 7.70/5.13 tff(131,plain,
% 7.70/5.13 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(B!6, unordered_pair(B!6, A!7)) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![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!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 7.70/5.13 inference(transitivity,[status(thm)],[130, 128])).
% 7.70/5.13 tff(132,plain,
% 7.70/5.13 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(B!6, unordered_pair(B!6, A!7)) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 7.70/5.13 inference(quant_inst,[status(thm)],[])).
% 7.70/5.13 tff(133,plain,
% 7.70/5.13 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 7.70/5.13 inference(modus_ponens,[status(thm)],[132, 131])).
% 7.70/5.13 tff(134,plain,
% 7.70/5.13 ($false),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[133, 79, 127])).
% 7.70/5.13 tff(135,plain,(~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))), inference(lemma,lemma(discharge,[]))).
% 7.70/5.13 tff(136,plain,
% 7.70/5.13 (((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))) | ((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))),
% 7.70/5.13 inference(tautology,[status(thm)],[])).
% 7.70/5.13 tff(137,plain,
% 7.70/5.13 ((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[136, 135])).
% 7.70/5.13 tff(138,plain,
% 7.70/5.13 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))),
% 7.70/5.13 inference(quant_inst,[status(thm)],[])).
% 7.70/5.13 tff(139,plain,
% 7.70/5.13 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[138, 96])).
% 7.70/5.13 tff(140,plain,
% 7.70/5.13 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | (~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7))),
% 7.70/5.13 inference(tautology,[status(thm)],[])).
% 7.70/5.13 tff(141,plain,
% 7.70/5.13 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(B!6, unordered_pair(B!6, A!7)))) | in(B!6, unordered_pair(B!6, A!7))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[140, 139])).
% 7.70/5.13 tff(142,plain,
% 7.70/5.13 (in(B!6, unordered_pair(B!6, A!7))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[141, 137])).
% 7.70/5.13 tff(143,plain,
% 7.70/5.13 ((B!6 = A!7) <=> (A!7 = B!6)),
% 7.70/5.13 inference(commutativity,[status(thm)],[])).
% 7.70/5.13 tff(144,plain,
% 7.70/5.13 ((A!7 = B!6) <=> (B!6 = A!7)),
% 7.70/5.13 inference(symmetry,[status(thm)],[143])).
% 7.70/5.13 tff(145,plain,
% 7.70/5.13 ((~(A!7 = B!6)) <=> (~(B!6 = A!7))),
% 7.70/5.13 inference(monotonicity,[status(thm)],[144])).
% 7.70/5.13 tff(146,plain,
% 7.70/5.13 (~(A!7 = B!6)),
% 7.70/5.13 inference(and_elim,[status(thm)],[114])).
% 7.70/5.13 tff(147,plain,
% 7.70/5.13 (~(B!6 = A!7)),
% 7.70/5.13 inference(modus_ponens,[status(thm)],[146, 145])).
% 7.70/5.13 tff(148,plain,
% 7.70/5.13 ((~(in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7))) | (~in(B!6, unordered_pair(B!6, A!7))) | (B!6 = A!7)),
% 7.70/5.13 inference(tautology,[status(thm)],[])).
% 7.70/5.13 tff(149,plain,
% 7.70/5.13 (~(in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[148, 147, 142])).
% 7.70/5.13 tff(150,plain,
% 7.70/5.13 ((~((~(unordered_pair(B!6, A!7) = singleton(A!7))) | (in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7)))) | (~(unordered_pair(B!6, A!7) = singleton(A!7))) | (in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7))),
% 7.70/5.13 inference(tautology,[status(thm)],[])).
% 7.70/5.13 tff(151,plain,
% 7.70/5.13 ((~((~(unordered_pair(B!6, A!7) = singleton(A!7))) | (in(B!6, unordered_pair(B!6, A!7)) <=> (B!6 = A!7)))) | (~(unordered_pair(B!6, A!7) = singleton(A!7)))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[150, 149])).
% 7.70/5.13 tff(152,plain,
% 7.70/5.13 (~(unordered_pair(B!6, A!7) = singleton(A!7))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[151, 126])).
% 7.70/5.13 tff(153,plain,
% 7.70/5.13 (~(unordered_pair(B!6, A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))),
% 7.70/5.13 inference(modus_ponens,[status(thm)],[152, 122])).
% 7.70/5.13 tff(154,plain,
% 7.70/5.13 ($false),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[153, 119])).
% 7.70/5.13 tff(155,plain,(~(singleton(A!7) = unordered_pair(A!7, B!6))), inference(lemma,lemma(discharge,[]))).
% 7.70/5.13 tff(156,plain,
% 7.70/5.13 ((~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | (singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))),
% 7.70/5.13 inference(tautology,[status(thm)],[])).
% 7.70/5.13 tff(157,plain,
% 7.70/5.13 ((~((singleton(A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))))) | ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[156, 155])).
% 7.70/5.13 tff(158,plain,
% 7.70/5.13 ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[157, 89])).
% 7.70/5.13 tff(159,plain,
% 7.70/5.13 ((~((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))) | in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) | ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))),
% 7.70/5.13 inference(tautology,[status(thm)],[])).
% 7.70/5.13 tff(160,plain,
% 7.70/5.13 (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) | ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[159, 158])).
% 7.70/5.13 tff(161,plain,
% 7.70/5.13 ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[160, 54])).
% 7.70/5.13 tff(162,plain,
% 7.70/5.13 ((~((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6))) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)),
% 7.70/5.13 inference(tautology,[status(thm)],[])).
% 7.70/5.13 tff(163,plain,
% 7.70/5.13 (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6),
% 7.70/5.13 inference(unit_resolution,[status(thm)],[162, 161, 1])).
% 7.70/5.13 tff(164,plain,
% 7.70/5.13 (B!6 = tptp_fun_D_1(singleton(A!7), B!6, A!7)),
% 7.70/5.13 inference(symmetry,[status(thm)],[163])).
% 7.70/5.13 tff(165,plain,
% 7.70/5.13 (in(B!6, singleton(A!7)) <=> in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))),
% 7.70/5.13 inference(monotonicity,[status(thm)],[164])).
% 7.70/5.13 tff(166,plain,
% 7.70/5.13 (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> in(B!6, singleton(A!7))),
% 7.70/5.13 inference(symmetry,[status(thm)],[165])).
% 7.70/5.13 tff(167,plain,
% 7.70/5.13 ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> (~in(B!6, singleton(A!7)))),
% 7.70/5.13 inference(monotonicity,[status(thm)],[166])).
% 7.70/5.13 tff(168,plain,
% 7.70/5.13 (~in(B!6, singleton(A!7))),
% 7.70/5.13 inference(modus_ponens,[status(thm)],[54, 167])).
% 7.70/5.13 tff(169,plain,
% 7.70/5.13 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))))),
% 7.70/5.13 inference(bind,[status(th)],[])).
% 7.70/5.13 tff(170,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(quant_intro,[status(thm)],[169])).
% 7.70/5.13 tff(171,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(pull_quant,[status(thm)],[])).
% 7.70/5.13 tff(172,plain,
% 7.70/5.13 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))))),
% 7.70/5.13 inference(bind,[status(th)],[])).
% 7.70/5.13 tff(173,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(quant_intro,[status(thm)],[172])).
% 7.70/5.13 tff(174,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(transitivity,[status(thm)],[173, 171])).
% 7.70/5.13 tff(175,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(transitivity,[status(thm)],[174, 170])).
% 7.70/5.13 tff(176,plain,
% 7.70/5.13 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))))),
% 7.70/5.13 inference(bind,[status(th)],[])).
% 7.70/5.13 tff(177,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(quant_intro,[status(thm)],[176])).
% 7.70/5.13 tff(178,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(transitivity,[status(thm)],[177, 175])).
% 7.70/5.13 tff(179,plain,
% 7.70/5.13 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))), rewrite(((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))) <=> ((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))))),
% 7.70/5.13 inference(bind,[status(th)],[])).
% 7.70/5.13 tff(180,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(quant_intro,[status(thm)],[179])).
% 7.70/5.13 tff(181,plain,
% 7.70/5.13 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))))),
% 7.70/5.13 inference(bind,[status(th)],[])).
% 7.70/5.13 tff(182,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))),
% 7.70/5.13 inference(quant_intro,[status(thm)],[181])).
% 7.70/5.13 tff(183,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 7.70/5.13 inference(rewrite,[status(thm)],[])).
% 7.70/5.13 tff(184,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 7.70/5.13 tff(185,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 7.70/5.13 inference(modus_ponens,[status(thm)],[184, 183])).
% 7.70/5.13 tff(186,plain,(
% 7.70/5.13 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B))))))),
% 7.70/5.13 inference(skolemize,[status(sab)],[185])).
% 7.70/5.13 tff(187,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & in(tptp_fun_D_2(C, B, A), B)))))),
% 7.70/5.13 inference(modus_ponens,[status(thm)],[186, 182])).
% 7.70/5.13 tff(188,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(modus_ponens,[status(thm)],[187, 180])).
% 7.70/5.13 tff(189,plain,
% 7.70/5.13 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))),
% 7.70/5.13 inference(modus_ponens,[status(thm)],[188, 178])).
% 7.70/5.13 tff(190,plain,
% 7.70/5.13 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5)))))))))),
% 7.70/5.13 inference(rewrite,[status(thm)],[])).
% 7.70/5.13 tff(191,plain,
% 7.70/5.13 ((~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, unordered_pair(B!6, A!7))) | (~in(B!6, C!5))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5)))))))) <=> (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 7.70/5.13 inference(rewrite,[status(thm)],[])).
% 7.70/5.13 tff(192,plain,
% 7.70/5.13 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, unordered_pair(B!6, A!7))) | (~in(B!6, C!5))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5)))))))))),
% 7.70/5.13 inference(monotonicity,[status(thm)],[191])).
% 7.70/5.13 tff(193,plain,
% 7.70/5.13 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, unordered_pair(B!6, A!7))) | (~in(B!6, C!5))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5)))))))))),
% 7.77/5.14 inference(transitivity,[status(thm)],[192, 190])).
% 7.77/5.14 tff(194,plain,
% 7.77/5.14 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, unordered_pair(B!6, A!7))) | (~in(B!6, C!5))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 7.77/5.14 inference(quant_inst,[status(thm)],[])).
% 7.77/5.14 tff(195,plain,
% 7.77/5.14 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 7.77/5.14 inference(modus_ponens,[status(thm)],[194, 193])).
% 7.77/5.14 tff(196,plain,
% 7.77/5.14 (~((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5)))))))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[195, 189])).
% 7.77/5.14 tff(197,plain,
% 7.77/5.14 (((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~((singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5)) | (in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), singleton(A!7)) <=> ((~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7))) | (~in(tptp_fun_D_2(singleton(A!7), C!5, unordered_pair(B!6, A!7)), C!5))))))) | ((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))),
% 7.77/5.14 inference(tautology,[status(thm)],[])).
% 7.77/5.14 tff(198,plain,
% 7.77/5.14 ((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[197, 196])).
% 7.77/5.14 tff(199,plain,
% 7.77/5.14 ((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))))),
% 7.77/5.14 inference(tautology,[status(thm)],[])).
% 7.77/5.14 tff(200,plain,
% 7.77/5.14 ((~((~(singleton(A!7) = set_intersection2(unordered_pair(B!6, A!7), C!5))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))))) | (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[199, 120])).
% 7.77/5.14 tff(201,plain,
% 7.77/5.14 (in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[200, 198])).
% 7.77/5.14 tff(202,plain,
% 7.77/5.14 (in(B!6, C!5)),
% 7.77/5.14 inference(and_elim,[status(thm)],[114])).
% 7.77/5.14 tff(203,plain,
% 7.77/5.14 ((~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))) | (~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7)))),
% 7.77/5.14 inference(tautology,[status(thm)],[])).
% 7.77/5.14 tff(204,plain,
% 7.77/5.14 ((~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))) | (~in(B!6, unordered_pair(B!6, A!7)))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[203, 202])).
% 7.77/5.14 tff(205,plain,
% 7.77/5.14 (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[204, 142])).
% 7.77/5.14 tff(206,plain,
% 7.77/5.14 ((~(in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))))) | in(B!6, singleton(A!7)) | ((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))),
% 7.77/5.14 inference(tautology,[status(thm)],[])).
% 7.77/5.14 tff(207,plain,
% 7.77/5.14 ((~(in(B!6, singleton(A!7)) <=> (~((~in(B!6, C!5)) | (~in(B!6, unordered_pair(B!6, A!7))))))) | in(B!6, singleton(A!7))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[206, 205])).
% 7.77/5.14 tff(208,plain,
% 7.77/5.14 (in(B!6, singleton(A!7))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[207, 201])).
% 7.77/5.14 tff(209,plain,
% 7.77/5.14 ($false),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[208, 168])).
% 7.77/5.14 tff(210,plain,(tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7), inference(lemma,lemma(discharge,[]))).
% 7.77/5.14 tff(211,plain,
% 7.77/5.14 (((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)) | (~(tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.77/5.14 inference(tautology,[status(thm)],[])).
% 7.77/5.14 tff(212,plain,
% 7.77/5.14 ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[211, 210])).
% 7.77/5.14 tff(213,plain,
% 7.77/5.14 ((~(in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) <=> (tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))) | in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) | (~(tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.77/5.14 inference(tautology,[status(thm)],[])).
% 7.77/5.14 tff(214,plain,
% 7.77/5.14 (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7)) | (~(tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[213, 51])).
% 7.77/5.14 tff(215,plain,
% 7.77/5.14 (in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[214, 210])).
% 7.77/5.14 tff(216,plain,
% 7.77/5.14 ((~((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) <=> ((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))) | (~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) | (~((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))),
% 7.77/5.14 inference(tautology,[status(thm)],[])).
% 7.77/5.14 tff(217,plain,
% 7.77/5.14 ((~in(tptp_fun_D_1(singleton(A!7), B!6, A!7), singleton(A!7))) | (~((tptp_fun_D_1(singleton(A!7), B!6, A!7) = A!7) | (tptp_fun_D_1(singleton(A!7), B!6, A!7) = B!6)))),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[216, 158])).
% 7.77/5.14 tff(218,plain,
% 7.77/5.14 ($false),
% 7.77/5.14 inference(unit_resolution,[status(thm)],[217, 215, 212])).
% 7.77/5.14 % SZS output end Proof
%------------------------------------------------------------------------------