TSTP Solution File: NUM385+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM385+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Sun Sep 18 13:09:27 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM385+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 10:09:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(tptp_fun_B_13_type, type, (
% 0.19/0.42 tptp_fun_B_13: $i)).
% 0.19/0.42 tff(tptp_fun_A_14_type, type, (
% 0.19/0.42 tptp_fun_A_14: $i)).
% 0.19/0.42 tff(in_type, type, (
% 0.19/0.42 in: ( $i * $i ) > $o)).
% 0.19/0.42 tff(singleton_type, type, (
% 0.19/0.42 singleton: $i > $i)).
% 0.19/0.42 tff(tptp_fun_C_0_type, type, (
% 0.19/0.42 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(succ_type, type, (
% 0.19/0.42 succ: $i > $i)).
% 0.19/0.42 tff(set_union2_type, type, (
% 0.19/0.42 set_union2: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_D_1_type, type, (
% 0.19/0.42 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(1,assumption,(~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))), introduced(assumption)).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(pull_quant,[status(thm)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[7, 3])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[10, 8])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 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')).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.42 tff(19,plain,(
% 0.19/0.42 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[18])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 ((~((~in(B!13, singleton(A!14))) <=> (B!13 = A!14))) <=> (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 ((((~in(B!13, singleton(A!14))) <=> (B!13 = A!14)) | $false) <=> ((~in(B!13, singleton(A!14))) <=> (B!13 = A!14))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 ((~$true) <=> $false),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (($true | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 ((singleton(A!14) = singleton(A!14)) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))) <=> $true),
% 0.19/0.43 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 ((~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))) <=> (~$true)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 ((~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))) <=> $false),
% 0.19/0.43 inference(transitivity,[status(thm)],[31, 26])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 ((~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> ((~in(B!13, singleton(A!14))) <=> (B!13 = A!14))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (($false | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 ((~(singleton(A!14) = singleton(A!14))) <=> (~$true)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 ((~(singleton(A!14) = singleton(A!14))) <=> $false),
% 0.19/0.43 inference(transitivity,[status(thm)],[35, 26])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> ($false | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))) <=> (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.19/0.43 inference(transitivity,[status(thm)],[37, 34])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 ((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) <=> (~(in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 ((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) <=> ((~in(B!13, singleton(A!14))) <=> (B!13 = A!14))),
% 0.19/0.43 inference(transitivity,[status(thm)],[39, 33])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))) <=> (((~in(B!13, singleton(A!14))) <=> (B!13 = A!14)) | $false)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[40, 32])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))) <=> ((~in(B!13, singleton(A!14))) <=> (B!13 = A!14))),
% 0.19/0.43 inference(transitivity,[status(thm)],[41, 25])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 ((~((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))))) <=> (~((~in(B!13, singleton(A!14))) <=> (B!13 = A!14)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 ((~((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14)))))) <=> (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.19/0.43 inference(transitivity,[status(thm)],[43, 24])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[45, 23])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!14) = singleton(A!14))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14)))) | (~((singleton(A!14) = singleton(A!14)) | ((~in(tptp_fun_C_0(singleton(A!14), A!14), singleton(A!14))) <=> (tptp_fun_C_0(singleton(A!14), A!14) = A!14))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(B!13, singleton(A!14)) <=> (B!13 = A!14))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[48, 22, 1])).
% 0.19/0.43 tff(50,plain,(in(B!13, singleton(A!14)) <=> (B!13 = A!14)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 ((B!13 = A!14) <=> (A!14 = B!13)),
% 0.19/0.43 inference(commutativity,[status(thm)],[])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 ((A!14 = B!13) <=> (B!13 = A!14)),
% 0.19/0.43 inference(symmetry,[status(thm)],[51])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 ((~(A!14 = B!13)) <=> (~(B!13 = A!14))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))) <=> (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((succ(A) = succ(B)) => (A = B))) <=> (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(56,axiom,(~![A: $i, B: $i] : ((succ(A) = succ(B)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_ordinal1')).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[59, 54])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[60, 54])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (~![A: $i, B: $i] : ((~(succ(A) = succ(B))) | (A = B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[62, 54])).
% 0.19/0.43 tff(64,plain,(
% 0.19/0.43 ~((~(succ(A!14) = succ(B!13))) | (A!14 = B!13))),
% 0.19/0.43 inference(skolemize,[status(sab)],[63])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (~(A!14 = B!13)),
% 0.19/0.43 inference(or_elim,[status(thm)],[64])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (~(B!13 = A!14)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[65, 53])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 ((~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))) | (~in(B!13, singleton(A!14))) | (B!13 = A!14)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 ((~(in(B!13, singleton(A!14)) <=> (B!13 = A!14))) | (~in(B!13, singleton(A!14)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (~in(B!13, singleton(A!14))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[68, 50])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.43 inference(pull_quant,[status(thm)],[])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[74, 72])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[75, 71])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), monotonicity(rewrite(((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))) <=> ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))), (((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(85,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.44 tff(87,plain,(
% 0.19/0.44 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[86])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (~((succ(B!13) = set_union2(A!14, singleton(A!14))) | ((~in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), succ(B!13))) <=> (in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), A!14) | in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), singleton(A!14))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (~((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (~((succ(B!13) = set_union2(A!14, singleton(A!14))) | ((~in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), succ(B!13))) <=> (in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), A!14) | in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), singleton(A!14)))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (~((succ(B!13) = set_union2(A!14, singleton(A!14))) | ((~in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), succ(B!13))) <=> (in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), A!14) | in(tptp_fun_D_1(succ(B!13), singleton(A!14), A!14), singleton(A!14))))))) | ((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 ((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(98,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.44 tff(100,plain,(
% 0.19/0.44 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[99])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(A!14) = set_union2(A!14, singleton(A!14)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (succ(A!14) = set_union2(A!14, singleton(A!14))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (succ(A!14) = succ(B!13)),
% 0.19/0.44 inference(or_elim,[status(thm)],[64])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (succ(B!13) = succ(A!14)),
% 0.19/0.44 inference(symmetry,[status(thm)],[104])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (succ(B!13) = set_union2(A!14, singleton(A!14))),
% 0.19/0.44 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 ((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 ((~((~(succ(B!13) = set_union2(A!14, singleton(A!14)))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))))) | (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[108, 94])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (^[A: $i] : refl(in(A, succ(A)) <=> in(A, succ(A)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(113,axiom,(![A: $i] : in(A, succ(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_ordinal1')).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 (![A: $i] : in(A, succ(A))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.44 tff(115,plain,(
% 0.19/0.44 ![A: $i] : in(A, succ(A))),
% 0.19/0.44 inference(skolemize,[status(sab)],[114])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 (![A: $i] : in(A, succ(A))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 ((~![A: $i] : in(A, succ(A))) | in(B!13, succ(B!13))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 (in(B!13, succ(B!13))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 ((~(in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))) | (~in(B!13, succ(B!13))) | (in(B!13, A!14) | in(B!13, singleton(A!14)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 ((~(in(B!13, succ(B!13)) <=> (in(B!13, A!14) | in(B!13, singleton(A!14))))) | (in(B!13, A!14) | in(B!13, singleton(A!14)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (in(B!13, A!14) | in(B!13, singleton(A!14))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[120, 109])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 ((~(in(B!13, A!14) | in(B!13, singleton(A!14)))) | in(B!13, A!14) | in(B!13, singleton(A!14))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 (in(B!13, A!14) | in(B!13, singleton(A!14))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (in(B!13, A!14)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[123, 69])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(126,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.44 tff(130,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.19/0.44 tff(133,plain,(
% 0.19/0.44 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[132])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!14, B!13)) | (~in(B!13, A!14)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!14, B!13)) | (~in(B!13, A!14)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 (((~in(B!13, A!14)) | (~in(A!14, B!13))) <=> ((~in(A!14, B!13)) | (~in(B!13, A!14)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(B!13, A!14)) | (~in(A!14, B!13)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!14, B!13)) | (~in(B!13, A!14))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[136])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(B!13, A!14)) | (~in(A!14, B!13)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!14, B!13)) | (~in(B!13, A!14)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[137, 135])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(B!13, A!14)) | (~in(A!14, B!13)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!14, B!13)) | (~in(B!13, A!14))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 (~in(A!14, B!13)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[140, 134, 124])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (~((succ(B!13) = set_union2(B!13, singleton(B!13))) | ((~in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), succ(B!13))) <=> (in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), B!13) | in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), singleton(B!13))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(143,plain,
% 0.19/0.44 (~((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (~((succ(B!13) = set_union2(B!13, singleton(B!13))) | ((~in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), succ(B!13))) <=> (in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), B!13) | in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), singleton(B!13)))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[142, 90])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (~((succ(B!13) = set_union2(B!13, singleton(B!13))) | ((~in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), succ(B!13))) <=> (in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), B!13) | in(tptp_fun_D_1(succ(B!13), singleton(B!13), B!13), singleton(B!13))))))) | ((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 ((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(B!13) = set_union2(B!13, singleton(B!13)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (succ(B!13) = set_union2(B!13, singleton(B!13))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[146, 101])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 ((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 ((~((~(succ(B!13) = set_union2(B!13, singleton(B!13)))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))))) | (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[149, 145])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 (in(A!14, succ(B!13)) <=> in(A!14, succ(A!14))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 (in(A!14, succ(A!14)) <=> in(A!14, succ(B!13))),
% 0.19/0.45 inference(symmetry,[status(thm)],[151])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 ((~![A: $i] : in(A, succ(A))) | in(A!14, succ(A!14))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 (in(A!14, succ(A!14))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[153, 116])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 (in(A!14, succ(B!13))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[154, 152])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 ((~(in(A!14, succ(B!13)) <=> (in(A!14, B!13) | in(A!14, singleton(B!13))))) | (~in(A!14, succ(B!13))) | (in(A!14, B!13) | in(A!14, singleton(B!13)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 (in(A!14, B!13) | in(A!14, singleton(B!13))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[156, 155, 150])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 ((~(in(A!14, B!13) | in(A!14, singleton(B!13)))) | in(A!14, B!13) | in(A!14, singleton(B!13))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 (in(A!14, B!13) | in(A!14, singleton(B!13))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.45 tff(160,plain,
% 0.19/0.45 (in(A!14, singleton(B!13))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[159, 141])).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 ((~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))) | (~in(A!14, singleton(B!13))) | (A!14 = B!13)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[161, 65, 160])).
% 0.19/0.45 tff(163,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 ((~((~in(A!14, singleton(B!13))) <=> (A!14 = B!13))) <=> (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 ((((~in(A!14, singleton(B!13))) <=> (A!14 = B!13)) | $false) <=> ((~in(A!14, singleton(B!13))) <=> (A!14 = B!13))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 (($true | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 ((singleton(B!13) = singleton(B!13)) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 (((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))) <=> ($true | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.45 tff(169,plain,
% 0.19/0.45 (((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))) <=> $true),
% 0.19/0.45 inference(transitivity,[status(thm)],[168, 166])).
% 0.19/0.45 tff(170,plain,
% 0.19/0.45 ((~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))) <=> (~$true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.45 tff(171,plain,
% 0.19/0.45 ((~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[170, 26])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 ((~(in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> ((~in(A!14, singleton(B!13))) <=> (A!14 = B!13))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 (($false | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 ((~(singleton(B!13) = singleton(B!13))) <=> (~$true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 ((~(singleton(B!13) = singleton(B!13))) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[174, 26])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> ($false | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[175])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))) <=> (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.19/0.45 inference(transitivity,[status(thm)],[176, 173])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 ((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) <=> (~(in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[177])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 ((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) <=> ((~in(A!14, singleton(B!13))) <=> (A!14 = B!13))),
% 0.19/0.45 inference(transitivity,[status(thm)],[178, 172])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 (((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))) <=> (((~in(A!14, singleton(B!13))) <=> (A!14 = B!13)) | $false)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[179, 171])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))) <=> ((~in(A!14, singleton(B!13))) <=> (A!14 = B!13))),
% 0.19/0.45 inference(transitivity,[status(thm)],[180, 165])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 ((~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))))) <=> (~((~in(A!14, singleton(B!13))) <=> (A!14 = B!13)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[181])).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 ((~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13)))))) <=> (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.19/0.46 inference(transitivity,[status(thm)],[182, 164])).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[183])).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[184, 163])).
% 0.19/0.46 tff(186,plain,
% 0.19/0.46 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(B!13) = singleton(B!13))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13)))) | (~((singleton(B!13) = singleton(B!13)) | ((~in(tptp_fun_C_0(singleton(B!13), B!13), singleton(B!13))) <=> (tptp_fun_C_0(singleton(B!13), B!13) = B!13))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(187,plain,
% 0.19/0.46 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!14, singleton(B!13)) <=> (A!14 = B!13))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.46 tff(188,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[187, 22, 162])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------