TSTP Solution File: NUM388+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:09:28 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.34 % Computer : n021.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri Sep 2 10:05:13 EDT 2022
% 0.11/0.34 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(subset_type, type, (
% 0.19/0.39 subset: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_B_14_type, type, (
% 0.19/0.39 tptp_fun_B_14: $i)).
% 0.19/0.39 tff(tptp_fun_A_13_type, type, (
% 0.19/0.39 tptp_fun_A_13: $i)).
% 0.19/0.39 tff(element_type, type, (
% 0.19/0.39 element: ( $i * $i ) > $o)).
% 0.19/0.39 tff(powerset_type, type, (
% 0.19/0.39 powerset: $i > $i)).
% 0.19/0.39 tff(in_type, type, (
% 0.19/0.39 in: ( $i * $i ) > $o)).
% 0.19/0.39 tff(epsilon_transitive_type, type, (
% 0.19/0.39 epsilon_transitive: $i > $o)).
% 0.19/0.39 tff(tptp_fun_B_0_type, type, (
% 0.19/0.39 tptp_fun_B_0: $i > $i)).
% 0.19/0.39 tff(epsilon_connected_type, type, (
% 0.19/0.39 epsilon_connected: $i > $o)).
% 0.19/0.39 tff(ordinal_type, type, (
% 0.19/0.39 ordinal: $i > $o)).
% 0.19/0.39 tff(tptp_fun_C_15_type, type, (
% 0.19/0.39 tptp_fun_C_15: $i)).
% 0.19/0.39 tff(empty_type, type, (
% 0.19/0.39 empty: $i > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(A!13, powerset(B!14)) <=> subset(A!13, B!14))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (element(A!13, powerset(B!14)) <=> subset(A!13, B!14)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[13, 11])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (^[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_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.40 tff(20,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.40 tff(23,plain,(
% 0.19/0.40 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (~((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14)))))) | ((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((ordinal(A!13) & (ordinal(B!14) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15)))))) <=> (ordinal(A!13) & ordinal(B!14) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (((~(~ordinal(B!14))) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15))))) <=> (ordinal(B!14) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((~(~ordinal(A!13))) <=> ordinal(A!13)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~(~ordinal(A!13))) & ((~(~ordinal(B!14))) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15)))))) <=> (ordinal(A!13) & (ordinal(B!14) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[32, 31])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~(~ordinal(A!13))) & ((~(~ordinal(B!14))) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15)))))) <=> (ordinal(A!13) & ordinal(B!14) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[33, 30])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C)))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => ![C: $i] : (epsilon_transitive(C) => ((in(C, A) & in(A, B)) => in(C, B)))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(37,axiom,(~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => ![C: $i] : (epsilon_transitive(C) => ((in(C, A) & in(A, B)) => in(C, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_ordinal1')).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | ![C: $i] : (in(C, B) | (~(in(C, A) & in(A, B))) | (~epsilon_transitive(C)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 35])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (ordinal(A!13) & ordinal(B!14) & (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (ordinal(B!14)),
% 0.19/0.40 inference(and_elim,[status(thm)],[45])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.40 tff(54,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.40 tff(57,plain,(
% 0.19/0.40 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[56])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[62, 59, 46])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14))) | epsilon_transitive(B!14)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (epsilon_transitive(B!14)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 29])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (~(in(C!15, B!14) | (~(in(C!15, A!13) & in(A!13, B!14))) | (~epsilon_transitive(C!15)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[45])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (in(C!15, A!13) & in(A!13, B!14)),
% 0.19/0.40 inference(or_elim,[status(thm)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (in(A!13, B!14)),
% 0.19/0.40 inference(and_elim,[status(thm)],[70])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | ((~in(A!13, B!14)) | subset(A!13, B!14))) <=> ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | (~in(A!13, B!14)) | subset(A!13, B!14))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | ((~in(A!13, B!14)) | subset(A!13, B!14))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | (~in(A!13, B!14)) | subset(A!13, B!14)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (subset(A!13, B!14)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 71, 68])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(81,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_boole')).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.40 tff(83,plain,(
% 0.19/0.40 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[82])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(B!14)) | (~in(A!13, B!14)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(B!14)) | (~in(A!13, B!14)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(B!14)) | (~in(A!13, B!14)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(B!14)) | (~in(A!13, B!14))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (~empty(B!14)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[88, 71, 85])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.41 tff(95,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.41 tff(98,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[97])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (~in(C!15, B!14)),
% 0.19/0.41 inference(or_elim,[status(thm)],[69])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(C!15, B!14) | empty(B!14) | (~element(C!15, B!14)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(C!15, B!14) | empty(B!14) | (~element(C!15, B!14)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((empty(B!14) | in(C!15, B!14) | (~element(C!15, B!14))) <=> (in(C!15, B!14) | empty(B!14) | (~element(C!15, B!14)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(C!15, B!14) | (~element(C!15, B!14)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(C!15, B!14) | empty(B!14) | (~element(C!15, B!14))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(C!15, B!14) | (~element(C!15, B!14)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(C!15, B!14) | empty(B!14) | (~element(C!15, B!14)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(C!15, B!14) | (~element(C!15, B!14)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(C!15, B!14) | empty(B!14) | (~element(C!15, B!14))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (empty(B!14) | (~element(C!15, B!14))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 100, 99])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (~element(C!15, B!14)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[107, 89])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.41 tff(116,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_subset')).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.19/0.41 tff(119,plain,(
% 0.19/0.41 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.41 inference(skolemize,[status(sab)],[118])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (in(C!15, A!13)),
% 0.19/0.41 inference(and_elim,[status(thm)],[70])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(C!15, B!14) | (~in(C!15, A!13)) | (~element(A!13, powerset(B!14))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(C!15, B!14) | (~in(C!15, A!13)) | (~element(A!13, powerset(B!14))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(C!15, B!14) | (~in(C!15, A!13)) | (~element(A!13, powerset(B!14))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(C!15, B!14) | (~in(C!15, A!13)) | (~element(A!13, powerset(B!14)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (~element(A!13, powerset(B!14))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 122, 121, 108])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 ((~(element(A!13, powerset(B!14)) <=> subset(A!13, B!14))) | element(A!13, powerset(B!14)) | (~subset(A!13, B!14))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 ((~(element(A!13, powerset(B!14)) <=> subset(A!13, B!14))) | (~subset(A!13, B!14))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[128, 75, 9])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------