TSTP Solution File: SEU236+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU236+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:28:24 EDT 2022
% Result : Theorem 0.16s 0.38s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU236+3 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n008.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Sep 3 10:57:10 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 0.16/0.38 % SZS status Theorem
% 0.16/0.38 % SZS output start Proof
% 0.16/0.38 tff(element_type, type, (
% 0.16/0.38 element: ( $i * $i ) > $o)).
% 0.16/0.38 tff(powerset_type, type, (
% 0.16/0.38 powerset: $i > $i)).
% 0.16/0.38 tff(tptp_fun_B_18_type, type, (
% 0.16/0.38 tptp_fun_B_18: $i)).
% 0.16/0.38 tff(set_union2_type, type, (
% 0.16/0.38 set_union2: ( $i * $i ) > $i)).
% 0.16/0.38 tff(singleton_type, type, (
% 0.16/0.38 singleton: $i > $i)).
% 0.16/0.38 tff(tptp_fun_A_17_type, type, (
% 0.16/0.38 tptp_fun_A_17: $i)).
% 0.16/0.38 tff(subset_type, type, (
% 0.16/0.38 subset: ( $i * $i ) > $o)).
% 0.16/0.38 tff(succ_type, type, (
% 0.16/0.38 succ: $i > $i)).
% 0.16/0.38 tff(ordinal_subset_type, type, (
% 0.16/0.38 ordinal_subset: ( $i * $i ) > $o)).
% 0.16/0.38 tff(in_type, type, (
% 0.16/0.38 in: ( $i * $i ) > $o)).
% 0.16/0.38 tff(tptp_fun_C_2_type, type, (
% 0.16/0.38 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.16/0.38 tff(tptp_fun_C_0_type, type, (
% 0.16/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.16/0.38 tff(ordinal_type, type, (
% 0.16/0.38 ordinal: $i > $o)).
% 0.16/0.38 tff(epsilon_transitive_type, type, (
% 0.16/0.38 epsilon_transitive: $i > $o)).
% 0.16/0.38 tff(tptp_fun_B_1_type, type, (
% 0.16/0.38 tptp_fun_B_1: $i > $i)).
% 0.16/0.38 tff(epsilon_connected_type, type, (
% 0.16/0.38 epsilon_connected: $i > $o)).
% 0.16/0.38 tff(empty_type, type, (
% 0.16/0.38 empty: $i > $o)).
% 0.16/0.38 tff(1,plain,
% 0.16/0.38 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(2,plain,
% 0.16/0.38 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.16/0.38 tff(3,plain,
% 0.16/0.38 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(4,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.16/0.38 tff(5,plain,
% 0.16/0.38 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.16/0.38 tff(6,plain,(
% 0.16/0.38 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.16/0.38 inference(skolemize,[status(sab)],[5])).
% 0.16/0.38 tff(7,plain,
% 0.16/0.38 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.16/0.38 tff(8,plain,
% 0.16/0.38 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(A!17) = set_union2(A!17, singleton(A!17)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(9,plain,
% 0.16/0.38 (succ(A!17) = set_union2(A!17, singleton(A!17))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.16/0.38 tff(10,plain,
% 0.16/0.38 (set_union2(A!17, singleton(A!17)) = succ(A!17)),
% 0.16/0.38 inference(symmetry,[status(thm)],[9])).
% 0.16/0.38 tff(11,plain,
% 0.16/0.38 (subset(set_union2(A!17, singleton(A!17)), B!18) <=> subset(succ(A!17), B!18)),
% 0.16/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.16/0.38 tff(12,plain,
% 0.16/0.38 (subset(succ(A!17), B!18) <=> subset(set_union2(A!17, singleton(A!17)), B!18)),
% 0.16/0.38 inference(symmetry,[status(thm)],[11])).
% 0.16/0.38 tff(13,plain,
% 0.16/0.38 (^[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)))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(14,plain,
% 0.16/0.38 (![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))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.16/0.38 tff(15,plain,
% 0.16/0.38 (![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))))))),
% 0.16/0.38 inference(pull_quant,[status(thm)],[])).
% 0.16/0.38 tff(16,plain,
% 0.16/0.38 (^[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))))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(17,plain,
% 0.16/0.38 (![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))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.16/0.38 tff(18,plain,
% 0.16/0.38 (![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))))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.16/0.38 tff(19,plain,
% 0.16/0.38 (![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))))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[18, 14])).
% 0.16/0.38 tff(20,plain,
% 0.16/0.38 (^[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)))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(21,plain,
% 0.16/0.38 (![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))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.16/0.38 tff(22,plain,
% 0.16/0.38 (![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))))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[21, 19])).
% 0.16/0.38 tff(23,plain,
% 0.16/0.38 (^[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))))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(24,plain,
% 0.16/0.38 (![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))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.16/0.38 tff(25,plain,
% 0.16/0.38 (^[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)))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(26,plain,
% 0.16/0.38 (![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))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.16/0.38 tff(27,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(28,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.16/0.38 tff(29,plain,
% 0.16/0.38 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.16/0.38 tff(30,plain,(
% 0.16/0.38 ![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)))))),
% 0.16/0.38 inference(skolemize,[status(sab)],[29])).
% 0.16/0.38 tff(31,plain,
% 0.16/0.38 (![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))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.16/0.39 tff(32,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.16/0.39 tff(33,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.16/0.39 tff(34,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(35,plain,
% 0.16/0.39 ((~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))) <=> (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(36,plain,
% 0.16/0.39 ((((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)) | $false) <=> ((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(37,plain,
% 0.16/0.39 ((~$true) <=> $false),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(38,plain,
% 0.16/0.39 (($true | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17))) <=> $true),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(39,plain,
% 0.16/0.39 ((singleton(A!17) = singleton(A!17)) <=> $true),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(40,plain,
% 0.16/0.39 (((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17)))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.16/0.39 tff(41,plain,
% 0.16/0.39 (((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17))) <=> $true),
% 0.16/0.39 inference(transitivity,[status(thm)],[40, 38])).
% 0.16/0.39 tff(42,plain,
% 0.16/0.39 ((~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17)))) <=> (~$true)),
% 0.16/0.39 inference(monotonicity,[status(thm)],[41])).
% 0.16/0.39 tff(43,plain,
% 0.16/0.39 ((~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17)))) <=> $false),
% 0.16/0.39 inference(transitivity,[status(thm)],[42, 37])).
% 0.16/0.39 tff(44,plain,
% 0.16/0.39 ((~(in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))) <=> ((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(45,plain,
% 0.16/0.39 (($false | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))) <=> (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(46,plain,
% 0.16/0.39 ((~(singleton(A!17) = singleton(A!17))) <=> (~$true)),
% 0.16/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.16/0.39 tff(47,plain,
% 0.16/0.39 ((~(singleton(A!17) = singleton(A!17))) <=> $false),
% 0.16/0.39 inference(transitivity,[status(thm)],[46, 37])).
% 0.16/0.39 tff(48,plain,
% 0.16/0.39 (((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))) <=> ($false | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.16/0.39 tff(49,plain,
% 0.16/0.39 (((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))) <=> (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(transitivity,[status(thm)],[48, 45])).
% 0.16/0.39 tff(50,plain,
% 0.16/0.39 ((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) <=> (~(in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.16/0.39 tff(51,plain,
% 0.16/0.39 ((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) <=> ((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(transitivity,[status(thm)],[50, 44])).
% 0.16/0.39 tff(52,plain,
% 0.16/0.39 (((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) | (~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17))))) <=> (((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)) | $false)),
% 0.16/0.39 inference(monotonicity,[status(thm)],[51, 43])).
% 0.16/0.39 tff(53,plain,
% 0.16/0.39 (((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) | (~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17))))) <=> ((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(transitivity,[status(thm)],[52, 36])).
% 0.16/0.39 tff(54,plain,
% 0.16/0.39 ((~((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) | (~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17)))))) <=> (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.16/0.39 tff(55,plain,
% 0.16/0.39 ((~((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) | (~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17)))))) <=> (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(transitivity,[status(thm)],[54, 35])).
% 0.16/0.39 tff(56,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) | (~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.16/0.39 tff(57,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) | (~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))),
% 0.16/0.39 inference(transitivity,[status(thm)],[56, 34])).
% 0.16/0.39 tff(58,plain,
% 0.16/0.39 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!17) = singleton(A!17))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)))) | (~((singleton(A!17) = singleton(A!17)) | ((~in(tptp_fun_C_0(singleton(A!17), A!17), singleton(A!17))) <=> (tptp_fun_C_0(singleton(A!17), A!17) = A!17))))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(59,plain,
% 0.16/0.39 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.16/0.39 tff(60,plain,
% 0.16/0.39 (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[59, 33])).
% 0.16/0.39 tff(61,plain,
% 0.16/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(62,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.16/0.39 tff(63,plain,
% 0.16/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(64,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.16/0.39 tff(65,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.16/0.39 inference(transitivity,[status(thm)],[64, 62])).
% 0.16/0.39 tff(66,plain,
% 0.16/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(67,plain,
% 0.16/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.16/0.39 tff(68,plain,
% 0.16/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(69,plain,
% 0.16/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(70,plain,
% 0.16/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.16/0.39 tff(71,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.16/0.39 tff(72,plain,
% 0.16/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.16/0.39 tff(73,plain,
% 0.16/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.16/0.39 tff(74,plain,(
% 0.16/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[73])).
% 0.16/0.39 tff(75,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.16/0.39 tff(76,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.16/0.39 tff(77,plain,
% 0.16/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(singleton(A!17), B!18)) | ![C: $i] : ((~in(C, singleton(A!17))) | in(C, B!18)))) | (~(subset(singleton(A!17), B!18) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)))))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(78,plain,
% 0.16/0.39 (~((~((~subset(singleton(A!17), B!18)) | ![C: $i] : ((~in(C, singleton(A!17))) | in(C, B!18)))) | (~(subset(singleton(A!17), B!18) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18))))))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.16/0.40 tff(79,plain,
% 0.16/0.40 (((~((~subset(singleton(A!17), B!18)) | ![C: $i] : ((~in(C, singleton(A!17))) | in(C, B!18)))) | (~(subset(singleton(A!17), B!18) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)))))) | (subset(singleton(A!17), B!18) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18))))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(80,plain,
% 0.16/0.40 (subset(singleton(A!17), B!18) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.16/0.40 tff(81,assumption,(~ordinal_subset(succ(A!17), B!18)), introduced(assumption)).
% 0.16/0.40 tff(82,plain,
% 0.16/0.40 ((~(in(A!17, B!18) <=> ordinal_subset(succ(A!17), B!18))) <=> ((~in(A!17, B!18)) <=> ordinal_subset(succ(A!17), B!18))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(83,plain,
% 0.16/0.40 (((~(~ordinal(A!17))) & (~((~ordinal(B!18)) | (in(A!17, B!18) <=> ordinal_subset(succ(A!17), B!18))))) <=> (ordinal(A!17) & (~((~ordinal(B!18)) | (in(A!17, B!18) <=> ordinal_subset(succ(A!17), B!18)))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(84,plain,
% 0.16/0.40 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(85,plain,
% 0.16/0.40 ((~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, B) <=> ordinal_subset(succ(A), B))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(86,axiom,(~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, B) <=> ordinal_subset(succ(A), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t33_ordinal1')).
% 0.16/0.40 tff(87,plain,
% 0.16/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.16/0.40 tff(88,plain,
% 0.16/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.16/0.40 tff(89,plain,
% 0.16/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.16/0.40 tff(90,plain,
% 0.16/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[89, 84])).
% 0.16/0.40 tff(91,plain,
% 0.16/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[90, 84])).
% 0.16/0.40 tff(92,plain,
% 0.16/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.16/0.40 tff(93,plain,
% 0.16/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[92, 84])).
% 0.16/0.40 tff(94,plain,
% 0.16/0.40 (ordinal(A!17) & (~((~ordinal(B!18)) | (in(A!17, B!18) <=> ordinal_subset(succ(A!17), B!18))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.16/0.40 tff(95,plain,
% 0.16/0.40 (~((~ordinal(B!18)) | (in(A!17, B!18) <=> ordinal_subset(succ(A!17), B!18)))),
% 0.16/0.40 inference(and_elim,[status(thm)],[94])).
% 0.16/0.40 tff(96,plain,
% 0.16/0.40 (~(in(A!17, B!18) <=> ordinal_subset(succ(A!17), B!18))),
% 0.16/0.40 inference(or_elim,[status(thm)],[95])).
% 0.16/0.40 tff(97,plain,
% 0.16/0.40 ((~in(A!17, B!18)) <=> ordinal_subset(succ(A!17), B!18)),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[96, 82])).
% 0.16/0.40 tff(98,plain,
% 0.16/0.40 (in(A!17, B!18) | ordinal_subset(succ(A!17), B!18) | (~((~in(A!17, B!18)) <=> ordinal_subset(succ(A!17), B!18)))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(99,plain,
% 0.16/0.40 (in(A!17, B!18) | ordinal_subset(succ(A!17), B!18)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.16/0.40 tff(100,plain,
% 0.16/0.40 (in(A!17, B!18)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[99, 81])).
% 0.16/0.40 tff(101,plain,
% 0.16/0.40 (^[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))))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(102,plain,
% 0.16/0.40 (![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)))))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.16/0.40 tff(103,plain,
% 0.16/0.40 (^[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))))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(104,plain,
% 0.16/0.40 (![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)))))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[103])).
% 0.16/0.40 tff(105,plain,
% 0.16/0.40 (![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)))))))),
% 0.16/0.40 inference(transitivity,[status(thm)],[104, 102])).
% 0.16/0.40 tff(106,plain,
% 0.16/0.40 (^[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)))))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(107,plain,
% 0.16/0.40 (![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)))))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.16/0.40 tff(108,plain,
% 0.16/0.40 (![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)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(109,plain,
% 0.16/0.40 (^[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))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(110,plain,
% 0.16/0.40 (![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)))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[109])).
% 0.16/0.40 tff(111,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.16/0.40 tff(112,plain,
% 0.16/0.40 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.16/0.40 tff(113,plain,
% 0.16/0.40 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.16/0.40 tff(114,plain,(
% 0.16/0.40 ![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)))))),
% 0.16/0.40 inference(skolemize,[status(sab)],[113])).
% 0.16/0.40 tff(115,plain,
% 0.16/0.40 (![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)))))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.16/0.40 tff(116,plain,
% 0.16/0.40 (![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)))))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.16/0.40 tff(117,plain,
% 0.16/0.40 ((~![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)))))))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(118,plain,
% 0.16/0.40 (~((~((~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))))))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.16/0.40 tff(119,plain,
% 0.16/0.40 (((~((~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)))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(120,plain,
% 0.16/0.40 ((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.16/0.40 tff(121,plain,
% 0.16/0.40 (ordinal(B!18)),
% 0.16/0.40 inference(or_elim,[status(thm)],[95])).
% 0.16/0.40 tff(122,plain,
% 0.16/0.40 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(123,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[122])).
% 0.16/0.40 tff(124,plain,
% 0.16/0.40 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(125,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[124])).
% 0.16/0.40 tff(126,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(127,plain,
% 0.16/0.40 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(128,plain,
% 0.16/0.40 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[127])).
% 0.16/0.40 tff(129,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.16/0.40 tff(130,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.16/0.40 tff(131,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.16/0.40 tff(132,plain,(
% 0.16/0.40 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.16/0.40 inference(skolemize,[status(sab)],[131])).
% 0.16/0.40 tff(133,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.16/0.40 tff(134,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.16/0.40 tff(135,plain,
% 0.16/0.40 (((~![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)))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(136,plain,
% 0.16/0.40 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(137,plain,
% 0.16/0.40 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.16/0.40 tff(138,plain,
% 0.16/0.40 (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[137, 134, 121])).
% 0.16/0.40 tff(139,plain,
% 0.16/0.40 (((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18))) | epsilon_transitive(B!18)),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(140,plain,
% 0.16/0.40 (epsilon_transitive(B!18)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.16/0.40 tff(141,plain,
% 0.16/0.40 ((~((~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))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(142,plain,
% 0.16/0.40 ((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.16/0.40 tff(143,plain,
% 0.16/0.40 (![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[142, 120])).
% 0.16/0.40 tff(144,plain,
% 0.16/0.40 (((~![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))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(145,plain,
% 0.16/0.40 ((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | ((~in(A!17, B!18)) | subset(A!17, B!18))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(146,plain,
% 0.16/0.40 ((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | (~in(A!17, B!18)) | subset(A!17, B!18)),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.16/0.40 tff(147,plain,
% 0.16/0.40 ((~in(A!17, B!18)) | subset(A!17, B!18)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[146, 143])).
% 0.16/0.40 tff(148,plain,
% 0.16/0.40 (subset(A!17, B!18)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[147, 100])).
% 0.16/0.40 tff(149,plain,
% 0.16/0.40 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(150,plain,
% 0.16/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[149])).
% 0.16/0.40 tff(151,plain,
% 0.16/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(152,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.16/0.40 tff(153,plain,
% 0.16/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.16/0.40 tff(154,plain,(
% 0.16/0.40 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.40 inference(skolemize,[status(sab)],[153])).
% 0.16/0.40 tff(155,plain,
% 0.16/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.16/0.40 tff(156,plain,
% 0.16/0.40 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!17, singleton(A!17)) = set_union2(singleton(A!17), A!17))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(157,plain,
% 0.16/0.40 (set_union2(A!17, singleton(A!17)) = set_union2(singleton(A!17), A!17)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.16/0.40 tff(158,plain,
% 0.16/0.40 (set_union2(singleton(A!17), A!17) = set_union2(A!17, singleton(A!17))),
% 0.16/0.40 inference(symmetry,[status(thm)],[157])).
% 0.16/0.40 tff(159,plain,
% 0.16/0.40 (set_union2(singleton(A!17), A!17) = succ(A!17)),
% 0.16/0.40 inference(transitivity,[status(thm)],[158, 10])).
% 0.16/0.40 tff(160,plain,
% 0.16/0.40 (subset(set_union2(singleton(A!17), A!17), B!18) <=> subset(succ(A!17), B!18)),
% 0.16/0.40 inference(monotonicity,[status(thm)],[159])).
% 0.16/0.40 tff(161,plain,
% 0.16/0.40 (subset(succ(A!17), B!18) <=> subset(set_union2(singleton(A!17), A!17), B!18)),
% 0.16/0.40 inference(symmetry,[status(thm)],[160])).
% 0.16/0.40 tff(162,plain,
% 0.16/0.40 ((~subset(succ(A!17), B!18)) <=> (~subset(set_union2(singleton(A!17), A!17), B!18))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[161])).
% 0.16/0.40 tff(163,plain,
% 0.16/0.40 (ordinal(A!17)),
% 0.16/0.40 inference(and_elim,[status(thm)],[94])).
% 0.16/0.40 tff(164,plain,
% 0.16/0.40 (^[A: $i] : refl(((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A)))))) <=> ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A)))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(165,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A)))))) <=> ![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[164])).
% 0.16/0.40 tff(166,plain,
% 0.16/0.40 (^[A: $i] : rewrite(((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) <=> ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A)))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(167,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) <=> ![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[166])).
% 0.16/0.40 tff(168,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) <=> ![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(169,plain,
% 0.16/0.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) <=> ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)))), (((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A))) <=> (((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A))) & ordinal(succ(A))))), rewrite((((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A))) & ordinal(succ(A))) <=> ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))), (((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A))) <=> ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))), ((ordinal(A) => ((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A)))) <=> (ordinal(A) => ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))))), rewrite((ordinal(A) => ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) <=> ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))), ((ordinal(A) => ((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A)))) <=> ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(170,plain,
% 0.16/0.40 (![A: $i] : (ordinal(A) => ((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A)))) <=> ![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[169])).
% 0.16/0.40 tff(171,axiom,(![A: $i] : (ordinal(A) => ((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc3_ordinal1')).
% 0.16/0.40 tff(172,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.16/0.40 tff(173,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.16/0.40 tff(174,plain,(
% 0.16/0.40 ![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.16/0.40 inference(skolemize,[status(sab)],[173])).
% 0.16/0.40 tff(175,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.16/0.40 tff(176,plain,
% 0.16/0.40 (![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[175, 165])).
% 0.16/0.40 tff(177,plain,
% 0.16/0.40 (((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | ((~ordinal(A!17)) | (~((~ordinal(succ(A!17))) | empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | (~ordinal(A!17)) | (~((~ordinal(succ(A!17))) | empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(178,plain,
% 0.16/0.40 (((~ordinal(A!17)) | (~(empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))) | (~ordinal(succ(A!17)))))) <=> ((~ordinal(A!17)) | (~((~ordinal(succ(A!17))) | empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(179,plain,
% 0.16/0.41 (((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | ((~ordinal(A!17)) | (~(empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))) | (~ordinal(succ(A!17))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | ((~ordinal(A!17)) | (~((~ordinal(succ(A!17))) | empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17)))))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[178])).
% 0.16/0.41 tff(180,plain,
% 0.16/0.41 (((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | ((~ordinal(A!17)) | (~(empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))) | (~ordinal(succ(A!17))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | (~ordinal(A!17)) | (~((~ordinal(succ(A!17))) | empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))))))),
% 0.16/0.41 inference(transitivity,[status(thm)],[179, 177])).
% 0.16/0.41 tff(181,plain,
% 0.16/0.41 ((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | ((~ordinal(A!17)) | (~(empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))) | (~ordinal(succ(A!17))))))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(182,plain,
% 0.16/0.41 ((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | (~ordinal(A!17)) | (~((~ordinal(succ(A!17))) | empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17)))))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.16/0.41 tff(183,plain,
% 0.16/0.41 (~((~ordinal(succ(A!17))) | empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17))))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[182, 176, 163])).
% 0.16/0.41 tff(184,plain,
% 0.16/0.41 (((~ordinal(succ(A!17))) | empty(succ(A!17)) | (~epsilon_transitive(succ(A!17))) | (~epsilon_connected(succ(A!17)))) | ordinal(succ(A!17))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(185,plain,
% 0.16/0.41 (ordinal(succ(A!17))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.16/0.41 tff(186,plain,
% 0.16/0.41 (^[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))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(187,plain,
% 0.16/0.41 (![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)))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[186])).
% 0.16/0.41 tff(188,plain,
% 0.16/0.41 (^[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)))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(189,plain,
% 0.16/0.41 (![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)))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[188])).
% 0.16/0.41 tff(190,plain,
% 0.16/0.41 (![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)))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(191,plain,
% 0.16/0.41 (^[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))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(192,plain,
% 0.16/0.41 (![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)))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[191])).
% 0.16/0.41 tff(193,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.16/0.41 tff(194,plain,
% 0.16/0.41 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.16/0.41 tff(195,plain,
% 0.16/0.41 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.16/0.41 tff(196,plain,(
% 0.16/0.41 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.16/0.41 inference(skolemize,[status(sab)],[195])).
% 0.16/0.41 tff(197,plain,
% 0.16/0.41 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.16/0.41 tff(198,plain,
% 0.16/0.41 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[197, 187])).
% 0.16/0.41 tff(199,plain,
% 0.16/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(B!18)) | (ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(succ(A!17))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(B!18)) | (ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(succ(A!17))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(200,plain,
% 0.16/0.41 (((ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(B!18)) | (~ordinal(succ(A!17)))) <=> ((~ordinal(B!18)) | (ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(succ(A!17))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(201,plain,
% 0.16/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(B!18)) | (~ordinal(succ(A!17))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(B!18)) | (ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(succ(A!17)))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[200])).
% 0.16/0.41 tff(202,plain,
% 0.16/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(B!18)) | (~ordinal(succ(A!17))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(B!18)) | (ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(succ(A!17))))),
% 0.16/0.41 inference(transitivity,[status(thm)],[201, 199])).
% 0.16/0.41 tff(203,plain,
% 0.16/0.41 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(B!18)) | (~ordinal(succ(A!17))))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(204,plain,
% 0.16/0.41 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(B!18)) | (ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(succ(A!17)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.16/0.41 tff(205,plain,
% 0.16/0.41 ((ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)) | (~ordinal(succ(A!17)))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[204, 198, 121])).
% 0.16/0.41 tff(206,plain,
% 0.16/0.41 (ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[205, 185])).
% 0.16/0.41 tff(207,plain,
% 0.16/0.41 ((~(ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18))) | ordinal_subset(succ(A!17), B!18) | (~subset(succ(A!17), B!18))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(208,plain,
% 0.16/0.41 (ordinal_subset(succ(A!17), B!18) | (~subset(succ(A!17), B!18))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.16/0.41 tff(209,plain,
% 0.16/0.41 (~subset(succ(A!17), B!18)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[208, 81])).
% 0.16/0.41 tff(210,plain,
% 0.16/0.41 (~subset(set_union2(singleton(A!17), A!17), B!18)),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[209, 162])).
% 0.16/0.41 tff(211,plain,
% 0.16/0.41 (^[A: $i, B: $i, C: $i] : refl((subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B))) <=> (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(212,plain,
% 0.16/0.41 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B))) <=> ![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[211])).
% 0.16/0.41 tff(213,plain,
% 0.16/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(C, B)) <=> (~((~subset(A, B)) | (~subset(C, B))))), ((~(subset(A, B) & subset(C, B))) <=> (~(~((~subset(A, B)) | (~subset(C, B))))))), rewrite((~(~((~subset(A, B)) | (~subset(C, B))))) <=> ((~subset(A, B)) | (~subset(C, B)))), ((~(subset(A, B) & subset(C, B))) <=> ((~subset(A, B)) | (~subset(C, B))))), (((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> (((~subset(A, B)) | (~subset(C, B))) | subset(set_union2(A, C), B)))), rewrite((((~subset(A, B)) | (~subset(C, B))) | subset(set_union2(A, C), B)) <=> (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))), (((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(214,plain,
% 0.16/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[213])).
% 0.16/0.41 tff(215,plain,
% 0.16/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(216,plain,
% 0.16/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B)) <=> ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(217,plain,
% 0.16/0.41 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[216])).
% 0.16/0.41 tff(218,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_xboole_1')).
% 0.16/0.41 tff(219,plain,
% 0.16/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.16/0.41 tff(220,plain,
% 0.16/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.16/0.41 tff(221,plain,(
% 0.16/0.41 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.16/0.41 inference(skolemize,[status(sab)],[220])).
% 0.16/0.41 tff(222,plain,
% 0.16/0.41 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.16/0.41 tff(223,plain,
% 0.16/0.41 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[222, 212])).
% 0.16/0.41 tff(224,plain,
% 0.16/0.41 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | ((~subset(A!17, B!18)) | (~subset(singleton(A!17), B!18)) | subset(set_union2(singleton(A!17), A!17), B!18))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | (~subset(A!17, B!18)) | (~subset(singleton(A!17), B!18)) | subset(set_union2(singleton(A!17), A!17), B!18))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(225,plain,
% 0.16/0.41 ((subset(set_union2(singleton(A!17), A!17), B!18) | (~subset(singleton(A!17), B!18)) | (~subset(A!17, B!18))) <=> ((~subset(A!17, B!18)) | (~subset(singleton(A!17), B!18)) | subset(set_union2(singleton(A!17), A!17), B!18))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(226,plain,
% 0.16/0.41 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | (subset(set_union2(singleton(A!17), A!17), B!18) | (~subset(singleton(A!17), B!18)) | (~subset(A!17, B!18)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | ((~subset(A!17, B!18)) | (~subset(singleton(A!17), B!18)) | subset(set_union2(singleton(A!17), A!17), B!18)))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[225])).
% 0.16/0.41 tff(227,plain,
% 0.16/0.41 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | (subset(set_union2(singleton(A!17), A!17), B!18) | (~subset(singleton(A!17), B!18)) | (~subset(A!17, B!18)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | (~subset(A!17, B!18)) | (~subset(singleton(A!17), B!18)) | subset(set_union2(singleton(A!17), A!17), B!18))),
% 0.16/0.41 inference(transitivity,[status(thm)],[226, 224])).
% 0.16/0.41 tff(228,plain,
% 0.16/0.41 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | (subset(set_union2(singleton(A!17), A!17), B!18) | (~subset(singleton(A!17), B!18)) | (~subset(A!17, B!18)))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(229,plain,
% 0.16/0.41 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(A, B)) | (~subset(C, B)))) | (~subset(A!17, B!18)) | (~subset(singleton(A!17), B!18)) | subset(set_union2(singleton(A!17), A!17), B!18)),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.16/0.41 tff(230,plain,
% 0.16/0.41 ((~subset(A!17, B!18)) | (~subset(singleton(A!17), B!18)) | subset(set_union2(singleton(A!17), A!17), B!18)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[229, 223])).
% 0.16/0.41 tff(231,plain,
% 0.16/0.41 (~subset(singleton(A!17), B!18)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[230, 210, 148])).
% 0.16/0.41 tff(232,plain,
% 0.16/0.41 ((~(subset(singleton(A!17), B!18) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18))))) | subset(singleton(A!17), B!18) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(233,plain,
% 0.16/0.41 ((~(subset(singleton(A!17), B!18) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18))))) | (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.16/0.41 tff(234,plain,
% 0.16/0.41 (~((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[233, 80])).
% 0.16/0.41 tff(235,plain,
% 0.16/0.41 (((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)) | in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(236,plain,
% 0.16/0.41 (in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.16/0.41 tff(237,plain,
% 0.16/0.41 ((~(in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))) | (~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(238,plain,
% 0.16/0.41 ((~(in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17)) <=> (tptp_fun_C_2(B!18, singleton(A!17)) = A!17))) | (tptp_fun_C_2(B!18, singleton(A!17)) = A!17)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.16/0.41 tff(239,plain,
% 0.16/0.41 (tptp_fun_C_2(B!18, singleton(A!17)) = A!17),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[238, 60])).
% 0.16/0.41 tff(240,plain,
% 0.16/0.41 (in(tptp_fun_C_2(B!18, singleton(A!17)), B!18) <=> in(A!17, B!18)),
% 0.16/0.41 inference(monotonicity,[status(thm)],[239])).
% 0.16/0.41 tff(241,plain,
% 0.16/0.41 (in(A!17, B!18) <=> in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)),
% 0.16/0.41 inference(symmetry,[status(thm)],[240])).
% 0.16/0.41 tff(242,plain,
% 0.16/0.41 (in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[100, 241])).
% 0.16/0.41 tff(243,plain,
% 0.16/0.41 (((~in(tptp_fun_C_2(B!18, singleton(A!17)), singleton(A!17))) | in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)) | (~in(tptp_fun_C_2(B!18, singleton(A!17)), B!18))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(244,plain,
% 0.16/0.41 (~in(tptp_fun_C_2(B!18, singleton(A!17)), B!18)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[243, 234])).
% 0.16/0.41 tff(245,plain,
% 0.16/0.41 ($false),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[244, 242])).
% 0.16/0.41 tff(246,plain,(ordinal_subset(succ(A!17), B!18)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.41 tff(247,plain,
% 0.16/0.41 ((~(ordinal_subset(succ(A!17), B!18) <=> subset(succ(A!17), B!18))) | (~ordinal_subset(succ(A!17), B!18)) | subset(succ(A!17), B!18)),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(248,plain,
% 0.16/0.41 ((~ordinal_subset(succ(A!17), B!18)) | subset(succ(A!17), B!18)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[247, 206])).
% 0.16/0.41 tff(249,plain,
% 0.16/0.41 (subset(succ(A!17), B!18)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[248, 246])).
% 0.16/0.41 tff(250,plain,
% 0.16/0.41 (subset(set_union2(A!17, singleton(A!17)), B!18)),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[249, 12])).
% 0.16/0.41 tff(251,plain,
% 0.16/0.41 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(252,plain,
% 0.16/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[251])).
% 0.16/0.41 tff(253,plain,
% 0.16/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(254,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.16/0.41 tff(255,plain,
% 0.16/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.16/0.41 tff(256,plain,(
% 0.16/0.41 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.16/0.41 inference(skolemize,[status(sab)],[255])).
% 0.16/0.41 tff(257,plain,
% 0.16/0.41 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.16/0.41 tff(258,plain,
% 0.16/0.41 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(set_union2(A!17, singleton(A!17)), powerset(B!18)) <=> subset(set_union2(A!17, singleton(A!17)), B!18))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(259,plain,
% 0.16/0.41 (element(set_union2(A!17, singleton(A!17)), powerset(B!18)) <=> subset(set_union2(A!17, singleton(A!17)), B!18)),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.16/0.41 tff(260,plain,
% 0.16/0.41 ((~(element(set_union2(A!17, singleton(A!17)), powerset(B!18)) <=> subset(set_union2(A!17, singleton(A!17)), B!18))) | element(set_union2(A!17, singleton(A!17)), powerset(B!18)) | (~subset(set_union2(A!17, singleton(A!17)), B!18))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(261,plain,
% 0.16/0.41 (element(set_union2(A!17, singleton(A!17)), powerset(B!18)) | (~subset(set_union2(A!17, singleton(A!17)), B!18))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.16/0.42 tff(262,plain,
% 0.16/0.42 (element(set_union2(A!17, singleton(A!17)), powerset(B!18))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[261, 250])).
% 0.16/0.42 tff(263,plain,
% 0.16/0.42 (in(A!17, set_union2(A!17, singleton(A!17))) <=> in(A!17, succ(A!17))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[10])).
% 0.16/0.42 tff(264,plain,
% 0.16/0.42 (in(A!17, succ(A!17)) <=> in(A!17, set_union2(A!17, singleton(A!17)))),
% 0.16/0.42 inference(symmetry,[status(thm)],[263])).
% 0.16/0.42 tff(265,plain,
% 0.16/0.42 (^[A: $i] : refl(in(A, succ(A)) <=> in(A, succ(A)))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(266,plain,
% 0.16/0.42 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[265])).
% 0.16/0.42 tff(267,plain,
% 0.16/0.42 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(268,axiom,(![A: $i] : in(A, succ(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_ordinal1')).
% 0.16/0.42 tff(269,plain,
% 0.16/0.42 (![A: $i] : in(A, succ(A))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.16/0.42 tff(270,plain,(
% 0.16/0.42 ![A: $i] : in(A, succ(A))),
% 0.16/0.42 inference(skolemize,[status(sab)],[269])).
% 0.16/0.42 tff(271,plain,
% 0.16/0.42 (![A: $i] : in(A, succ(A))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.16/0.42 tff(272,plain,
% 0.16/0.42 ((~![A: $i] : in(A, succ(A))) | in(A!17, succ(A!17))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(273,plain,
% 0.16/0.42 (in(A!17, succ(A!17))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.16/0.42 tff(274,plain,
% 0.16/0.42 (in(A!17, set_union2(A!17, singleton(A!17)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[273, 264])).
% 0.16/0.42 tff(275,plain,
% 0.16/0.42 ((~in(A!17, B!18)) | (~ordinal_subset(succ(A!17), B!18)) | (~((~in(A!17, B!18)) <=> ordinal_subset(succ(A!17), B!18)))),
% 0.16/0.42 inference(tautology,[status(thm)],[])).
% 0.16/0.42 tff(276,plain,
% 0.16/0.42 ((~in(A!17, B!18)) | (~ordinal_subset(succ(A!17), B!18))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[275, 97])).
% 0.16/0.42 tff(277,plain,
% 0.16/0.42 (~in(A!17, B!18)),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[276, 246])).
% 0.16/0.42 tff(278,plain,
% 0.16/0.42 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(279,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[278])).
% 0.16/0.42 tff(280,plain,
% 0.16/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(281,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[280])).
% 0.16/0.42 tff(282,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(283,plain,
% 0.16/0.42 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(284,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[283])).
% 0.16/0.42 tff(285,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 0.16/0.42 tff(286,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.16/0.42 tff(287,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.16/0.42 tff(288,plain,(
% 0.16/0.42 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.16/0.42 inference(skolemize,[status(sab)],[287])).
% 0.16/0.42 tff(289,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[288, 281])).
% 0.16/0.42 tff(290,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[289, 279])).
% 0.16/0.42 tff(291,plain,
% 0.16/0.42 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!18)) | (~in(A!17, set_union2(A!17, singleton(A!17)))) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(B!18)) | (~in(A!17, set_union2(A!17, singleton(A!17)))) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(292,plain,
% 0.16/0.42 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!18)) | (~in(A!17, set_union2(A!17, singleton(A!17)))) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18))))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(293,plain,
% 0.16/0.42 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(B!18)) | (~in(A!17, set_union2(A!17, singleton(A!17)))) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.16/0.42 tff(294,plain,
% 0.16/0.42 ((~empty(B!18)) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18)))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[293, 290, 274])).
% 0.16/0.42 tff(295,plain,
% 0.16/0.42 (~empty(B!18)),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[294, 262])).
% 0.16/0.42 tff(296,plain,
% 0.16/0.42 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(297,plain,
% 0.16/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[296])).
% 0.16/0.42 tff(298,plain,
% 0.16/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(299,plain,
% 0.16/0.42 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(300,plain,
% 0.16/0.42 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[299])).
% 0.16/0.42 tff(301,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.16/0.42 tff(302,plain,
% 0.16/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.16/0.42 tff(303,plain,
% 0.16/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.16/0.42 tff(304,plain,(
% 0.16/0.42 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.16/0.42 inference(skolemize,[status(sab)],[303])).
% 0.16/0.42 tff(305,plain,
% 0.16/0.42 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.16/0.42 tff(306,plain,
% 0.16/0.42 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(A!17, B!18) | empty(B!18) | (~element(A!17, B!18)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(A!17, B!18) | empty(B!18) | (~element(A!17, B!18)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(307,plain,
% 0.16/0.42 ((empty(B!18) | in(A!17, B!18) | (~element(A!17, B!18))) <=> (in(A!17, B!18) | empty(B!18) | (~element(A!17, B!18)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(308,plain,
% 0.16/0.42 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!18) | in(A!17, B!18) | (~element(A!17, B!18)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(A!17, B!18) | empty(B!18) | (~element(A!17, B!18))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[307])).
% 0.16/0.42 tff(309,plain,
% 0.16/0.42 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!18) | in(A!17, B!18) | (~element(A!17, B!18)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(A!17, B!18) | empty(B!18) | (~element(A!17, B!18)))),
% 0.16/0.42 inference(transitivity,[status(thm)],[308, 306])).
% 0.16/0.42 tff(310,plain,
% 0.16/0.42 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!18) | in(A!17, B!18) | (~element(A!17, B!18)))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(311,plain,
% 0.16/0.42 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(A!17, B!18) | empty(B!18) | (~element(A!17, B!18))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.16/0.42 tff(312,plain,
% 0.16/0.42 (in(A!17, B!18) | empty(B!18) | (~element(A!17, B!18))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[311, 305])).
% 0.16/0.42 tff(313,plain,
% 0.16/0.42 (~element(A!17, B!18)),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[312, 295, 277])).
% 0.16/0.42 tff(314,plain,
% 0.16/0.42 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(315,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[314])).
% 0.16/0.42 tff(316,plain,
% 0.16/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(317,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[316])).
% 0.16/0.42 tff(318,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(319,plain,
% 0.16/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(320,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[319])).
% 0.16/0.42 tff(321,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 0.16/0.42 tff(322,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.16/0.42 tff(323,plain,
% 0.16/0.42 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[322, 318])).
% 0.16/0.43 tff(324,plain,(
% 0.16/0.43 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.16/0.43 inference(skolemize,[status(sab)],[323])).
% 0.16/0.43 tff(325,plain,
% 0.16/0.43 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[324, 317])).
% 0.16/0.43 tff(326,plain,
% 0.16/0.43 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[325, 315])).
% 0.16/0.43 tff(327,plain,
% 0.16/0.43 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!17, B!18) | (~in(A!17, set_union2(A!17, singleton(A!17)))) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(A!17, B!18) | (~in(A!17, set_union2(A!17, singleton(A!17)))) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18))))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(328,plain,
% 0.16/0.43 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(A!17, B!18) | (~in(A!17, set_union2(A!17, singleton(A!17)))) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18))))),
% 0.16/0.43 inference(quant_inst,[status(thm)],[])).
% 0.16/0.43 tff(329,plain,
% 0.16/0.43 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(A!17, B!18) | (~in(A!17, set_union2(A!17, singleton(A!17)))) | (~element(set_union2(A!17, singleton(A!17)), powerset(B!18)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.16/0.43 tff(330,plain,
% 0.16/0.43 ($false),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[329, 326, 313, 274, 262])).
% 0.16/0.43 % SZS output end Proof
%------------------------------------------------------------------------------