TSTP Solution File: NUM401+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM401+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 13:09:30 EDT 2022
% Result : Theorem 0.11s 0.30s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : NUM401+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.25 % Computer : n010.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Fri Sep 2 10:03:12 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.26 Usage: tptp [options] [-file:]file
% 0.07/0.26 -h, -? prints this message.
% 0.07/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.26 -m, -model generate model.
% 0.07/0.26 -p, -proof generate proof.
% 0.07/0.26 -c, -core generate unsat core of named formulas.
% 0.07/0.26 -st, -statistics display statistics.
% 0.07/0.26 -t:timeout set timeout (in second).
% 0.07/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.26 -<param>:<value> configuration parameter and value.
% 0.07/0.26 -o:<output-file> file to place output in.
% 0.11/0.30 % SZS status Theorem
% 0.11/0.30 % SZS output start Proof
% 0.11/0.30 tff(in_type, type, (
% 0.11/0.30 in: ( $i * $i ) > $o)).
% 0.11/0.30 tff(set_union2_type, type, (
% 0.11/0.30 set_union2: ( $i * $i ) > $i)).
% 0.11/0.30 tff(singleton_type, type, (
% 0.11/0.30 singleton: $i > $i)).
% 0.11/0.30 tff(tptp_fun_B_18_type, type, (
% 0.11/0.30 tptp_fun_B_18: $i)).
% 0.11/0.30 tff(tptp_fun_A_17_type, type, (
% 0.11/0.30 tptp_fun_A_17: $i)).
% 0.11/0.30 tff(succ_type, type, (
% 0.11/0.30 succ: $i > $i)).
% 0.11/0.30 tff(tptp_fun_D_2_type, type, (
% 0.11/0.30 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.11/0.30 tff(tptp_fun_C_0_type, type, (
% 0.11/0.30 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.11/0.30 tff(ordinal_type, type, (
% 0.11/0.30 ordinal: $i > $o)).
% 0.11/0.30 tff(ordinal_subset_type, type, (
% 0.11/0.30 ordinal_subset: ( $i * $i ) > $o)).
% 0.11/0.30 tff(subset_type, type, (
% 0.11/0.30 subset: ( $i * $i ) > $o)).
% 0.11/0.30 tff(epsilon_transitive_type, type, (
% 0.11/0.30 epsilon_transitive: $i > $o)).
% 0.11/0.30 tff(tptp_fun_B_1_type, type, (
% 0.11/0.30 tptp_fun_B_1: $i > $i)).
% 0.11/0.30 tff(epsilon_connected_type, type, (
% 0.11/0.30 epsilon_connected: $i > $o)).
% 0.11/0.30 tff(1,plain,
% 0.11/0.30 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(2,plain,
% 0.11/0.30 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.30 tff(3,plain,
% 0.11/0.30 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(4,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.11/0.30 tff(5,plain,
% 0.11/0.30 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.30 tff(6,plain,(
% 0.11/0.30 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.11/0.30 inference(skolemize,[status(sab)],[5])).
% 0.11/0.30 tff(7,plain,
% 0.11/0.30 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.30 tff(8,plain,
% 0.11/0.30 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(B!18) = set_union2(B!18, singleton(B!18)))),
% 0.11/0.30 inference(quant_inst,[status(thm)],[])).
% 0.11/0.30 tff(9,plain,
% 0.11/0.30 (succ(B!18) = set_union2(B!18, singleton(B!18))),
% 0.11/0.30 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.30 tff(10,plain,
% 0.11/0.30 (set_union2(B!18, singleton(B!18)) = succ(B!18)),
% 0.11/0.30 inference(symmetry,[status(thm)],[9])).
% 0.11/0.30 tff(11,plain,
% 0.11/0.30 (in(A!17, set_union2(B!18, singleton(B!18))) <=> in(A!17, succ(B!18))),
% 0.11/0.30 inference(monotonicity,[status(thm)],[10])).
% 0.11/0.30 tff(12,plain,
% 0.11/0.30 (in(A!17, succ(B!18)) <=> in(A!17, set_union2(B!18, singleton(B!18)))),
% 0.11/0.30 inference(symmetry,[status(thm)],[11])).
% 0.11/0.30 tff(13,plain,
% 0.11/0.30 ((~in(A!17, succ(B!18))) <=> (~in(A!17, set_union2(B!18, singleton(B!18))))),
% 0.11/0.30 inference(monotonicity,[status(thm)],[12])).
% 0.11/0.30 tff(14,assumption,(~in(A!17, succ(B!18))), introduced(assumption)).
% 0.11/0.30 tff(15,plain,
% 0.11/0.30 (~in(A!17, set_union2(B!18, singleton(B!18)))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.11/0.30 tff(16,plain,
% 0.11/0.30 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(17,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.30 tff(18,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(pull_quant,[status(thm)],[])).
% 0.11/0.30 tff(19,plain,
% 0.11/0.30 (^[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, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(20,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.30 tff(21,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(transitivity,[status(thm)],[20, 18])).
% 0.11/0.30 tff(22,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(transitivity,[status(thm)],[21, 17])).
% 0.11/0.30 tff(23,plain,
% 0.11/0.30 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(24,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.30 tff(25,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(transitivity,[status(thm)],[24, 22])).
% 0.11/0.30 tff(26,plain,
% 0.11/0.30 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(27,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[26])).
% 0.11/0.30 tff(28,plain,
% 0.11/0.30 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(29,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.30 tff(30,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(31,plain,
% 0.11/0.30 (^[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)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(32,plain,
% 0.11/0.30 (![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, B) | in(D, A))))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[31])).
% 0.11/0.30 tff(33,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/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.11/0.30 tff(34,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.30 tff(35,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.11/0.30 tff(36,plain,(
% 0.11/0.30 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))),
% 0.11/0.30 inference(skolemize,[status(sab)],[35])).
% 0.11/0.30 tff(37,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.11/0.30 tff(38,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.11/0.30 tff(39,plain,
% 0.11/0.30 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[38, 25])).
% 0.11/0.30 tff(40,plain,
% 0.11/0.30 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(41,plain,
% 0.11/0.30 ((~((~in(A!17, set_union2(B!18, singleton(B!18)))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(42,plain,
% 0.11/0.30 ((((~in(A!17, set_union2(B!18, singleton(B!18)))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))) | $false) <=> ((~in(A!17, set_union2(B!18, singleton(B!18)))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(43,plain,
% 0.11/0.30 ((~$true) <=> $false),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(44,plain,
% 0.11/0.30 (($true | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))) <=> $true),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(45,plain,
% 0.11/0.30 (((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))) <=> ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(46,plain,
% 0.11/0.30 ((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) <=> $true),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(47,plain,
% 0.11/0.30 (((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))) <=> ($true | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))),
% 0.11/0.30 inference(monotonicity,[status(thm)],[46, 45])).
% 0.11/0.30 tff(48,plain,
% 0.11/0.30 (((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))) <=> $true),
% 0.11/0.30 inference(transitivity,[status(thm)],[47, 44])).
% 0.11/0.30 tff(49,plain,
% 0.11/0.30 ((~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))) <=> (~$true)),
% 0.11/0.30 inference(monotonicity,[status(thm)],[48])).
% 0.11/0.30 tff(50,plain,
% 0.11/0.30 ((~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))) <=> $false),
% 0.11/0.30 inference(transitivity,[status(thm)],[49, 43])).
% 0.11/0.30 tff(51,plain,
% 0.11/0.30 ((~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> ((~in(A!17, set_union2(B!18, singleton(B!18)))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(52,plain,
% 0.11/0.30 (($false | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(53,plain,
% 0.11/0.30 ((in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(54,plain,
% 0.11/0.30 ((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) <=> (~$true)),
% 0.11/0.30 inference(monotonicity,[status(thm)],[46])).
% 0.11/0.30 tff(55,plain,
% 0.11/0.30 ((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) <=> $false),
% 0.11/0.30 inference(transitivity,[status(thm)],[54, 43])).
% 0.11/0.30 tff(56,plain,
% 0.11/0.30 (((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> ($false | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.11/0.30 inference(monotonicity,[status(thm)],[55, 53])).
% 0.11/0.30 tff(57,plain,
% 0.11/0.30 (((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.30 inference(transitivity,[status(thm)],[56, 52])).
% 0.11/0.30 tff(58,plain,
% 0.11/0.30 ((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) <=> (~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.11/0.30 inference(monotonicity,[status(thm)],[57])).
% 0.11/0.30 tff(59,plain,
% 0.11/0.30 ((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) <=> ((~in(A!17, set_union2(B!18, singleton(B!18)))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.30 inference(transitivity,[status(thm)],[58, 51])).
% 0.11/0.30 tff(60,plain,
% 0.11/0.30 (((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))) <=> (((~in(A!17, set_union2(B!18, singleton(B!18)))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))) | $false)),
% 0.11/0.31 inference(monotonicity,[status(thm)],[59, 50])).
% 0.11/0.31 tff(61,plain,
% 0.11/0.31 (((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))) <=> ((~in(A!17, set_union2(B!18, singleton(B!18)))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.31 inference(transitivity,[status(thm)],[60, 42])).
% 0.11/0.31 tff(62,plain,
% 0.11/0.31 ((~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))))) <=> (~((~in(A!17, set_union2(B!18, singleton(B!18)))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.11/0.31 inference(monotonicity,[status(thm)],[61])).
% 0.11/0.31 tff(63,plain,
% 0.11/0.31 ((~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.31 inference(transitivity,[status(thm)],[62, 41])).
% 0.11/0.31 tff(64,plain,
% 0.11/0.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.11/0.31 inference(monotonicity,[status(thm)],[63])).
% 0.11/0.31 tff(65,plain,
% 0.11/0.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.11/0.31 inference(transitivity,[status(thm)],[64, 40])).
% 0.11/0.31 tff(66,plain,
% 0.11/0.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | ((~in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18)))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))))),
% 0.11/0.31 inference(quant_inst,[status(thm)],[])).
% 0.11/0.31 tff(67,plain,
% 0.11/0.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.11/0.31 tff(68,plain,
% 0.11/0.31 (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[67, 39])).
% 0.11/0.31 tff(69,plain,
% 0.11/0.31 ((~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) | in(A!17, set_union2(B!18, singleton(B!18))) | (~(in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.31 inference(tautology,[status(thm)],[])).
% 0.11/0.31 tff(70,plain,
% 0.11/0.31 (in(A!17, set_union2(B!18, singleton(B!18))) | (~(in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.11/0.31 tff(71,plain,
% 0.11/0.31 (~(in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[70, 15])).
% 0.11/0.31 tff(72,plain,
% 0.11/0.31 ((in(A!17, singleton(B!18)) | in(A!17, B!18)) | (~in(A!17, B!18))),
% 0.11/0.31 inference(tautology,[status(thm)],[])).
% 0.11/0.31 tff(73,plain,
% 0.11/0.31 (~in(A!17, B!18)),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.11/0.31 tff(74,assumption,(~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))), introduced(assumption)).
% 0.11/0.31 tff(75,plain,
% 0.11/0.31 (^[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)))))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(76,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[75])).
% 0.11/0.31 tff(77,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(pull_quant,[status(thm)],[])).
% 0.11/0.31 tff(78,plain,
% 0.11/0.31 (^[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))))))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(79,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[78])).
% 0.11/0.31 tff(80,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(transitivity,[status(thm)],[79, 77])).
% 0.11/0.31 tff(81,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(transitivity,[status(thm)],[80, 76])).
% 0.11/0.31 tff(82,plain,
% 0.11/0.31 (^[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)))))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(83,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[82])).
% 0.11/0.31 tff(84,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(transitivity,[status(thm)],[83, 81])).
% 0.11/0.31 tff(85,plain,
% 0.11/0.31 (^[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))))))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(86,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[85])).
% 0.11/0.31 tff(87,plain,
% 0.11/0.31 (^[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)))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(88,plain,
% 0.11/0.31 (![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))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[87])).
% 0.11/0.31 tff(89,plain,
% 0.11/0.31 (![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)))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(90,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.11/0.31 tff(91,plain,
% 0.11/0.31 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.11/0.31 tff(92,plain,(
% 0.11/0.31 ![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)))))),
% 0.11/0.31 inference(skolemize,[status(sab)],[91])).
% 0.11/0.31 tff(93,plain,
% 0.11/0.31 (![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))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.11/0.31 tff(94,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.11/0.31 tff(95,plain,
% 0.11/0.31 (![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))))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.11/0.31 tff(96,plain,
% 0.11/0.31 (((~![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!17, singleton(B!18)) <=> (A!17 = B!18))) <=> ((~![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!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(97,plain,
% 0.11/0.31 ((~((~in(A!17, singleton(B!18))) <=> (A!17 = B!18))) <=> (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(98,plain,
% 0.11/0.31 ((((~in(A!17, singleton(B!18))) <=> (A!17 = B!18)) | $false) <=> ((~in(A!17, singleton(B!18))) <=> (A!17 = B!18))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(99,plain,
% 0.11/0.31 (($true | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))) <=> $true),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(100,plain,
% 0.11/0.31 ((singleton(B!18) = singleton(B!18)) <=> $true),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(101,plain,
% 0.11/0.31 (((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))) <=> ($true | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))),
% 0.11/0.31 inference(monotonicity,[status(thm)],[100])).
% 0.11/0.31 tff(102,plain,
% 0.11/0.31 (((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))) <=> $true),
% 0.11/0.31 inference(transitivity,[status(thm)],[101, 99])).
% 0.11/0.31 tff(103,plain,
% 0.11/0.31 ((~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))) <=> (~$true)),
% 0.11/0.31 inference(monotonicity,[status(thm)],[102])).
% 0.11/0.31 tff(104,plain,
% 0.11/0.31 ((~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))) <=> $false),
% 0.11/0.31 inference(transitivity,[status(thm)],[103, 43])).
% 0.11/0.31 tff(105,plain,
% 0.11/0.31 ((~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> ((~in(A!17, singleton(B!18))) <=> (A!17 = B!18))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(106,plain,
% 0.11/0.31 (($false | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(107,plain,
% 0.11/0.31 ((~(singleton(B!18) = singleton(B!18))) <=> (~$true)),
% 0.11/0.31 inference(monotonicity,[status(thm)],[100])).
% 0.11/0.31 tff(108,plain,
% 0.11/0.31 ((~(singleton(B!18) = singleton(B!18))) <=> $false),
% 0.11/0.31 inference(transitivity,[status(thm)],[107, 43])).
% 0.11/0.31 tff(109,plain,
% 0.11/0.31 (((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> ($false | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.11/0.31 inference(monotonicity,[status(thm)],[108])).
% 0.11/0.31 tff(110,plain,
% 0.11/0.31 (((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.11/0.31 inference(transitivity,[status(thm)],[109, 106])).
% 0.11/0.31 tff(111,plain,
% 0.11/0.31 ((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) <=> (~(in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.11/0.31 inference(monotonicity,[status(thm)],[110])).
% 0.11/0.31 tff(112,plain,
% 0.11/0.31 ((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) <=> ((~in(A!17, singleton(B!18))) <=> (A!17 = B!18))),
% 0.11/0.31 inference(transitivity,[status(thm)],[111, 105])).
% 0.11/0.31 tff(113,plain,
% 0.11/0.31 (((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))) <=> (((~in(A!17, singleton(B!18))) <=> (A!17 = B!18)) | $false)),
% 0.11/0.31 inference(monotonicity,[status(thm)],[112, 104])).
% 0.11/0.31 tff(114,plain,
% 0.11/0.31 (((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))) <=> ((~in(A!17, singleton(B!18))) <=> (A!17 = B!18))),
% 0.11/0.31 inference(transitivity,[status(thm)],[113, 98])).
% 0.11/0.31 tff(115,plain,
% 0.11/0.31 ((~((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))))) <=> (~((~in(A!17, singleton(B!18))) <=> (A!17 = B!18)))),
% 0.11/0.31 inference(monotonicity,[status(thm)],[114])).
% 0.11/0.31 tff(116,plain,
% 0.11/0.31 ((~((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))))) <=> (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.11/0.31 inference(transitivity,[status(thm)],[115, 97])).
% 0.11/0.31 tff(117,plain,
% 0.11/0.31 (((~![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!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))))) <=> ((~![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!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.11/0.31 inference(monotonicity,[status(thm)],[116])).
% 0.11/0.31 tff(118,plain,
% 0.11/0.31 (((~![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!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))))) <=> ((~![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!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.11/0.31 inference(transitivity,[status(thm)],[117, 96])).
% 0.11/0.31 tff(119,plain,
% 0.11/0.31 ((~![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!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | ((~in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18))) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))))),
% 0.11/0.31 inference(quant_inst,[status(thm)],[])).
% 0.11/0.31 tff(120,plain,
% 0.11/0.31 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.11/0.31 tff(121,plain,
% 0.11/0.31 ($false),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[120, 95, 74])).
% 0.11/0.31 tff(122,plain,(in(A!17, singleton(B!18)) <=> (A!17 = B!18)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.31 tff(123,plain,
% 0.11/0.31 ((in(A!17, singleton(B!18)) | in(A!17, B!18)) | (~in(A!17, singleton(B!18)))),
% 0.11/0.31 inference(tautology,[status(thm)],[])).
% 0.11/0.31 tff(124,plain,
% 0.11/0.31 (~in(A!17, singleton(B!18))),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[123, 71])).
% 0.11/0.31 tff(125,plain,
% 0.11/0.31 ((~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))) | in(A!17, singleton(B!18)) | (~(A!17 = B!18))),
% 0.11/0.31 inference(tautology,[status(thm)],[])).
% 0.11/0.31 tff(126,plain,
% 0.11/0.31 (~(A!17 = B!18)),
% 0.11/0.31 inference(unit_resolution,[status(thm)],[125, 124, 122])).
% 0.11/0.31 tff(127,plain,
% 0.11/0.31 (((~(~ordinal(A!17))) & (~((~ordinal(B!18)) | (in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18))))) <=> (ordinal(A!17) & (~((~ordinal(B!18)) | (in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18)))))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(128,plain,
% 0.11/0.31 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B)))))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(129,plain,
% 0.11/0.31 ((~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, succ(B)) <=> ordinal_subset(A, B))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B)))))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(130,axiom,(~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, succ(B)) <=> ordinal_subset(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_ordinal1')).
% 0.11/0.31 tff(131,plain,
% 0.11/0.31 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.11/0.31 tff(132,plain,
% 0.11/0.31 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[131, 128])).
% 0.11/0.31 tff(133,plain,
% 0.11/0.31 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.11/0.31 tff(134,plain,
% 0.11/0.31 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[133, 128])).
% 0.11/0.31 tff(135,plain,
% 0.11/0.31 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[134, 128])).
% 0.11/0.31 tff(136,plain,
% 0.11/0.31 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.11/0.31 tff(137,plain,
% 0.11/0.31 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[136, 128])).
% 0.11/0.31 tff(138,plain,
% 0.11/0.31 (ordinal(A!17) & (~((~ordinal(B!18)) | (in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.11/0.31 tff(139,plain,
% 0.11/0.31 (ordinal(A!17)),
% 0.11/0.31 inference(and_elim,[status(thm)],[138])).
% 0.11/0.31 tff(140,plain,
% 0.11/0.31 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(141,plain,
% 0.11/0.31 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[140])).
% 0.11/0.31 tff(142,plain,
% 0.11/0.31 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(143,plain,
% 0.11/0.31 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[142])).
% 0.11/0.31 tff(144,plain,
% 0.11/0.31 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.11/0.31 inference(transitivity,[status(thm)],[143, 141])).
% 0.11/0.31 tff(145,plain,
% 0.11/0.31 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(146,plain,
% 0.11/0.31 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[145])).
% 0.11/0.31 tff(147,plain,
% 0.11/0.31 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.11/0.31 inference(rewrite,[status(thm)],[])).
% 0.11/0.31 tff(148,plain,
% 0.11/0.31 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))) <=> (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> (ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), rewrite((ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), (![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))))),
% 0.11/0.31 inference(bind,[status(th)],[])).
% 0.11/0.31 tff(149,plain,
% 0.11/0.31 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.11/0.31 inference(quant_intro,[status(thm)],[148])).
% 0.11/0.31 tff(150,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_ordinal1')).
% 0.11/0.31 tff(151,plain,
% 0.11/0.31 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.11/0.31 tff(152,plain,
% 0.11/0.31 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.11/0.31 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.11/0.31 tff(153,plain,(
% 0.11/0.31 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.11/0.31 inference(skolemize,[status(sab)],[152])).
% 0.11/0.31 tff(154,plain,
% 0.11/0.31 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.11/0.32 tff(155,plain,
% 0.11/0.32 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.11/0.32 tff(156,plain,
% 0.11/0.32 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B)))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(157,plain,
% 0.11/0.32 (((~ordinal(A!17)) | ![B: $i] : (in(B, A!17) | in(A!17, B) | (A!17 = B) | (~ordinal(B)))) <=> ((~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B)))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(158,plain,
% 0.11/0.32 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : (in(B, A!17) | in(A!17, B) | (A!17 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))))),
% 0.11/0.32 inference(monotonicity,[status(thm)],[157])).
% 0.11/0.32 tff(159,plain,
% 0.11/0.32 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : (in(B, A!17) | in(A!17, B) | (A!17 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B)))),
% 0.11/0.32 inference(transitivity,[status(thm)],[158, 156])).
% 0.11/0.32 tff(160,plain,
% 0.11/0.32 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : (in(B, A!17) | in(A!17, B) | (A!17 = B) | (~ordinal(B))))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(161,plain,
% 0.11/0.32 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.11/0.32 tff(162,plain,
% 0.11/0.32 (![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[161, 155, 139])).
% 0.11/0.32 tff(163,plain,
% 0.11/0.32 (~((~ordinal(B!18)) | (in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18)))),
% 0.11/0.32 inference(and_elim,[status(thm)],[138])).
% 0.11/0.32 tff(164,plain,
% 0.11/0.32 (ordinal(B!18)),
% 0.11/0.32 inference(or_elim,[status(thm)],[163])).
% 0.11/0.32 tff(165,plain,
% 0.11/0.32 (((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | (~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(166,plain,
% 0.11/0.32 (((~ordinal(B!18)) | in(B!18, A!17) | in(A!17, B!18) | (A!17 = B!18)) <=> ((~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(167,plain,
% 0.11/0.32 (((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | in(B!18, A!17) | in(A!17, B!18) | (A!17 = B!18))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17)))),
% 0.11/0.32 inference(monotonicity,[status(thm)],[166])).
% 0.11/0.32 tff(168,plain,
% 0.11/0.32 (((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | in(B!18, A!17) | in(A!17, B!18) | (A!17 = B!18))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | (~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17))),
% 0.11/0.32 inference(transitivity,[status(thm)],[167, 165])).
% 0.11/0.32 tff(169,plain,
% 0.11/0.32 ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | in(B!18, A!17) | in(A!17, B!18) | (A!17 = B!18))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(170,plain,
% 0.11/0.32 ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | (~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17)),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.11/0.32 tff(171,plain,
% 0.11/0.32 ((A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[170, 164, 162])).
% 0.11/0.32 tff(172,plain,
% 0.11/0.32 (in(B!18, A!17)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[171, 126, 73])).
% 0.11/0.32 tff(173,plain,
% 0.11/0.32 ((~(in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18))) <=> ((~in(A!17, succ(B!18))) <=> ordinal_subset(A!17, B!18))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(174,plain,
% 0.11/0.32 (~(in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18))),
% 0.11/0.32 inference(or_elim,[status(thm)],[163])).
% 0.11/0.32 tff(175,plain,
% 0.11/0.32 ((~in(A!17, succ(B!18))) <=> ordinal_subset(A!17, B!18)),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.11/0.32 tff(176,plain,
% 0.11/0.32 (in(A!17, succ(B!18)) | ordinal_subset(A!17, B!18) | (~((~in(A!17, succ(B!18))) <=> ordinal_subset(A!17, B!18)))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(177,plain,
% 0.11/0.32 (in(A!17, succ(B!18)) | ordinal_subset(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.11/0.32 tff(178,plain,
% 0.11/0.32 (ordinal_subset(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[177, 14])).
% 0.11/0.32 tff(179,plain,
% 0.11/0.32 (^[A: $i, B: $i] : refl(((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(180,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[179])).
% 0.11/0.32 tff(181,plain,
% 0.11/0.32 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> (((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))))), rewrite((((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(182,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[181])).
% 0.11/0.32 tff(183,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(184,plain,
% 0.11/0.32 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(185,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[184])).
% 0.11/0.32 tff(186,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.11/0.32 tff(187,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.11/0.32 tff(188,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.11/0.32 tff(189,plain,(
% 0.11/0.32 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.11/0.32 inference(skolemize,[status(sab)],[188])).
% 0.11/0.32 tff(190,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.11/0.32 tff(191,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[190, 180])).
% 0.11/0.32 tff(192,plain,
% 0.11/0.32 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(193,plain,
% 0.11/0.32 (((ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)) | (~ordinal(B!18)) | (~ordinal(A!17))) <=> ((~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(194,plain,
% 0.11/0.32 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)) | (~ordinal(B!18)) | (~ordinal(A!17)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18))))),
% 0.11/0.32 inference(monotonicity,[status(thm)],[193])).
% 0.11/0.32 tff(195,plain,
% 0.11/0.32 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)) | (~ordinal(B!18)) | (~ordinal(A!17)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)))),
% 0.11/0.32 inference(transitivity,[status(thm)],[194, 192])).
% 0.11/0.32 tff(196,plain,
% 0.11/0.32 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)) | (~ordinal(B!18)) | (~ordinal(A!17)))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(197,plain,
% 0.11/0.32 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.11/0.32 tff(198,plain,
% 0.11/0.32 (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[197, 191, 139, 164])).
% 0.11/0.32 tff(199,plain,
% 0.11/0.32 ((~(ordinal_subset(A!17, B!18) <=> subset(A!17, B!18))) | (~ordinal_subset(A!17, B!18)) | subset(A!17, B!18)),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(200,plain,
% 0.11/0.32 ((~ordinal_subset(A!17, B!18)) | subset(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.11/0.32 tff(201,plain,
% 0.11/0.32 (subset(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[200, 178])).
% 0.11/0.32 tff(202,plain,
% 0.11/0.32 (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(203,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[202])).
% 0.11/0.32 tff(204,plain,
% 0.11/0.32 (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(205,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[204])).
% 0.11/0.32 tff(206,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(207,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.11/0.32 tff(208,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.11/0.32 tff(209,plain,(
% 0.11/0.32 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.11/0.32 inference(skolemize,[status(sab)],[208])).
% 0.11/0.32 tff(210,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.11/0.32 tff(211,plain,
% 0.11/0.32 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.11/0.32 tff(212,plain,
% 0.11/0.32 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((A!17 = B!18) <=> (~((~subset(A!17, B!18)) | (~subset(B!18, A!17)))))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(213,plain,
% 0.11/0.32 ((A!17 = B!18) <=> (~((~subset(A!17, B!18)) | (~subset(B!18, A!17))))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.11/0.32 tff(214,plain,
% 0.11/0.32 ((~((A!17 = B!18) <=> (~((~subset(A!17, B!18)) | (~subset(B!18, A!17)))))) | (A!17 = B!18) | ((~subset(A!17, B!18)) | (~subset(B!18, A!17)))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(215,plain,
% 0.11/0.32 ((A!17 = B!18) | ((~subset(A!17, B!18)) | (~subset(B!18, A!17)))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.11/0.32 tff(216,plain,
% 0.11/0.32 ((~subset(A!17, B!18)) | (~subset(B!18, A!17))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[215, 126])).
% 0.11/0.32 tff(217,plain,
% 0.11/0.32 ((~((~subset(A!17, B!18)) | (~subset(B!18, A!17)))) | (~subset(A!17, B!18)) | (~subset(B!18, A!17))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(218,plain,
% 0.11/0.32 (~subset(B!18, A!17)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[217, 216, 201])).
% 0.11/0.32 tff(219,plain,
% 0.11/0.32 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(220,plain,
% 0.11/0.32 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[219])).
% 0.11/0.32 tff(221,plain,
% 0.11/0.32 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(222,plain,
% 0.11/0.32 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[221])).
% 0.11/0.32 tff(223,plain,
% 0.11/0.32 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.11/0.32 inference(transitivity,[status(thm)],[222, 220])).
% 0.11/0.32 tff(224,plain,
% 0.11/0.32 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(225,plain,
% 0.11/0.32 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[224])).
% 0.11/0.32 tff(226,plain,
% 0.11/0.32 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(227,plain,
% 0.11/0.32 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(228,plain,
% 0.11/0.32 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[227])).
% 0.11/0.32 tff(229,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.11/0.32 tff(230,plain,
% 0.11/0.32 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.11/0.32 tff(231,plain,
% 0.11/0.32 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.11/0.32 tff(232,plain,(
% 0.11/0.32 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))),
% 0.11/0.32 inference(skolemize,[status(sab)],[231])).
% 0.11/0.32 tff(233,plain,
% 0.11/0.32 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.11/0.32 tff(234,plain,
% 0.11/0.32 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[233, 223])).
% 0.11/0.32 tff(235,plain,
% 0.11/0.32 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))) | (~((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_1(A!17), A!17)) | subset(tptp_fun_B_1(A!17), A!17)))))))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(236,plain,
% 0.11/0.32 (~((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_1(A!17), A!17)) | subset(tptp_fun_B_1(A!17), A!17))))))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.11/0.32 tff(237,plain,
% 0.11/0.32 (((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_1(A!17), A!17)) | subset(tptp_fun_B_1(A!17), A!17)))))) | ((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(238,plain,
% 0.11/0.32 ((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.11/0.32 tff(239,plain,
% 0.11/0.32 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(240,plain,
% 0.11/0.32 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[239])).
% 0.11/0.32 tff(241,plain,
% 0.11/0.32 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(242,plain,
% 0.11/0.32 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[241])).
% 0.11/0.32 tff(243,plain,
% 0.11/0.32 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(244,plain,
% 0.11/0.32 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.11/0.32 inference(bind,[status(th)],[])).
% 0.11/0.32 tff(245,plain,
% 0.11/0.32 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.32 inference(quant_intro,[status(thm)],[244])).
% 0.11/0.32 tff(246,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.11/0.32 tff(247,plain,
% 0.11/0.32 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.11/0.32 tff(248,plain,
% 0.11/0.32 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.11/0.32 tff(249,plain,(
% 0.11/0.32 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.11/0.32 inference(skolemize,[status(sab)],[248])).
% 0.11/0.32 tff(250,plain,
% 0.11/0.32 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.11/0.32 tff(251,plain,
% 0.11/0.32 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[250, 240])).
% 0.11/0.32 tff(252,plain,
% 0.11/0.32 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!17)) | (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!17)) | (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(253,plain,
% 0.11/0.32 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!17)) | (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(254,plain,
% 0.11/0.32 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!17)) | (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.11/0.32 tff(255,plain,
% 0.11/0.32 (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[254, 251, 139])).
% 0.11/0.32 tff(256,plain,
% 0.11/0.32 (((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) | epsilon_transitive(A!17)),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(257,plain,
% 0.11/0.32 (epsilon_transitive(A!17)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[256, 255])).
% 0.11/0.32 tff(258,plain,
% 0.11/0.32 ((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(259,plain,
% 0.11/0.32 ((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.11/0.32 tff(260,plain,
% 0.11/0.32 (![B: $i] : ((~in(B, A!17)) | subset(B, A!17))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[259, 238])).
% 0.11/0.32 tff(261,plain,
% 0.11/0.32 (((~![B: $i] : ((~in(B, A!17)) | subset(B, A!17))) | ((~in(B!18, A!17)) | subset(B!18, A!17))) <=> ((~![B: $i] : ((~in(B, A!17)) | subset(B, A!17))) | (~in(B!18, A!17)) | subset(B!18, A!17))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(262,plain,
% 0.11/0.32 ((~![B: $i] : ((~in(B, A!17)) | subset(B, A!17))) | ((~in(B!18, A!17)) | subset(B!18, A!17))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(263,plain,
% 0.11/0.32 ((~![B: $i] : ((~in(B, A!17)) | subset(B, A!17))) | (~in(B!18, A!17)) | subset(B!18, A!17)),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.11/0.32 tff(264,plain,
% 0.11/0.32 ($false),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[263, 260, 218, 172])).
% 0.11/0.32 tff(265,plain,(in(A!17, succ(B!18))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.32 tff(266,plain,
% 0.11/0.32 (in(A!17, set_union2(B!18, singleton(B!18)))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[265, 12])).
% 0.11/0.32 tff(267,plain,
% 0.11/0.32 ((~in(A!17, succ(B!18))) | (~ordinal_subset(A!17, B!18)) | (~((~in(A!17, succ(B!18))) <=> ordinal_subset(A!17, B!18)))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(268,plain,
% 0.11/0.32 ((~in(A!17, succ(B!18))) | (~ordinal_subset(A!17, B!18))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[267, 175])).
% 0.11/0.32 tff(269,plain,
% 0.11/0.32 (~ordinal_subset(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[268, 265])).
% 0.11/0.32 tff(270,plain,
% 0.11/0.32 ((~(ordinal_subset(A!17, B!18) <=> subset(A!17, B!18))) | ordinal_subset(A!17, B!18) | (~subset(A!17, B!18))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(271,plain,
% 0.11/0.32 (ordinal_subset(A!17, B!18) | (~subset(A!17, B!18))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[270, 198])).
% 0.11/0.32 tff(272,plain,
% 0.11/0.32 (~subset(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[271, 269])).
% 0.11/0.32 tff(273,plain,
% 0.11/0.32 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))) | (~((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | (~(epsilon_transitive(B!18) | (~((~in(tptp_fun_B_1(B!18), B!18)) | subset(tptp_fun_B_1(B!18), B!18)))))))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(274,plain,
% 0.11/0.32 (~((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | (~(epsilon_transitive(B!18) | (~((~in(tptp_fun_B_1(B!18), B!18)) | subset(tptp_fun_B_1(B!18), B!18))))))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[273, 234])).
% 0.11/0.32 tff(275,plain,
% 0.11/0.32 (((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | (~(epsilon_transitive(B!18) | (~((~in(tptp_fun_B_1(B!18), B!18)) | subset(tptp_fun_B_1(B!18), B!18)))))) | ((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(276,plain,
% 0.11/0.32 ((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[275, 274])).
% 0.11/0.32 tff(277,plain,
% 0.11/0.32 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(278,plain,
% 0.11/0.32 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(279,plain,
% 0.11/0.32 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18))))),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.11/0.32 tff(280,plain,
% 0.11/0.32 (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[279, 251, 164])).
% 0.11/0.32 tff(281,plain,
% 0.11/0.32 (((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18))) | epsilon_transitive(B!18)),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(282,plain,
% 0.11/0.32 (epsilon_transitive(B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[281, 280])).
% 0.11/0.32 tff(283,plain,
% 0.11/0.32 ((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | (~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(284,plain,
% 0.11/0.32 ((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.11/0.32 tff(285,plain,
% 0.11/0.32 (![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[284, 276])).
% 0.11/0.32 tff(286,plain,
% 0.11/0.32 (((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | ((~in(A!17, B!18)) | subset(A!17, B!18))) <=> ((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | (~in(A!17, B!18)) | subset(A!17, B!18))),
% 0.11/0.32 inference(rewrite,[status(thm)],[])).
% 0.11/0.32 tff(287,plain,
% 0.11/0.32 ((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | ((~in(A!17, B!18)) | subset(A!17, B!18))),
% 0.11/0.32 inference(quant_inst,[status(thm)],[])).
% 0.11/0.32 tff(288,plain,
% 0.11/0.32 ((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | (~in(A!17, B!18)) | subset(A!17, B!18)),
% 0.11/0.32 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.11/0.32 tff(289,plain,
% 0.11/0.32 ((~in(A!17, B!18)) | subset(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[288, 285])).
% 0.11/0.32 tff(290,plain,
% 0.11/0.32 (~in(A!17, B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[289, 272])).
% 0.11/0.32 tff(291,plain,
% 0.11/0.32 (((~subset(A!17, B!18)) | (~subset(B!18, A!17))) | subset(A!17, B!18)),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(292,plain,
% 0.11/0.32 ((~subset(A!17, B!18)) | (~subset(B!18, A!17))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[291, 272])).
% 0.11/0.32 tff(293,plain,
% 0.11/0.32 ((~((A!17 = B!18) <=> (~((~subset(A!17, B!18)) | (~subset(B!18, A!17)))))) | (~(A!17 = B!18)) | (~((~subset(A!17, B!18)) | (~subset(B!18, A!17))))),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(294,plain,
% 0.11/0.32 ((~(A!17 = B!18)) | (~((~subset(A!17, B!18)) | (~subset(B!18, A!17))))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[293, 213])).
% 0.11/0.32 tff(295,plain,
% 0.11/0.32 (~(A!17 = B!18)),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[294, 292])).
% 0.11/0.32 tff(296,plain,
% 0.11/0.32 ((~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))) | (~in(A!17, singleton(B!18))) | (A!17 = B!18)),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(297,plain,
% 0.11/0.32 (~in(A!17, singleton(B!18))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[296, 295, 122])).
% 0.11/0.32 tff(298,plain,
% 0.11/0.32 ((~(in(A!17, singleton(B!18)) | in(A!17, B!18))) | in(A!17, singleton(B!18)) | in(A!17, B!18)),
% 0.11/0.32 inference(tautology,[status(thm)],[])).
% 0.11/0.32 tff(299,plain,
% 0.11/0.32 (~(in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.11/0.32 inference(unit_resolution,[status(thm)],[298, 297, 290])).
% 0.11/0.32 tff(300,plain,
% 0.11/0.32 ((~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) | (~in(A!17, set_union2(B!18, singleton(B!18)))) | (in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.11/0.33 inference(tautology,[status(thm)],[])).
% 0.11/0.33 tff(301,plain,
% 0.11/0.33 ((~in(A!17, set_union2(B!18, singleton(B!18)))) | (in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[300, 68])).
% 0.11/0.33 tff(302,plain,
% 0.11/0.33 (~in(A!17, set_union2(B!18, singleton(B!18)))),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[301, 299])).
% 0.11/0.33 tff(303,plain,
% 0.11/0.33 ($false),
% 0.11/0.33 inference(unit_resolution,[status(thm)],[302, 266])).
% 0.11/0.33 % SZS output end Proof
%------------------------------------------------------------------------------