TSTP Solution File: SEU114+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU114+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:32 EDT 2022
% Result : Theorem 0.86s 0.84s
% Output : Proof 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU114+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:29:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.86/0.84 % SZS status Theorem
% 0.86/0.84 % SZS output start Proof
% 0.86/0.84 tff(subset_type, type, (
% 0.86/0.84 subset: ( $i * $i ) > $o)).
% 0.86/0.84 tff(tptp_fun_A_11_type, type, (
% 0.86/0.84 tptp_fun_A_11: $i)).
% 0.86/0.84 tff(tptp_fun_C_0_type, type, (
% 0.86/0.84 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.86/0.84 tff(powerset_type, type, (
% 0.86/0.84 powerset: $i > $i)).
% 0.86/0.84 tff(finite_subsets_type, type, (
% 0.86/0.84 finite_subsets: $i > $i)).
% 0.86/0.84 tff(element_type, type, (
% 0.86/0.84 element: ( $i * $i ) > $o)).
% 0.86/0.84 tff(finite_type, type, (
% 0.86/0.84 finite: $i > $o)).
% 0.86/0.84 tff(in_type, type, (
% 0.86/0.84 in: ( $i * $i ) > $o)).
% 0.86/0.84 tff(preboolean_type, type, (
% 0.86/0.84 preboolean: $i > $o)).
% 0.86/0.84 tff(tptp_fun_C_1_type, type, (
% 0.86/0.84 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.86/0.84 tff(1,plain,
% 0.86/0.84 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(2,plain,
% 0.86/0.84 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[1])).
% 0.86/0.84 tff(3,plain,
% 0.86/0.84 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.86/0.84 tff(5,plain,
% 0.86/0.84 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.86/0.84 tff(6,plain,(
% 0.86/0.84 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.86/0.84 inference(skolemize,[status(sab)],[5])).
% 0.86/0.84 tff(7,plain,
% 0.86/0.84 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.86/0.84 tff(8,plain,
% 0.86/0.84 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(9,plain,
% 0.86/0.84 (element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.86/0.84 tff(10,plain,
% 0.86/0.84 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(11,plain,
% 0.86/0.84 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[10])).
% 0.86/0.84 tff(12,plain,
% 0.86/0.84 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(13,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.86/0.84 tff(14,plain,
% 0.86/0.84 (![A: $i] : preboolean(finite_subsets(A))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.86/0.84 tff(15,plain,(
% 0.86/0.84 ![A: $i] : preboolean(finite_subsets(A))),
% 0.86/0.84 inference(skolemize,[status(sab)],[14])).
% 0.86/0.84 tff(16,plain,
% 0.86/0.84 (![A: $i] : preboolean(finite_subsets(A))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.86/0.84 tff(17,plain,
% 0.86/0.84 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!11))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(18,plain,
% 0.86/0.84 (preboolean(finite_subsets(A!11))),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.86/0.84 tff(19,plain,
% 0.86/0.84 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))) <=> ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A)))))))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(20,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[19])).
% 0.86/0.84 tff(21,plain,
% 0.86/0.84 (^[A: $i, B: $i] : refl(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(22,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[21])).
% 0.86/0.84 tff(23,plain,
% 0.86/0.84 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(24,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[23])).
% 0.86/0.84 tff(25,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))))))),
% 0.86/0.84 inference(transitivity,[status(thm)],[24, 22])).
% 0.86/0.84 tff(26,plain,
% 0.86/0.84 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_1(B, A), B)) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))))))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(27,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_1(B, A), B)) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[26])).
% 0.86/0.84 tff(28,plain,
% 0.86/0.84 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_1(B, A), B) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A)))))))) <=> ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_1(B, A), B)) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A))))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(29,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_1(B, A), B) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A)))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_1(B, A), B)) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A)))))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[28])).
% 0.86/0.84 tff(30,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(31,plain,
% 0.86/0.84 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) <=> ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))), ((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))))), rewrite((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))), ((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(32,plain,
% 0.86/0.84 (![A: $i, B: $i] : (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[31])).
% 0.86/0.84 tff(33,axiom,(![A: $i, B: $i] : (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_finsub_1')).
% 0.86/0.84 tff(34,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.86/0.84 tff(35,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.86/0.84 tff(36,plain,(
% 0.86/0.84 ![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_1(B, A), B) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A))))))))),
% 0.86/0.84 inference(skolemize,[status(sab)],[35])).
% 0.86/0.84 tff(37,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | ((~in(tptp_fun_C_1(B, A), B)) <=> (subset(tptp_fun_C_1(B, A), A) & finite(tptp_fun_C_1(B, A)))))))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.86/0.84 tff(38,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))))))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.86/0.84 tff(39,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))) | (~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))))))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[38, 25])).
% 0.86/0.84 tff(40,plain,
% 0.86/0.84 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[39, 20])).
% 0.86/0.84 tff(41,plain,
% 0.86/0.84 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(42,plain,
% 0.86/0.84 (((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (in(tptp_fun_C_1(finite_subsets(A!11), A!11), finite_subsets(A!11)) <=> ((~subset(tptp_fun_C_1(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_1(finite_subsets(A!11), A!11))))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))))))) <=> ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(43,plain,
% 0.86/0.84 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (in(tptp_fun_C_1(finite_subsets(A!11), A!11), finite_subsets(A!11)) <=> ((~subset(tptp_fun_C_1(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_1(finite_subsets(A!11), A!11))))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[42])).
% 0.86/0.84 tff(44,plain,
% 0.86/0.84 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (in(tptp_fun_C_1(finite_subsets(A!11), A!11), finite_subsets(A!11)) <=> ((~subset(tptp_fun_C_1(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_1(finite_subsets(A!11), A!11))))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))),
% 0.86/0.84 inference(transitivity,[status(thm)],[43, 41])).
% 0.86/0.84 tff(45,plain,
% 0.86/0.84 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | ((~preboolean(finite_subsets(A!11))) | (~((~((finite_subsets(A!11) = finite_subsets(A!11)) | (in(tptp_fun_C_1(finite_subsets(A!11), A!11), finite_subsets(A!11)) <=> ((~subset(tptp_fun_C_1(finite_subsets(A!11), A!11), A!11)) | (~finite(tptp_fun_C_1(finite_subsets(A!11), A!11))))))) | (~((~(finite_subsets(A!11) = finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11))))))))))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(46,plain,
% 0.86/0.84 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (in(tptp_fun_C_1(B, A), B) <=> ((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A))))))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (~((~finite(C)) | (~subset(C, A))))))))))) | (~preboolean(finite_subsets(A!11))) | ![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.86/0.84 tff(47,plain,
% 0.86/0.84 (![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[46, 40, 18])).
% 0.86/0.84 tff(48,plain,
% 0.86/0.84 ((~![C: $i] : (in(C, finite_subsets(A!11)) <=> (~((~finite(C)) | (~subset(C, A!11)))))) | (in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)))))),
% 0.86/0.84 inference(quant_inst,[status(thm)],[])).
% 0.86/0.84 tff(49,plain,
% 0.86/0.84 (in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))))),
% 0.86/0.84 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.86/0.84 tff(50,plain,
% 0.86/0.84 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(51,plain,
% 0.86/0.84 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[50])).
% 0.86/0.84 tff(52,plain,
% 0.86/0.84 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(53,plain,
% 0.86/0.84 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[52])).
% 0.86/0.84 tff(54,plain,
% 0.86/0.84 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.86/0.84 inference(transitivity,[status(thm)],[53, 51])).
% 0.86/0.84 tff(55,plain,
% 0.86/0.84 (^[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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(56,plain,
% 0.86/0.84 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[55])).
% 0.86/0.84 tff(57,plain,
% 0.86/0.84 (![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)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(58,plain,
% 0.86/0.84 (^[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))))),
% 0.86/0.84 inference(bind,[status(th)],[])).
% 0.86/0.84 tff(59,plain,
% 0.86/0.84 (![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)))),
% 0.86/0.84 inference(quant_intro,[status(thm)],[58])).
% 0.86/0.84 tff(60,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')).
% 0.86/0.84 tff(61,plain,
% 0.86/0.84 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.86/0.84 tff(62,plain,
% 0.86/0.84 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.86/0.84 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.86/0.84 tff(63,plain,(
% 0.86/0.84 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.98/0.84 inference(skolemize,[status(sab)],[62])).
% 0.98/0.84 tff(64,plain,
% 0.98/0.84 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.98/0.84 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.98/0.84 tff(65,plain,
% 0.98/0.84 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.98/0.84 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.98/0.84 tff(66,plain,
% 0.98/0.84 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(powerset(A!11), finite_subsets(A!11))) | ![C: $i] : ((~in(C, powerset(A!11))) | in(C, finite_subsets(A!11))))) | (~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))))))),
% 0.98/0.84 inference(quant_inst,[status(thm)],[])).
% 0.98/0.84 tff(67,plain,
% 0.98/0.84 (~((~((~subset(powerset(A!11), finite_subsets(A!11))) | ![C: $i] : ((~in(C, powerset(A!11))) | in(C, finite_subsets(A!11))))) | (~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))))))),
% 0.98/0.84 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.98/0.84 tff(68,plain,
% 0.98/0.84 (((~((~subset(powerset(A!11), finite_subsets(A!11))) | ![C: $i] : ((~in(C, powerset(A!11))) | in(C, finite_subsets(A!11))))) | (~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))))) | (subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))))),
% 0.98/0.84 inference(tautology,[status(thm)],[])).
% 0.98/0.84 tff(69,plain,
% 0.98/0.84 (subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))),
% 0.98/0.84 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.98/0.84 tff(70,plain,
% 0.98/0.84 (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.98/0.84 inference(bind,[status(th)],[])).
% 0.98/0.84 tff(71,plain,
% 0.98/0.84 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.98/0.84 inference(quant_intro,[status(thm)],[70])).
% 0.98/0.84 tff(72,plain,
% 0.98/0.84 (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.98/0.84 inference(bind,[status(th)],[])).
% 0.98/0.84 tff(73,plain,
% 0.98/0.84 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.98/0.84 inference(quant_intro,[status(thm)],[72])).
% 0.98/0.84 tff(74,plain,
% 0.98/0.84 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.98/0.84 inference(rewrite,[status(thm)],[])).
% 0.98/0.84 tff(75,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.98/0.84 tff(76,plain,
% 0.98/0.84 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.98/0.84 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.98/0.84 tff(77,plain,(
% 0.98/0.84 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.98/0.84 inference(skolemize,[status(sab)],[76])).
% 0.98/0.84 tff(78,plain,
% 0.98/0.84 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.98/0.84 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.98/0.84 tff(79,plain,
% 0.98/0.84 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.98/0.85 tff(80,plain,
% 0.98/0.85 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((finite_subsets(A!11) = powerset(A!11)) <=> (~((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(81,plain,
% 0.98/0.85 ((finite_subsets(A!11) = powerset(A!11)) <=> (~((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.98/0.85 tff(82,plain,
% 0.98/0.85 ((~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))) <=> (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(83,plain,
% 0.98/0.85 ((~![A: $i] : (finite(A) => (finite_subsets(A) = powerset(A)))) <=> (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(84,axiom,(~![A: $i] : (finite(A) => (finite_subsets(A) = powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t27_finsub_1')).
% 0.98/0.85 tff(85,plain,
% 0.98/0.85 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.98/0.85 tff(86,plain,
% 0.98/0.85 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.98/0.85 tff(87,plain,
% 0.98/0.85 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.98/0.85 tff(88,plain,
% 0.98/0.85 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[87, 82])).
% 0.98/0.85 tff(89,plain,
% 0.98/0.85 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[88, 82])).
% 0.98/0.85 tff(90,plain,
% 0.98/0.85 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.98/0.85 tff(91,plain,
% 0.98/0.85 (~![A: $i] : ((~finite(A)) | (finite_subsets(A) = powerset(A)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[90, 82])).
% 0.98/0.85 tff(92,plain,(
% 0.98/0.85 ~((~finite(A!11)) | (finite_subsets(A!11) = powerset(A!11)))),
% 0.98/0.85 inference(skolemize,[status(sab)],[91])).
% 0.98/0.85 tff(93,plain,
% 0.98/0.85 (~(finite_subsets(A!11) = powerset(A!11))),
% 0.98/0.85 inference(or_elim,[status(thm)],[92])).
% 0.98/0.85 tff(94,plain,
% 0.98/0.85 ((~((finite_subsets(A!11) = powerset(A!11)) <=> (~((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))))) | (finite_subsets(A!11) = powerset(A!11)) | ((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))),
% 0.98/0.85 inference(tautology,[status(thm)],[])).
% 0.98/0.85 tff(95,plain,
% 0.98/0.85 ((~((finite_subsets(A!11) = powerset(A!11)) <=> (~((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))))) | ((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.98/0.85 tff(96,plain,
% 0.98/0.85 ((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[95, 81])).
% 0.98/0.85 tff(97,plain,
% 0.98/0.85 (^[A: $i] : refl(subset(finite_subsets(A), powerset(A)) <=> subset(finite_subsets(A), powerset(A)))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(98,plain,
% 0.98/0.85 (![A: $i] : subset(finite_subsets(A), powerset(A)) <=> ![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[97])).
% 0.98/0.85 tff(99,plain,
% 0.98/0.85 (![A: $i] : subset(finite_subsets(A), powerset(A)) <=> ![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(100,axiom,(![A: $i] : subset(finite_subsets(A), powerset(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_finsub_1')).
% 0.98/0.85 tff(101,plain,
% 0.98/0.85 (![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.98/0.85 tff(102,plain,(
% 0.98/0.85 ![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.98/0.85 inference(skolemize,[status(sab)],[101])).
% 0.98/0.85 tff(103,plain,
% 0.98/0.85 (![A: $i] : subset(finite_subsets(A), powerset(A))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.98/0.85 tff(104,plain,
% 0.98/0.85 ((~![A: $i] : subset(finite_subsets(A), powerset(A))) | subset(finite_subsets(A!11), powerset(A!11))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(105,plain,
% 0.98/0.85 (subset(finite_subsets(A!11), powerset(A!11))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.98/0.85 tff(106,plain,
% 0.98/0.85 ((~((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))) | (~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11)))),
% 0.98/0.85 inference(tautology,[status(thm)],[])).
% 0.98/0.85 tff(107,plain,
% 0.98/0.85 ((~((~subset(finite_subsets(A!11), powerset(A!11))) | (~subset(powerset(A!11), finite_subsets(A!11))))) | (~subset(powerset(A!11), finite_subsets(A!11)))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.98/0.85 tff(108,plain,
% 0.98/0.85 (~subset(powerset(A!11), finite_subsets(A!11))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[107, 96])).
% 0.98/0.85 tff(109,plain,
% 0.98/0.85 ((~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))))) | subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))),
% 0.98/0.85 inference(tautology,[status(thm)],[])).
% 0.98/0.85 tff(110,plain,
% 0.98/0.85 ((~(subset(powerset(A!11), finite_subsets(A!11)) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))))) | (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.98/0.85 tff(111,plain,
% 0.98/0.85 (~((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[110, 69])).
% 0.98/0.85 tff(112,plain,
% 0.98/0.85 (((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))) | (~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)))),
% 0.98/0.85 inference(tautology,[status(thm)],[])).
% 0.98/0.85 tff(113,plain,
% 0.98/0.85 (~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.98/0.85 tff(114,plain,
% 0.98/0.85 ((~(in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)))))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)) | ((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)))),
% 0.98/0.85 inference(tautology,[status(thm)],[])).
% 0.98/0.85 tff(115,plain,
% 0.98/0.85 ((~(in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)))))) | ((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.98/0.85 tff(116,plain,
% 0.98/0.85 ((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[115, 49])).
% 0.98/0.85 tff(117,plain,
% 0.98/0.85 (((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), finite_subsets(A!11))) | in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))),
% 0.98/0.85 inference(tautology,[status(thm)],[])).
% 0.98/0.85 tff(118,plain,
% 0.98/0.85 (in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[117, 111])).
% 0.98/0.85 tff(119,plain,
% 0.98/0.85 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(120,plain,
% 0.98/0.85 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[119])).
% 0.98/0.85 tff(121,plain,
% 0.98/0.85 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(122,plain,
% 0.98/0.85 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(123,plain,
% 0.98/0.85 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[122])).
% 0.98/0.85 tff(124,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.98/0.85 tff(125,plain,
% 0.98/0.85 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.98/0.85 tff(126,plain,
% 0.98/0.85 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.98/0.85 tff(127,plain,(
% 0.98/0.85 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.98/0.85 inference(skolemize,[status(sab)],[126])).
% 0.98/0.85 tff(128,plain,
% 0.98/0.85 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.98/0.85 tff(129,plain,
% 0.98/0.85 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(130,plain,
% 0.98/0.85 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(131,plain,
% 0.98/0.85 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.98/0.85 tff(132,plain,
% 0.98/0.85 (element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[131, 128, 118])).
% 0.98/0.85 tff(133,plain,
% 0.98/0.85 (finite(A!11)),
% 0.98/0.85 inference(or_elim,[status(thm)],[92])).
% 0.98/0.85 tff(134,plain,
% 0.98/0.85 (^[A: $i] : refl(((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(135,plain,
% 0.98/0.85 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[134])).
% 0.98/0.85 tff(136,plain,
% 0.98/0.85 (^[A: $i] : rewrite(((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(137,plain,
% 0.98/0.85 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[136])).
% 0.98/0.85 tff(138,plain,
% 0.98/0.85 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(transitivity,[status(thm)],[137, 135])).
% 0.98/0.85 tff(139,plain,
% 0.98/0.85 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(140,plain,
% 0.98/0.85 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(A)) => finite(B)) <=> (finite(B) | (~element(B, powerset(A)))))), (![B: $i] : (element(B, powerset(A)) => finite(B)) <=> ![B: $i] : (finite(B) | (~element(B, powerset(A)))))), ((finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> (finite(A) => ![B: $i] : (finite(B) | (~element(B, powerset(A))))))), rewrite((finite(A) => ![B: $i] : (finite(B) | (~element(B, powerset(A))))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))), ((finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))))),
% 0.98/0.85 inference(bind,[status(th)],[])).
% 0.98/0.85 tff(141,plain,
% 0.98/0.85 (![A: $i] : (finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B))) <=> ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(quant_intro,[status(thm)],[140])).
% 0.98/0.85 tff(142,axiom,(![A: $i] : (finite(A) => ![B: $i] : (element(B, powerset(A)) => finite(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc2_finset_1')).
% 0.98/0.85 tff(143,plain,
% 0.98/0.85 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.98/0.85 tff(144,plain,
% 0.98/0.85 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.98/0.85 tff(145,plain,(
% 0.98/0.85 ![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(skolemize,[status(sab)],[144])).
% 0.98/0.85 tff(146,plain,
% 0.98/0.85 (![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.98/0.85 tff(147,plain,
% 0.98/0.85 (((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | ((~finite(A!11)) | ![B: $i] : (finite(B) | (~element(B, powerset(A!11)))))) <=> ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | (~finite(A!11)) | ![B: $i] : (finite(B) | (~element(B, powerset(A!11)))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(148,plain,
% 0.98/0.85 ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | ((~finite(A!11)) | ![B: $i] : (finite(B) | (~element(B, powerset(A!11)))))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(149,plain,
% 0.98/0.85 ((~![A: $i] : ((~finite(A)) | ![B: $i] : (finite(B) | (~element(B, powerset(A)))))) | (~finite(A!11)) | ![B: $i] : (finite(B) | (~element(B, powerset(A!11))))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.98/0.85 tff(150,plain,
% 0.98/0.85 (![B: $i] : (finite(B) | (~element(B, powerset(A!11))))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[149, 146, 133])).
% 0.98/0.85 tff(151,plain,
% 0.98/0.85 (((~![B: $i] : (finite(B) | (~element(B, powerset(A!11))))) | (finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))))) <=> ((~![B: $i] : (finite(B) | (~element(B, powerset(A!11))))) | finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))))),
% 0.98/0.85 inference(rewrite,[status(thm)],[])).
% 0.98/0.85 tff(152,plain,
% 0.98/0.85 ((~![B: $i] : (finite(B) | (~element(B, powerset(A!11))))) | (finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))))),
% 0.98/0.85 inference(quant_inst,[status(thm)],[])).
% 0.98/0.85 tff(153,plain,
% 0.98/0.85 ((~![B: $i] : (finite(B) | (~element(B, powerset(A!11))))) | finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)))),
% 0.98/0.85 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.98/0.85 tff(154,plain,
% 0.98/0.85 (finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[153, 150, 132])).
% 0.98/0.85 tff(155,plain,
% 0.98/0.85 ((~((~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)))) | (~finite(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)))) | (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))),
% 0.98/0.85 inference(tautology,[status(thm)],[])).
% 0.98/0.85 tff(156,plain,
% 0.98/0.85 (~subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[155, 154, 116])).
% 0.98/0.85 tff(157,plain,
% 0.98/0.85 ((~(element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) | (~element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11))) | subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)),
% 0.98/0.85 inference(tautology,[status(thm)],[])).
% 0.98/0.85 tff(158,plain,
% 0.98/0.85 ((~(element(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), powerset(A!11)) <=> subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11))) | subset(tptp_fun_C_0(finite_subsets(A!11), powerset(A!11)), A!11)),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[157, 132])).
% 0.98/0.85 tff(159,plain,
% 0.98/0.85 ($false),
% 0.98/0.85 inference(unit_resolution,[status(thm)],[158, 156, 9])).
% 0.98/0.85 % SZS output end Proof
%------------------------------------------------------------------------------