TSTP Solution File: SET919+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET919+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 6.58s 4.48s
% Output : Proof 6.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET919+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 08:32:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 6.58/4.48 % SZS status Theorem
% 6.58/4.48 % SZS output start Proof
% 6.58/4.48 tff(tptp_fun_A_7_type, type, (
% 6.58/4.48 tptp_fun_A_7: $i)).
% 6.58/4.48 tff(tptp_fun_C_0_type, type, (
% 6.58/4.48 tptp_fun_C_0: ( $i * $i ) > $i)).
% 6.58/4.48 tff(set_intersection2_type, type, (
% 6.58/4.48 set_intersection2: ( $i * $i ) > $i)).
% 6.58/4.48 tff(unordered_pair_type, type, (
% 6.58/4.48 unordered_pair: ( $i * $i ) > $i)).
% 6.58/4.48 tff(tptp_fun_C_5_type, type, (
% 6.58/4.48 tptp_fun_C_5: $i)).
% 6.58/4.48 tff(tptp_fun_B_6_type, type, (
% 6.58/4.48 tptp_fun_B_6: $i)).
% 6.58/4.48 tff(in_type, type, (
% 6.58/4.48 in: ( $i * $i ) > $o)).
% 6.58/4.48 tff(singleton_type, type, (
% 6.58/4.48 singleton: $i > $i)).
% 6.58/4.48 tff(tptp_fun_D_2_type, type, (
% 6.58/4.48 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 6.58/4.48 tff(tptp_fun_D_1_type, type, (
% 6.58/4.48 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 6.58/4.48 tff(1,assumption,((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))))), introduced(assumption)).
% 6.58/4.48 tff(2,plain,
% 6.58/4.48 (^[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)))))))),
% 6.58/4.48 inference(bind,[status(th)],[])).
% 6.58/4.48 tff(3,plain,
% 6.58/4.48 (![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))))))),
% 6.58/4.48 inference(quant_intro,[status(thm)],[2])).
% 6.58/4.48 tff(4,plain,
% 6.58/4.48 (![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))))))),
% 6.58/4.48 inference(pull_quant,[status(thm)],[])).
% 6.58/4.48 tff(5,plain,
% 6.58/4.48 (^[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))))))))),
% 6.66/4.48 inference(bind,[status(th)],[])).
% 6.66/4.48 tff(6,plain,
% 6.66/4.48 (![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))))))),
% 6.66/4.48 inference(quant_intro,[status(thm)],[5])).
% 6.66/4.48 tff(7,plain,
% 6.66/4.48 (![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))))))),
% 6.66/4.48 inference(transitivity,[status(thm)],[6, 4])).
% 6.66/4.48 tff(8,plain,
% 6.66/4.48 (![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))))))),
% 6.66/4.48 inference(transitivity,[status(thm)],[7, 3])).
% 6.66/4.48 tff(9,plain,
% 6.66/4.48 (^[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)))))))),
% 6.66/4.48 inference(bind,[status(th)],[])).
% 6.66/4.48 tff(10,plain,
% 6.66/4.48 (![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))))))),
% 6.66/4.48 inference(quant_intro,[status(thm)],[9])).
% 6.66/4.48 tff(11,plain,
% 6.66/4.48 (![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))))))),
% 6.66/4.48 inference(transitivity,[status(thm)],[10, 8])).
% 6.66/4.48 tff(12,plain,
% 6.66/4.48 (^[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))))))))),
% 6.66/4.48 inference(bind,[status(th)],[])).
% 6.66/4.48 tff(13,plain,
% 6.66/4.48 (![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))))))),
% 6.66/4.48 inference(quant_intro,[status(thm)],[12])).
% 6.66/4.48 tff(14,plain,
% 6.66/4.48 (^[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)))))),
% 6.66/4.48 inference(bind,[status(th)],[])).
% 6.66/4.48 tff(15,plain,
% 6.66/4.48 (![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))))),
% 6.66/4.48 inference(quant_intro,[status(thm)],[14])).
% 6.66/4.48 tff(16,plain,
% 6.66/4.48 (![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)))),
% 6.66/4.48 inference(rewrite,[status(thm)],[])).
% 6.66/4.48 tff(17,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 6.66/4.48 tff(18,plain,
% 6.66/4.48 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 6.66/4.48 inference(modus_ponens,[status(thm)],[17, 16])).
% 6.66/4.48 tff(19,plain,(
% 6.66/4.48 ![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)))))),
% 6.66/4.48 inference(skolemize,[status(sab)],[18])).
% 6.66/4.48 tff(20,plain,
% 6.66/4.48 (![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))))),
% 6.66/4.48 inference(modus_ponens,[status(thm)],[19, 15])).
% 6.66/4.48 tff(21,plain,
% 6.66/4.48 (![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))))))),
% 6.66/4.48 inference(modus_ponens,[status(thm)],[20, 13])).
% 6.66/4.48 tff(22,plain,
% 6.66/4.48 (![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))))))),
% 6.66/4.48 inference(modus_ponens,[status(thm)],[21, 11])).
% 6.66/4.48 tff(23,plain,
% 6.66/4.48 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))))))),
% 6.66/4.48 inference(quant_inst,[status(thm)],[])).
% 6.66/4.48 tff(24,plain,
% 6.66/4.48 ($false),
% 6.66/4.48 inference(unit_resolution,[status(thm)],[23, 22, 1])).
% 6.66/4.48 tff(25,plain,(~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.48 tff(26,assumption,((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), B!6))))))), introduced(assumption)).
% 6.66/4.48 tff(27,plain,
% 6.66/4.48 (^[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)))))))))),
% 6.66/4.48 inference(bind,[status(th)],[])).
% 6.66/4.48 tff(28,plain,
% 6.66/4.48 (![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))))))))),
% 6.66/4.48 inference(quant_intro,[status(thm)],[27])).
% 6.66/4.48 tff(29,plain,
% 6.66/4.48 (![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))))))))),
% 6.66/4.48 inference(pull_quant,[status(thm)],[])).
% 6.66/4.48 tff(30,plain,
% 6.66/4.48 (^[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))))))))))),
% 6.66/4.48 inference(bind,[status(th)],[])).
% 6.66/4.48 tff(31,plain,
% 6.66/4.48 (![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))))))))),
% 6.66/4.48 inference(quant_intro,[status(thm)],[30])).
% 6.66/4.48 tff(32,plain,
% 6.66/4.48 (![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))))))))),
% 6.66/4.48 inference(transitivity,[status(thm)],[31, 29])).
% 6.66/4.48 tff(33,plain,
% 6.66/4.48 (![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))))))))),
% 6.66/4.48 inference(transitivity,[status(thm)],[32, 28])).
% 6.66/4.48 tff(34,plain,
% 6.66/4.48 (^[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)))))))))),
% 6.66/4.48 inference(bind,[status(th)],[])).
% 6.66/4.48 tff(35,plain,
% 6.66/4.48 (![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))))))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[34])).
% 6.66/4.49 tff(36,plain,
% 6.66/4.49 (![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))))))))),
% 6.66/4.49 inference(transitivity,[status(thm)],[35, 33])).
% 6.66/4.49 tff(37,plain,
% 6.66/4.49 (^[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))))))))))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(38,plain,
% 6.66/4.49 (![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))))))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[37])).
% 6.66/4.49 tff(39,plain,
% 6.66/4.49 (^[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))))))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(40,plain,
% 6.66/4.49 (![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)))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[39])).
% 6.66/4.49 tff(41,plain,
% 6.66/4.49 (![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))))),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(42,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')).
% 6.66/4.49 tff(43,plain,
% 6.66/4.49 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[42, 41])).
% 6.66/4.49 tff(44,plain,(
% 6.66/4.49 ![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))))))),
% 6.66/4.49 inference(skolemize,[status(sab)],[43])).
% 6.66/4.49 tff(45,plain,
% 6.66/4.49 (![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)))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[44, 40])).
% 6.66/4.49 tff(46,plain,
% 6.66/4.49 (![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))))))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[45, 38])).
% 6.66/4.49 tff(47,plain,
% 6.66/4.49 (![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))))))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[46, 36])).
% 6.66/4.49 tff(48,plain,
% 6.66/4.49 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | (~in(tptp_fun_D_2(C, B, A), B))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), B!6))))))))),
% 6.66/4.49 inference(quant_inst,[status(thm)],[])).
% 6.66/4.49 tff(49,plain,
% 6.66/4.49 ($false),
% 6.66/4.49 inference(unit_resolution,[status(thm)],[48, 47, 26])).
% 6.66/4.49 tff(50,plain,(~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), B!6)))))))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.49 tff(51,plain,
% 6.66/4.49 (((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), B!6))))))) | ((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))))),
% 6.66/4.49 inference(tautology,[status(thm)],[])).
% 6.66/4.49 tff(52,plain,
% 6.66/4.49 ((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))))),
% 6.66/4.49 inference(unit_resolution,[status(thm)],[51, 50])).
% 6.66/4.49 tff(53,plain,
% 6.66/4.49 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(54,plain,
% 6.66/4.49 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[53])).
% 6.66/4.49 tff(55,plain,
% 6.66/4.49 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(56,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 6.66/4.49 tff(57,plain,
% 6.66/4.49 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[56, 55])).
% 6.66/4.49 tff(58,plain,(
% 6.66/4.49 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 6.66/4.49 inference(skolemize,[status(sab)],[57])).
% 6.66/4.49 tff(59,plain,
% 6.66/4.49 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[58, 54])).
% 6.66/4.49 tff(60,plain,
% 6.66/4.49 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, C!5) = unordered_pair(C!5, A!7))),
% 6.66/4.49 inference(quant_inst,[status(thm)],[])).
% 6.66/4.49 tff(61,plain,
% 6.66/4.49 (unordered_pair(A!7, C!5) = unordered_pair(C!5, A!7)),
% 6.66/4.49 inference(unit_resolution,[status(thm)],[60, 59])).
% 6.66/4.49 tff(62,plain,
% 6.66/4.49 (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)),
% 6.66/4.49 inference(symmetry,[status(thm)],[61])).
% 6.66/4.49 tff(63,plain,
% 6.66/4.49 (set_intersection2(unordered_pair(C!5, A!7), B!6) = set_intersection2(unordered_pair(A!7, C!5), B!6)),
% 6.66/4.49 inference(monotonicity,[status(thm)],[62])).
% 6.66/4.49 tff(64,plain,
% 6.66/4.49 (set_intersection2(unordered_pair(A!7, C!5), B!6) = set_intersection2(unordered_pair(C!5, A!7), B!6)),
% 6.66/4.49 inference(symmetry,[status(thm)],[63])).
% 6.66/4.49 tff(65,plain,
% 6.66/4.49 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(66,plain,
% 6.66/4.49 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[65])).
% 6.66/4.49 tff(67,plain,
% 6.66/4.49 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(68,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 6.66/4.49 tff(69,plain,
% 6.66/4.49 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[68, 67])).
% 6.66/4.49 tff(70,plain,(
% 6.66/4.49 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 6.66/4.49 inference(skolemize,[status(sab)],[69])).
% 6.66/4.49 tff(71,plain,
% 6.66/4.49 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[70, 66])).
% 6.66/4.49 tff(72,plain,
% 6.66/4.49 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(unordered_pair(A!7, C!5), B!6) = set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 6.66/4.49 inference(quant_inst,[status(thm)],[])).
% 6.66/4.49 tff(73,plain,
% 6.66/4.49 (set_intersection2(unordered_pair(A!7, C!5), B!6) = set_intersection2(B!6, unordered_pair(A!7, C!5))),
% 6.66/4.49 inference(unit_resolution,[status(thm)],[72, 71])).
% 6.66/4.49 tff(74,plain,
% 6.66/4.49 (set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(A!7, C!5), B!6)),
% 6.66/4.49 inference(symmetry,[status(thm)],[73])).
% 6.66/4.49 tff(75,plain,
% 6.66/4.49 (set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6)),
% 6.66/4.49 inference(transitivity,[status(thm)],[74, 64])).
% 6.66/4.49 tff(76,plain,
% 6.66/4.49 ((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))))) | (~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))))),
% 6.66/4.49 inference(tautology,[status(thm)],[])).
% 6.66/4.49 tff(77,plain,
% 6.66/4.49 ((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))))),
% 6.66/4.49 inference(unit_resolution,[status(thm)],[76, 75])).
% 6.66/4.49 tff(78,plain,
% 6.66/4.49 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))),
% 6.66/4.49 inference(unit_resolution,[status(thm)],[77, 52])).
% 6.66/4.49 tff(79,assumption,((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))), introduced(assumption)).
% 6.66/4.49 tff(80,assumption,(~(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)), introduced(assumption)).
% 6.66/4.49 tff(81,plain,
% 6.66/4.49 (^[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))))))))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(82,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[81])).
% 6.66/4.49 tff(83,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(pull_quant,[status(thm)],[])).
% 6.66/4.49 tff(84,plain,
% 6.66/4.49 (^[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)))))))))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(85,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[84])).
% 6.66/4.49 tff(86,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(transitivity,[status(thm)],[85, 83])).
% 6.66/4.49 tff(87,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(transitivity,[status(thm)],[86, 82])).
% 6.66/4.49 tff(88,plain,
% 6.66/4.49 (^[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))))))))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(89,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[88])).
% 6.66/4.49 tff(90,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(transitivity,[status(thm)],[89, 87])).
% 6.66/4.49 tff(91,plain,
% 6.66/4.49 (^[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)))))))))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(92,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[91])).
% 6.66/4.49 tff(93,plain,
% 6.66/4.49 (^[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))))))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(94,plain,
% 6.66/4.49 (![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)))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[93])).
% 6.66/4.49 tff(95,plain,
% 6.66/4.49 (![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))))),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(96,plain,
% 6.66/4.49 (^[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)))))),
% 6.66/4.49 inference(bind,[status(th)],[])).
% 6.66/4.49 tff(97,plain,
% 6.66/4.49 (![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))))),
% 6.66/4.49 inference(quant_intro,[status(thm)],[96])).
% 6.66/4.49 tff(98,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')).
% 6.66/4.49 tff(99,plain,
% 6.66/4.49 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[98, 97])).
% 6.66/4.49 tff(100,plain,
% 6.66/4.49 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[99, 95])).
% 6.66/4.49 tff(101,plain,(
% 6.66/4.49 ![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))))))),
% 6.66/4.49 inference(skolemize,[status(sab)],[100])).
% 6.66/4.49 tff(102,plain,
% 6.66/4.49 (![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)))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[101, 94])).
% 6.66/4.49 tff(103,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[102, 92])).
% 6.66/4.49 tff(104,plain,
% 6.66/4.49 (![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)))))))),
% 6.66/4.49 inference(modus_ponens,[status(thm)],[103, 90])).
% 6.66/4.49 tff(105,plain,
% 6.66/4.49 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(106,plain,
% 6.66/4.49 ((~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))) <=> (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(107,plain,
% 6.66/4.49 ((((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))) | $false) <=> ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(108,plain,
% 6.66/4.49 ((~$true) <=> $false),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(109,plain,
% 6.66/4.49 (($true | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))) <=> $true),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(110,plain,
% 6.66/4.49 ((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) <=> $true),
% 6.66/4.49 inference(rewrite,[status(thm)],[])).
% 6.66/4.49 tff(111,plain,
% 6.66/4.49 (((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))) <=> ($true | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))),
% 6.66/4.50 inference(monotonicity,[status(thm)],[110])).
% 6.66/4.50 tff(112,plain,
% 6.66/4.50 (((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))) <=> $true),
% 6.66/4.50 inference(transitivity,[status(thm)],[111, 109])).
% 6.66/4.50 tff(113,plain,
% 6.66/4.50 ((~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))) <=> (~$true)),
% 6.66/4.50 inference(monotonicity,[status(thm)],[112])).
% 6.66/4.50 tff(114,plain,
% 6.66/4.50 ((~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))) <=> $false),
% 6.66/4.50 inference(transitivity,[status(thm)],[113, 108])).
% 6.66/4.50 tff(115,plain,
% 6.66/4.50 ((~(in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.50 inference(rewrite,[status(thm)],[])).
% 6.66/4.50 tff(116,plain,
% 6.66/4.50 (($false | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))) <=> (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.50 inference(rewrite,[status(thm)],[])).
% 6.66/4.50 tff(117,plain,
% 6.66/4.50 ((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) <=> (~$true)),
% 6.66/4.50 inference(monotonicity,[status(thm)],[110])).
% 6.66/4.50 tff(118,plain,
% 6.66/4.50 ((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) <=> $false),
% 6.66/4.50 inference(transitivity,[status(thm)],[117, 108])).
% 6.66/4.50 tff(119,plain,
% 6.66/4.50 (((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))) <=> ($false | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))),
% 6.66/4.50 inference(monotonicity,[status(thm)],[118])).
% 6.66/4.50 tff(120,plain,
% 6.66/4.50 (((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))) <=> (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.50 inference(transitivity,[status(thm)],[119, 116])).
% 6.66/4.50 tff(121,plain,
% 6.66/4.50 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) <=> (~(in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))),
% 6.66/4.50 inference(monotonicity,[status(thm)],[120])).
% 6.66/4.50 tff(122,plain,
% 6.66/4.50 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.50 inference(transitivity,[status(thm)],[121, 115])).
% 6.66/4.50 tff(123,plain,
% 6.66/4.50 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))) <=> (((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))) | $false)),
% 6.66/4.50 inference(monotonicity,[status(thm)],[122, 114])).
% 6.66/4.50 tff(124,plain,
% 6.66/4.50 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.50 inference(transitivity,[status(thm)],[123, 107])).
% 6.66/4.50 tff(125,plain,
% 6.66/4.50 ((~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))),
% 6.66/4.50 inference(monotonicity,[status(thm)],[124])).
% 6.66/4.50 tff(126,plain,
% 6.66/4.50 ((~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))) <=> (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.50 inference(transitivity,[status(thm)],[125, 106])).
% 6.66/4.50 tff(127,plain,
% 6.66/4.50 (((~![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(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))),
% 6.66/4.50 inference(monotonicity,[status(thm)],[126])).
% 6.66/4.50 tff(128,plain,
% 6.66/4.50 (((~![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(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))),
% 6.66/4.50 inference(transitivity,[status(thm)],[127, 105])).
% 6.66/4.50 tff(129,plain,
% 6.66/4.50 ((~![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(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))))),
% 6.66/4.50 inference(quant_inst,[status(thm)],[])).
% 6.66/4.50 tff(130,plain,
% 6.66/4.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))),
% 6.66/4.50 inference(modus_ponens,[status(thm)],[129, 128])).
% 6.66/4.50 tff(131,plain,
% 6.66/4.50 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))),
% 6.66/4.50 inference(unit_resolution,[status(thm)],[130, 104])).
% 6.66/4.50 tff(132,plain,
% 6.66/4.50 (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> ((~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(set_intersection2(B!6, unordered_pair(A!7, C!5)), B!6, unordered_pair(C!5, A!7)), B!6)))))))),
% 6.66/4.50 inference(unit_resolution,[status(thm)],[48, 47])).
% 6.66/4.50 tff(133,plain,
% 6.66/4.50 ((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))))),
% 6.66/4.50 inference(unit_resolution,[status(thm)],[51, 132])).
% 6.66/4.50 tff(134,plain,
% 6.66/4.50 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))),
% 6.66/4.50 inference(unit_resolution,[status(thm)],[77, 133])).
% 6.66/4.50 tff(135,plain,
% 6.66/4.50 ((~![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))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))))))),
% 6.66/4.50 inference(quant_inst,[status(thm)],[])).
% 6.66/4.50 tff(136,plain,
% 6.66/4.50 (~((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))))),
% 6.66/4.50 inference(unit_resolution,[status(thm)],[135, 22])).
% 6.66/4.50 tff(137,plain,
% 6.66/4.50 (((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))))) | ((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))),
% 6.66/4.50 inference(tautology,[status(thm)],[])).
% 6.66/4.50 tff(138,plain,
% 6.66/4.50 ((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))),
% 6.66/4.50 inference(unit_resolution,[status(thm)],[137, 136])).
% 6.66/4.50 tff(139,plain,
% 6.66/4.50 ((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) <=> (set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7))),
% 6.66/4.50 inference(monotonicity,[status(thm)],[74])).
% 6.66/4.50 tff(140,plain,
% 6.66/4.50 ((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) <=> (set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))),
% 6.66/4.50 inference(symmetry,[status(thm)],[139])).
% 6.66/4.50 tff(141,plain,
% 6.66/4.50 ((~(set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7))) <=> (~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)))),
% 6.66/4.50 inference(monotonicity,[status(thm)],[140])).
% 6.66/4.50 tff(142,plain,
% 6.66/4.50 ((~((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) | (in(C!5, B!6) & (~(A!7 = C!5))) | (~in(A!7, B!6)))) <=> (~((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) | (in(C!5, B!6) & (~(A!7 = C!5))) | (~in(A!7, B!6))))),
% 6.66/4.50 inference(rewrite,[status(thm)],[])).
% 6.66/4.50 tff(143,plain,
% 6.66/4.50 ((~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))) <=> (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B))))),
% 6.66/4.50 inference(rewrite,[status(thm)],[])).
% 6.66/4.50 tff(144,plain,
% 6.66/4.50 ((~![A: $i, B: $i, C: $i] : (in(A, B) => ((in(C, B) & (~(A = C))) | (set_intersection2(unordered_pair(A, C), B) = singleton(A))))) <=> (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B))))),
% 6.66/4.50 inference(rewrite,[status(thm)],[])).
% 6.66/4.50 tff(145,axiom,(~![A: $i, B: $i, C: $i] : (in(A, B) => ((in(C, B) & (~(A = C))) | (set_intersection2(unordered_pair(A, C), B) = singleton(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_zfmisc_1')).
% 6.66/4.50 tff(146,plain,
% 6.66/4.50 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 6.66/4.50 inference(modus_ponens,[status(thm)],[145, 144])).
% 6.66/4.50 tff(147,plain,
% 6.66/4.50 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 6.66/4.50 inference(modus_ponens,[status(thm)],[146, 143])).
% 6.66/4.51 tff(148,plain,
% 6.66/4.51 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[147, 143])).
% 6.66/4.51 tff(149,plain,
% 6.66/4.51 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[148, 143])).
% 6.66/4.51 tff(150,plain,
% 6.66/4.51 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[149, 143])).
% 6.66/4.51 tff(151,plain,
% 6.66/4.51 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[150, 143])).
% 6.66/4.51 tff(152,plain,
% 6.66/4.51 (~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, C), B) = singleton(A)) | (in(C, B) & (~(A = C))) | (~in(A, B)))),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[151, 143])).
% 6.66/4.51 tff(153,plain,(
% 6.66/4.51 ~((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) | (in(C!5, B!6) & (~(A!7 = C!5))) | (~in(A!7, B!6)))),
% 6.66/4.51 inference(skolemize,[status(sab)],[152])).
% 6.66/4.51 tff(154,plain,
% 6.66/4.51 (~((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) | (in(C!5, B!6) & (~(A!7 = C!5))) | (~in(A!7, B!6)))),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[153, 142])).
% 6.66/4.51 tff(155,plain,
% 6.66/4.51 (~(set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7))),
% 6.66/4.51 inference(or_elim,[status(thm)],[154])).
% 6.66/4.51 tff(156,plain,
% 6.66/4.51 (~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[155, 141])).
% 6.66/4.51 tff(157,plain,
% 6.66/4.51 ((~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))) | (set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(158,plain,
% 6.66/4.51 ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[157, 156, 138])).
% 6.66/4.51 tff(159,plain,
% 6.66/4.51 ((~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))) | in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(160,plain,
% 6.66/4.51 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[159, 80, 158])).
% 6.66/4.51 tff(161,plain,
% 6.66/4.51 ((~(in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(162,plain,
% 6.66/4.51 (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[161, 160, 134])).
% 6.66/4.51 tff(163,plain,
% 6.66/4.51 (((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))) | in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(164,plain,
% 6.66/4.51 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[163, 162])).
% 6.66/4.51 tff(165,plain,
% 6.66/4.51 ((~(in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(166,plain,
% 6.66/4.51 ((~(in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)))) | ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[165, 164])).
% 6.66/4.51 tff(167,plain,
% 6.66/4.51 ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[166, 131])).
% 6.66/4.51 tff(168,plain,
% 6.66/4.51 ((~((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5))) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5)),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(169,plain,
% 6.66/4.51 (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = C!5),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[168, 167, 80])).
% 6.66/4.51 tff(170,plain,
% 6.66/4.51 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6) <=> in(C!5, B!6)),
% 6.66/4.51 inference(monotonicity,[status(thm)],[169])).
% 6.66/4.51 tff(171,plain,
% 6.66/4.51 (in(C!5, B!6) <=> in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)),
% 6.66/4.51 inference(symmetry,[status(thm)],[170])).
% 6.66/4.51 tff(172,plain,
% 6.66/4.51 ((~in(C!5, B!6)) <=> (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))),
% 6.66/4.51 inference(monotonicity,[status(thm)],[171])).
% 6.66/4.51 tff(173,assumption,(~in(C!5, B!6)), introduced(assumption)).
% 6.66/4.51 tff(174,plain,
% 6.66/4.51 (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[173, 172])).
% 6.66/4.51 tff(175,plain,
% 6.66/4.51 (((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))) | in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(176,plain,
% 6.66/4.51 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[175, 162])).
% 6.66/4.51 tff(177,plain,
% 6.66/4.51 ($false),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[176, 174])).
% 6.66/4.51 tff(178,plain,((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) | in(C!5, B!6)), inference(lemma,lemma(discharge,[]))).
% 6.66/4.51 tff(179,plain,
% 6.66/4.51 (in(C!5, B!6)),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[178, 80])).
% 6.66/4.51 tff(180,plain,
% 6.66/4.51 ((~(~((~in(C!5, B!6)) | (A!7 = C!5)))) <=> ((~in(C!5, B!6)) | (A!7 = C!5))),
% 6.66/4.51 inference(rewrite,[status(thm)],[])).
% 6.66/4.51 tff(181,plain,
% 6.66/4.51 ((in(C!5, B!6) & (~(A!7 = C!5))) <=> (~((~in(C!5, B!6)) | (A!7 = C!5)))),
% 6.66/4.51 inference(rewrite,[status(thm)],[])).
% 6.66/4.51 tff(182,plain,
% 6.66/4.51 ((~(in(C!5, B!6) & (~(A!7 = C!5)))) <=> (~(~((~in(C!5, B!6)) | (A!7 = C!5))))),
% 6.66/4.51 inference(monotonicity,[status(thm)],[181])).
% 6.66/4.51 tff(183,plain,
% 6.66/4.51 ((~(in(C!5, B!6) & (~(A!7 = C!5)))) <=> ((~in(C!5, B!6)) | (A!7 = C!5))),
% 6.66/4.51 inference(transitivity,[status(thm)],[182, 180])).
% 6.66/4.51 tff(184,plain,
% 6.66/4.51 (~(in(C!5, B!6) & (~(A!7 = C!5)))),
% 6.66/4.51 inference(or_elim,[status(thm)],[154])).
% 6.66/4.51 tff(185,plain,
% 6.66/4.51 ((~in(C!5, B!6)) | (A!7 = C!5)),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[184, 183])).
% 6.66/4.51 tff(186,plain,
% 6.66/4.51 (A!7 = C!5),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[185, 179])).
% 6.66/4.51 tff(187,assumption,(A!7 = C!5), introduced(assumption)).
% 6.66/4.51 tff(188,plain,
% 6.66/4.51 ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)),
% 6.66/4.51 inference(monotonicity,[status(thm)],[187])).
% 6.66/4.51 tff(189,plain,
% 6.66/4.51 ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 6.66/4.51 inference(symmetry,[status(thm)],[188])).
% 6.66/4.51 tff(190,assumption,((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5))))), introduced(assumption)).
% 6.66/4.51 tff(191,plain,
% 6.66/4.51 (((~![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(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5)))))))),
% 6.66/4.51 inference(rewrite,[status(thm)],[])).
% 6.66/4.51 tff(192,plain,
% 6.66/4.51 ((~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5))))))) <=> (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5))))))),
% 6.66/4.51 inference(rewrite,[status(thm)],[])).
% 6.66/4.51 tff(193,plain,
% 6.66/4.51 (((~![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(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5)))))))),
% 6.66/4.51 inference(monotonicity,[status(thm)],[192])).
% 6.66/4.51 tff(194,plain,
% 6.66/4.51 (((~![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(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5)))))))),
% 6.66/4.51 inference(transitivity,[status(thm)],[193, 191])).
% 6.66/4.51 tff(195,plain,
% 6.66/4.51 ((~![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(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5)))))))),
% 6.66/4.51 inference(quant_inst,[status(thm)],[])).
% 6.66/4.51 tff(196,plain,
% 6.66/4.51 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5))))))),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[195, 194])).
% 6.66/4.51 tff(197,plain,
% 6.66/4.51 ($false),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[196, 104, 190])).
% 6.66/4.51 tff(198,plain,(~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5)))))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.51 tff(199,plain,
% 6.66/4.51 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5), unordered_pair(C!5, A!7))) <=> (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, C!5) = C!5))))) | ((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(200,plain,
% 6.66/4.51 ((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5))),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[199, 198])).
% 6.66/4.51 tff(201,plain,
% 6.66/4.51 (C!5 = A!7),
% 6.66/4.51 inference(symmetry,[status(thm)],[187])).
% 6.66/4.51 tff(202,plain,
% 6.66/4.51 (unordered_pair(C!5, C!5) = unordered_pair(A!7, C!5)),
% 6.66/4.51 inference(monotonicity,[status(thm)],[201])).
% 6.66/4.51 tff(203,plain,
% 6.66/4.51 (unordered_pair(A!7, C!5) = unordered_pair(C!5, C!5)),
% 6.66/4.51 inference(symmetry,[status(thm)],[202])).
% 6.66/4.51 tff(204,plain,
% 6.66/4.51 (unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5)),
% 6.66/4.51 inference(transitivity,[status(thm)],[62, 203])).
% 6.66/4.51 tff(205,plain,
% 6.66/4.51 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)))) | (~(unordered_pair(C!5, A!7) = unordered_pair(C!5, C!5))) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(206,plain,
% 6.66/4.51 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[205, 204, 200])).
% 6.66/4.51 tff(207,assumption,(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))), introduced(assumption)).
% 6.66/4.51 tff(208,assumption,(~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))), introduced(assumption)).
% 6.66/4.51 tff(209,plain,
% 6.66/4.51 (((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))) | in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(210,plain,
% 6.66/4.51 ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[209, 208])).
% 6.66/4.51 tff(211,plain,
% 6.66/4.51 ((~(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))) | in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) | (~((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(212,plain,
% 6.66/4.51 ($false),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[211, 210, 208, 207])).
% 6.66/4.51 tff(213,plain,(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) | (~(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.51 tff(214,plain,
% 6.66/4.51 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[213, 207])).
% 6.66/4.51 tff(215,plain,
% 6.66/4.51 ((~(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5)),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.51 tff(216,plain,
% 6.66/4.51 (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = C!5),
% 6.66/4.51 inference(unit_resolution,[status(thm)],[215, 214, 206])).
% 6.66/4.51 tff(217,plain,
% 6.66/4.51 (tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7),
% 6.66/4.51 inference(modus_ponens,[status(thm)],[216, 189])).
% 6.66/4.51 tff(218,plain,
% 6.66/4.51 ((~(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))),
% 6.66/4.51 inference(tautology,[status(thm)],[])).
% 6.66/4.52 tff(219,plain,
% 6.66/4.52 ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[218, 214, 207])).
% 6.66/4.52 tff(220,plain,
% 6.66/4.52 ((~((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))),
% 6.66/4.52 inference(tautology,[status(thm)],[])).
% 6.66/4.52 tff(221,plain,
% 6.66/4.52 (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[220, 214, 219])).
% 6.66/4.52 tff(222,assumption,(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7), introduced(assumption)).
% 6.66/4.52 tff(223,plain,
% 6.66/4.52 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6) <=> in(A!7, B!6)),
% 6.66/4.52 inference(monotonicity,[status(thm)],[222])).
% 6.66/4.52 tff(224,plain,
% 6.66/4.52 (in(A!7, B!6) <=> in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 6.66/4.52 inference(symmetry,[status(thm)],[223])).
% 6.66/4.52 tff(225,plain,
% 6.66/4.52 (in(A!7, B!6)),
% 6.66/4.52 inference(or_elim,[status(thm)],[154])).
% 6.66/4.52 tff(226,plain,
% 6.66/4.52 (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)),
% 6.66/4.52 inference(modus_ponens,[status(thm)],[225, 224])).
% 6.66/4.52 tff(227,assumption,(~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)), introduced(assumption)).
% 6.66/4.52 tff(228,plain,
% 6.66/4.52 ($false),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[227, 226])).
% 6.66/4.52 tff(229,plain,((~(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)) | in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)), inference(lemma,lemma(discharge,[]))).
% 6.66/4.52 tff(230,plain,
% 6.66/4.52 (~(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)) = A!7)),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[229, 221])).
% 6.66/4.52 tff(231,plain,
% 6.66/4.52 ($false),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[230, 217])).
% 6.66/4.52 tff(232,plain,((~(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))) | (~(A!7 = C!5))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.52 tff(233,plain,
% 6.66/4.52 (~(in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[232, 186])).
% 6.66/4.52 tff(234,plain,
% 6.66/4.52 (((~![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))))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, B!6)) | (~in(A!7, unordered_pair(C!5, A!7)))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))))))) <=> ((~![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))))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, B!6)) | (~in(A!7, unordered_pair(C!5, A!7)))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))))))))),
% 6.66/4.52 inference(rewrite,[status(thm)],[])).
% 6.66/4.52 tff(235,plain,
% 6.66/4.52 ((~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, unordered_pair(C!5, A!7))) | (~in(A!7, B!6))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))))))) <=> (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, B!6)) | (~in(A!7, unordered_pair(C!5, A!7)))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))))))),
% 6.66/4.52 inference(rewrite,[status(thm)],[])).
% 6.66/4.52 tff(236,plain,
% 6.66/4.52 (((~![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))))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, unordered_pair(C!5, A!7))) | (~in(A!7, B!6))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))))))) <=> ((~![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))))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, B!6)) | (~in(A!7, unordered_pair(C!5, A!7)))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))))))))),
% 6.66/4.52 inference(monotonicity,[status(thm)],[235])).
% 6.66/4.52 tff(237,plain,
% 6.66/4.52 (((~![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))))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, unordered_pair(C!5, A!7))) | (~in(A!7, B!6))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))))))) <=> ((~![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))))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, B!6)) | (~in(A!7, unordered_pair(C!5, A!7)))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))))))))),
% 6.66/4.52 inference(transitivity,[status(thm)],[236, 234])).
% 6.66/4.52 tff(238,plain,
% 6.66/4.52 ((~![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))))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, unordered_pair(C!5, A!7))) | (~in(A!7, B!6))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))))))),
% 6.66/4.52 inference(quant_inst,[status(thm)],[])).
% 6.66/4.52 tff(239,plain,
% 6.66/4.52 ((~![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))))))))) | (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, B!6)) | (~in(A!7, unordered_pair(C!5, A!7)))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))))))),
% 6.66/4.52 inference(modus_ponens,[status(thm)],[238, 237])).
% 6.66/4.52 tff(240,plain,
% 6.66/4.52 (~((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, B!6)) | (~in(A!7, unordered_pair(C!5, A!7)))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))))))),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[239, 47])).
% 6.66/4.52 tff(241,plain,
% 6.66/4.52 (((~((~(unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (~((~in(A!7, B!6)) | (~in(A!7, unordered_pair(C!5, A!7)))))))) | (~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))))) | ((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))))),
% 6.66/4.52 inference(tautology,[status(thm)],[])).
% 6.66/4.52 tff(242,plain,
% 6.66/4.52 ((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[241, 240])).
% 6.66/4.52 tff(243,plain,
% 6.66/4.52 ((~((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6)))))) | (unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))),
% 6.66/4.52 inference(tautology,[status(thm)],[])).
% 6.66/4.52 tff(244,plain,
% 6.66/4.52 ((unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)) | (in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7)) <=> ((~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7))) | (~in(tptp_fun_D_2(unordered_pair(C!5, A!7), B!6, unordered_pair(C!5, A!7)), B!6))))),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[243, 242])).
% 6.66/4.52 tff(245,plain,
% 6.66/4.52 (unordered_pair(C!5, A!7) = set_intersection2(unordered_pair(C!5, A!7), B!6)),
% 6.66/4.52 inference(unit_resolution,[status(thm)],[244, 233])).
% 6.66/4.52 tff(246,plain,
% 6.66/4.52 (set_intersection2(unordered_pair(C!5, A!7), B!6) = unordered_pair(C!5, A!7)),
% 6.66/4.52 inference(symmetry,[status(thm)],[245])).
% 6.66/4.52 tff(247,plain,
% 6.66/4.52 (set_intersection2(B!6, unordered_pair(A!7, C!5)) = unordered_pair(C!5, A!7)),
% 6.66/4.52 inference(transitivity,[status(thm)],[74, 64, 246])).
% 6.66/4.52 tff(248,plain,
% 6.66/4.52 (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = tptp_fun_C_0(unordered_pair(C!5, A!7), A!7)),
% 6.66/4.52 inference(monotonicity,[status(thm)],[247])).
% 6.66/4.52 tff(249,plain,
% 6.66/4.52 ((tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)),
% 6.66/4.52 inference(monotonicity,[status(thm)],[248, 186])).
% 6.66/4.52 tff(250,plain,
% 6.66/4.52 ((~(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)) <=> (~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))),
% 6.66/4.52 inference(monotonicity,[status(thm)],[249])).
% 6.66/4.52 tff(251,plain,
% 6.66/4.52 (~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)),
% 6.66/4.52 inference(modus_ponens,[status(thm)],[80, 250])).
% 6.66/4.52 tff(252,plain,
% 6.66/4.52 (set_intersection2(unordered_pair(A!7, C!5), B!6) = unordered_pair(C!5, A!7)),
% 6.66/4.52 inference(transitivity,[status(thm)],[64, 246])).
% 6.66/4.52 tff(253,plain,
% 6.66/4.52 ((set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7)) <=> (unordered_pair(C!5, A!7) = singleton(A!7))),
% 6.66/4.52 inference(monotonicity,[status(thm)],[252])).
% 6.66/4.52 tff(254,plain,
% 6.66/4.52 ((~(set_intersection2(unordered_pair(A!7, C!5), B!6) = singleton(A!7))) <=> (~(unordered_pair(C!5, A!7) = singleton(A!7)))),
% 6.66/4.52 inference(monotonicity,[status(thm)],[253])).
% 6.66/4.52 tff(255,plain,
% 6.66/4.52 (~(unordered_pair(C!5, A!7) = singleton(A!7))),
% 6.66/4.52 inference(modus_ponens,[status(thm)],[155, 254])).
% 6.66/4.52 tff(256,plain,
% 6.66/4.52 (((~![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(C!5, A!7) = singleton(A!7))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, 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))))))) | (~((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))))))),
% 6.66/4.52 inference(rewrite,[status(thm)],[])).
% 6.66/4.52 tff(257,plain,
% 6.66/4.52 ((~((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (A!7 = A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))))) <=> (~((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))))),
% 6.66/4.52 inference(rewrite,[status(thm)],[])).
% 6.66/4.52 tff(258,plain,
% 6.66/4.52 (((~![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(C!5, A!7) = singleton(A!7))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (A!7 = A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, 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))))))) | (~((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))))))),
% 6.66/4.52 inference(monotonicity,[status(thm)],[257])).
% 6.66/4.52 tff(259,plain,
% 6.66/4.52 (((~![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(C!5, A!7) = singleton(A!7))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (A!7 = A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, 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))))))) | (~((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))))))),
% 6.66/4.52 inference(transitivity,[status(thm)],[258, 256])).
% 6.66/4.52 tff(260,plain,
% 6.66/4.52 ((~![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(C!5, A!7) = singleton(A!7))) | (in(A!7, unordered_pair(C!5, A!7)) <=> (A!7 = A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))))),
% 6.66/4.53 inference(quant_inst,[status(thm)],[])).
% 6.66/4.53 tff(261,plain,
% 6.66/4.53 ((~![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(C!5, A!7) = singleton(A!7))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))))),
% 6.66/4.53 inference(modus_ponens,[status(thm)],[260, 259])).
% 6.66/4.53 tff(262,plain,
% 6.66/4.53 (~((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))))),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[261, 22])).
% 6.66/4.53 tff(263,plain,
% 6.66/4.53 (((~((~(unordered_pair(C!5, A!7) = singleton(A!7))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))))) | ((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))),
% 6.66/4.53 inference(tautology,[status(thm)],[])).
% 6.66/4.53 tff(264,plain,
% 6.66/4.53 ((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[263, 262])).
% 6.66/4.53 tff(265,plain,
% 6.66/4.53 ((~((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))) | (unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))),
% 6.66/4.53 inference(tautology,[status(thm)],[])).
% 6.66/4.53 tff(266,plain,
% 6.66/4.53 ((unordered_pair(C!5, A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[265, 264])).
% 6.66/4.53 tff(267,plain,
% 6.66/4.53 ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[266, 255])).
% 6.66/4.53 tff(268,assumption,(~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)), introduced(assumption)).
% 6.66/4.53 tff(269,assumption,((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)), introduced(assumption)).
% 6.66/4.53 tff(270,plain,
% 6.66/4.53 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))),
% 6.66/4.53 inference(rewrite,[status(thm)],[])).
% 6.66/4.53 tff(271,plain,
% 6.66/4.53 ((~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) <=> (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(rewrite,[status(thm)],[])).
% 6.66/4.53 tff(272,plain,
% 6.66/4.53 ((((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))) | $false) <=> ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(rewrite,[status(thm)],[])).
% 6.66/4.53 tff(273,plain,
% 6.66/4.53 ((~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) <=> ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(rewrite,[status(thm)],[])).
% 6.66/4.53 tff(274,plain,
% 6.66/4.53 (($false | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) <=> (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(rewrite,[status(thm)],[])).
% 6.66/4.53 tff(275,plain,
% 6.66/4.53 (((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) <=> ($false | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))),
% 6.66/4.53 inference(monotonicity,[status(thm)],[118])).
% 6.66/4.53 tff(276,plain,
% 6.66/4.53 (((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) <=> (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(transitivity,[status(thm)],[275, 274])).
% 6.66/4.53 tff(277,plain,
% 6.66/4.53 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) <=> (~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))),
% 6.66/4.53 inference(monotonicity,[status(thm)],[276])).
% 6.66/4.53 tff(278,plain,
% 6.66/4.53 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) <=> ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(transitivity,[status(thm)],[277, 273])).
% 6.66/4.53 tff(279,plain,
% 6.66/4.53 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))) <=> (((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))) | $false)),
% 6.66/4.53 inference(monotonicity,[status(thm)],[278, 114])).
% 6.66/4.53 tff(280,plain,
% 6.66/4.53 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))) <=> ((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(transitivity,[status(thm)],[279, 272])).
% 6.66/4.53 tff(281,plain,
% 6.66/4.53 ((~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))) <=> (~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))),
% 6.66/4.53 inference(monotonicity,[status(thm)],[280])).
% 6.66/4.53 tff(282,plain,
% 6.66/4.53 ((~((~((~(unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5))))))) <=> (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(transitivity,[status(thm)],[281, 271])).
% 6.66/4.53 tff(283,plain,
% 6.66/4.53 (((~![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(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))),
% 6.66/4.53 inference(monotonicity,[status(thm)],[282])).
% 6.66/4.53 tff(284,plain,
% 6.66/4.53 (((~![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(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))),
% 6.66/4.53 inference(transitivity,[status(thm)],[283, 270])).
% 6.66/4.53 tff(285,plain,
% 6.66/4.53 ((~![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(C!5, A!7) = unordered_pair(C!5, A!7))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(C!5, A!7)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = A!7) | (tptp_fun_D_1(unordered_pair(C!5, A!7), A!7, C!5) = C!5)))))))),
% 6.66/4.53 inference(quant_inst,[status(thm)],[])).
% 6.66/4.53 tff(286,plain,
% 6.66/4.53 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(modus_ponens,[status(thm)],[285, 284])).
% 6.66/4.53 tff(287,plain,
% 6.66/4.53 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[286, 104])).
% 6.66/4.53 tff(288,assumption,(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7), introduced(assumption)).
% 6.66/4.53 tff(289,plain,
% 6.66/4.53 ((~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) | (~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))),
% 6.66/4.53 inference(tautology,[status(thm)],[])).
% 6.66/4.53 tff(290,plain,
% 6.66/4.53 (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[289, 288, 269])).
% 6.66/4.53 tff(291,plain,
% 6.66/4.53 (((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)) | (~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))),
% 6.66/4.53 inference(tautology,[status(thm)],[])).
% 6.66/4.53 tff(292,plain,
% 6.66/4.53 ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[291, 288])).
% 6.66/4.53 tff(293,plain,
% 6.66/4.53 ((~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) | in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) | (~((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))),
% 6.66/4.53 inference(tautology,[status(thm)],[])).
% 6.66/4.53 tff(294,plain,
% 6.66/4.53 ($false),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[293, 292, 290, 287])).
% 6.66/4.53 tff(295,plain,((~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)) | (~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.53 tff(296,plain,
% 6.66/4.53 (~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[295, 269])).
% 6.66/4.53 tff(297,assumption,(~(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)), introduced(assumption)).
% 6.66/4.53 tff(298,plain,
% 6.66/4.53 ((~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))) | in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)),
% 6.66/4.53 inference(tautology,[status(thm)],[])).
% 6.66/4.53 tff(299,plain,
% 6.66/4.53 (in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[298, 297, 269])).
% 6.66/4.53 tff(300,plain,
% 6.66/4.53 ((~((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)),
% 6.66/4.53 inference(tautology,[status(thm)],[])).
% 6.66/4.53 tff(301,plain,
% 6.66/4.53 (~((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[300, 297, 268])).
% 6.66/4.53 tff(302,plain,
% 6.66/4.53 ((~(in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)))) | (~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) | ((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5))),
% 6.66/4.53 inference(tautology,[status(thm)],[])).
% 6.66/4.53 tff(303,plain,
% 6.66/4.53 ($false),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[302, 301, 299, 287])).
% 6.66/4.53 tff(304,plain,((tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5) | (~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7)))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.53 tff(305,plain,
% 6.66/4.53 ($false),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[304, 296, 269, 268])).
% 6.66/4.53 tff(306,plain,((~((~in(tptp_fun_C_0(unordered_pair(C!5, A!7), A!7), unordered_pair(C!5, A!7))) <=> (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = A!7))) | (tptp_fun_C_0(unordered_pair(C!5, A!7), A!7) = C!5)), inference(lemma,lemma(discharge,[]))).
% 6.66/4.53 tff(307,plain,
% 6.66/4.53 ($false),
% 6.66/4.53 inference(unit_resolution,[status(thm)],[306, 267, 251])).
% 6.66/4.53 tff(308,plain,(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7), inference(lemma,lemma(discharge,[]))).
% 6.66/4.53 tff(309,plain,
% 6.66/4.53 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7)) <=> in(A!7, unordered_pair(A!7, C!5))),
% 6.66/4.53 inference(monotonicity,[status(thm)],[308, 62])).
% 6.66/4.53 tff(310,plain,
% 6.66/4.53 (in(A!7, unordered_pair(A!7, C!5)) <=> in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))),
% 6.66/4.53 inference(symmetry,[status(thm)],[309])).
% 6.66/4.53 tff(311,plain,
% 6.66/4.53 (in(A!7, unordered_pair(C!5, A!7)) <=> in(A!7, unordered_pair(A!7, C!5))),
% 6.66/4.53 inference(monotonicity,[status(thm)],[62])).
% 6.66/4.53 tff(312,assumption,((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))), introduced(assumption)).
% 6.66/4.53 tff(313,plain,
% 6.66/4.53 (((~![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(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, 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(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))))),
% 6.66/4.53 inference(rewrite,[status(thm)],[])).
% 6.66/4.53 tff(314,plain,
% 6.66/4.53 ((~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(A!7, unordered_pair(C!5, A!7)) <=> ((A!7 = C!5) | (A!7 = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))) <=> (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))))),
% 6.66/4.53 inference(rewrite,[status(thm)],[])).
% 6.66/4.53 tff(315,plain,
% 6.66/4.53 (((~![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(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(A!7, unordered_pair(C!5, A!7)) <=> ((A!7 = C!5) | (A!7 = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, 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(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))))),
% 6.66/4.53 inference(monotonicity,[status(thm)],[314])).
% 6.66/4.53 tff(316,plain,
% 6.66/4.53 (((~![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(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(A!7, unordered_pair(C!5, A!7)) <=> ((A!7 = C!5) | (A!7 = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, 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(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))))),
% 6.66/4.54 inference(transitivity,[status(thm)],[315, 313])).
% 6.66/4.54 tff(317,plain,
% 6.66/4.54 ((~![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(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(A!7, unordered_pair(C!5, A!7)) <=> ((A!7 = C!5) | (A!7 = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))))),
% 6.66/4.54 inference(quant_inst,[status(thm)],[])).
% 6.66/4.54 tff(318,plain,
% 6.66/4.54 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))))),
% 6.66/4.54 inference(modus_ponens,[status(thm)],[317, 316])).
% 6.66/4.54 tff(319,plain,
% 6.66/4.54 ($false),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[318, 104, 312])).
% 6.66/4.54 tff(320,plain,(~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.54 tff(321,plain,
% 6.66/4.54 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_1(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))) | ((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))),
% 6.66/4.54 inference(tautology,[status(thm)],[])).
% 6.66/4.54 tff(322,plain,
% 6.66/4.54 ((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[321, 320])).
% 6.66/4.54 tff(323,plain,
% 6.66/4.54 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))),
% 6.66/4.54 inference(quant_inst,[status(thm)],[])).
% 6.66/4.54 tff(324,plain,
% 6.66/4.54 (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[323, 59])).
% 6.66/4.54 tff(325,plain,
% 6.66/4.54 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | (~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7))),
% 6.66/4.54 inference(tautology,[status(thm)],[])).
% 6.66/4.54 tff(326,plain,
% 6.66/4.54 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | in(A!7, unordered_pair(C!5, A!7)))) | in(A!7, unordered_pair(C!5, A!7))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[325, 324])).
% 6.66/4.54 tff(327,plain,
% 6.66/4.54 (in(A!7, unordered_pair(C!5, A!7))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[326, 322])).
% 6.66/4.54 tff(328,plain,
% 6.66/4.54 (in(A!7, unordered_pair(A!7, C!5))),
% 6.66/4.54 inference(modus_ponens,[status(thm)],[327, 311])).
% 6.66/4.54 tff(329,plain,
% 6.66/4.54 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))),
% 6.66/4.54 inference(modus_ponens,[status(thm)],[328, 310])).
% 6.66/4.54 tff(330,plain,
% 6.66/4.54 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6) <=> in(A!7, B!6)),
% 6.66/4.54 inference(monotonicity,[status(thm)],[308])).
% 6.66/4.54 tff(331,plain,
% 6.66/4.54 (in(A!7, B!6) <=> in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)),
% 6.66/4.54 inference(symmetry,[status(thm)],[330])).
% 6.66/4.54 tff(332,plain,
% 6.66/4.54 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)),
% 6.66/4.54 inference(modus_ponens,[status(thm)],[225, 331])).
% 6.66/4.54 tff(333,plain,
% 6.66/4.54 ((~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6))),
% 6.66/4.54 inference(tautology,[status(thm)],[])).
% 6.66/4.54 tff(334,plain,
% 6.66/4.54 ($false),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[333, 332, 329, 79])).
% 6.66/4.54 tff(335,plain,(~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))), inference(lemma,lemma(discharge,[]))).
% 6.66/4.54 tff(336,plain,
% 6.66/4.54 ((~(in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))))) | in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))),
% 6.66/4.54 inference(tautology,[status(thm)],[])).
% 6.66/4.54 tff(337,plain,
% 6.66/4.54 ((~(in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), unordered_pair(C!5, A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), B!6)))))) | in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[336, 335])).
% 6.66/4.54 tff(338,plain,
% 6.66/4.54 (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[337, 78])).
% 6.66/4.54 tff(339,plain,
% 6.66/4.54 ((~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) | (~(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))),
% 6.66/4.54 inference(tautology,[status(thm)],[])).
% 6.66/4.54 tff(340,plain,
% 6.66/4.54 ((~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))) | (~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[339, 308])).
% 6.66/4.54 tff(341,plain,
% 6.66/4.54 (~((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[340, 338])).
% 6.66/4.54 tff(342,plain,
% 6.66/4.54 ((~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[157, 156])).
% 6.66/4.54 tff(343,plain,
% 6.66/4.54 (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[342, 341])).
% 6.66/4.54 tff(344,plain,
% 6.66/4.54 (((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))))) | ((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))),
% 6.66/4.54 inference(tautology,[status(thm)],[])).
% 6.66/4.54 tff(345,plain,
% 6.66/4.54 ((~((~(set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7))) | (in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7)))) | (~((set_intersection2(B!6, unordered_pair(A!7, C!5)) = singleton(A!7)) | ((~in(tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7), set_intersection2(B!6, unordered_pair(A!7, C!5)))) <=> (tptp_fun_C_0(set_intersection2(B!6, unordered_pair(A!7, C!5)), A!7) = A!7))))),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[344, 343])).
% 6.66/4.54 tff(346,plain,
% 6.66/4.54 ($false),
% 6.66/4.54 inference(unit_resolution,[status(thm)],[345, 25])).
% 6.66/4.54 % SZS output end Proof
%------------------------------------------------------------------------------