TSTP Solution File: SEU110+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU110+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 07:27:31 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU110+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 09:30:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 tff(subset_type, type, (
% 0.21/0.46 subset: ( $i * $i ) > $o)).
% 0.21/0.46 tff(tptp_fun_B_11_type, type, (
% 0.21/0.46 tptp_fun_B_11: $i)).
% 0.21/0.46 tff(tptp_fun_C_0_type, type, (
% 0.21/0.46 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.46 tff(finite_subsets_type, type, (
% 0.21/0.46 finite_subsets: $i > $i)).
% 0.21/0.46 tff(tptp_fun_A_12_type, type, (
% 0.21/0.46 tptp_fun_A_12: $i)).
% 0.21/0.46 tff(finite_type, type, (
% 0.21/0.46 finite: $i > $o)).
% 0.21/0.46 tff(in_type, type, (
% 0.21/0.46 in: ( $i * $i ) > $o)).
% 0.21/0.46 tff(preboolean_type, type, (
% 0.21/0.46 preboolean: $i > $o)).
% 0.21/0.46 tff(tptp_fun_C_1_type, type, (
% 0.21/0.46 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.21/0.46 tff(element_type, type, (
% 0.21/0.46 element: ( $i * $i ) > $o)).
% 0.21/0.46 tff(1,plain,
% 0.21/0.46 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(2,plain,
% 0.21/0.46 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.46 tff(3,plain,
% 0.21/0.46 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(4,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 (![A: $i] : preboolean(finite_subsets(A))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.46 tff(6,plain,(
% 0.21/0.46 ![A: $i] : preboolean(finite_subsets(A))),
% 0.21/0.46 inference(skolemize,[status(sab)],[5])).
% 0.21/0.46 tff(7,plain,
% 0.21/0.46 (![A: $i] : preboolean(finite_subsets(A))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.46 tff(8,plain,
% 0.21/0.46 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(B!11))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 (preboolean(finite_subsets(B!11))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 (^[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)))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(11,plain,
% 0.21/0.46 (![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))))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.46 tff(12,plain,
% 0.21/0.46 (^[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)))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(13,plain,
% 0.21/0.46 (![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))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (^[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)))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[15, 13])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (^[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)))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (^[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))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (![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)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 (![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)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (^[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)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (![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)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.47 tff(24,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')).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.47 tff(27,plain,(
% 0.21/0.47 ![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))))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[26])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (![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)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (![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))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (((~![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(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!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(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (((~preboolean(finite_subsets(B!11))) | (~((~((finite_subsets(B!11) = finite_subsets(B!11)) | (in(tptp_fun_C_1(finite_subsets(B!11), B!11), finite_subsets(B!11)) <=> ((~subset(tptp_fun_C_1(finite_subsets(B!11), B!11), B!11)) | (~finite(tptp_fun_C_1(finite_subsets(B!11), B!11))))))) | (~((~(finite_subsets(B!11) = finite_subsets(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11)))))))))) <=> ((~preboolean(finite_subsets(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (((~![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(B!11))) | (~((~((finite_subsets(B!11) = finite_subsets(B!11)) | (in(tptp_fun_C_1(finite_subsets(B!11), B!11), finite_subsets(B!11)) <=> ((~subset(tptp_fun_C_1(finite_subsets(B!11), B!11), B!11)) | (~finite(tptp_fun_C_1(finite_subsets(B!11), B!11))))))) | (~((~(finite_subsets(B!11) = finite_subsets(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!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(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11)))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (((~![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(B!11))) | (~((~((finite_subsets(B!11) = finite_subsets(B!11)) | (in(tptp_fun_C_1(finite_subsets(B!11), B!11), finite_subsets(B!11)) <=> ((~subset(tptp_fun_C_1(finite_subsets(B!11), B!11), B!11)) | (~finite(tptp_fun_C_1(finite_subsets(B!11), B!11))))))) | (~((~(finite_subsets(B!11) = finite_subsets(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!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(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 ((~![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(B!11))) | (~((~((finite_subsets(B!11) = finite_subsets(B!11)) | (in(tptp_fun_C_1(finite_subsets(B!11), B!11), finite_subsets(B!11)) <=> ((~subset(tptp_fun_C_1(finite_subsets(B!11), B!11), B!11)) | (~finite(tptp_fun_C_1(finite_subsets(B!11), B!11))))))) | (~((~(finite_subsets(B!11) = finite_subsets(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11))))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 ((~![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(B!11))) | ![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[37, 31, 9])).
% 0.21/0.47 tff(39,plain,
% 0.21/0.47 ((~![C: $i] : (in(C, finite_subsets(B!11)) <=> (~((~finite(C)) | (~subset(C, B!11)))))) | (in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (^[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))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (![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)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 (^[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))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 (![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)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 (![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)))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[44, 42])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (^[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)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 (![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)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.47 tff(51,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')).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.47 tff(54,plain,(
% 0.21/0.47 ![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)))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[53])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (![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)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 (![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)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 ((~![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(finite_subsets(A!12), finite_subsets(B!11))) | ![C: $i] : ((~in(C, finite_subsets(A!12))) | in(C, finite_subsets(B!11))))) | (~(subset(finite_subsets(A!12), finite_subsets(B!11)) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 (~((~((~subset(finite_subsets(A!12), finite_subsets(B!11))) | ![C: $i] : ((~in(C, finite_subsets(A!12))) | in(C, finite_subsets(B!11))))) | (~(subset(finite_subsets(A!12), finite_subsets(B!11)) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 (((~((~subset(finite_subsets(A!12), finite_subsets(B!11))) | ![C: $i] : ((~in(C, finite_subsets(A!12))) | in(C, finite_subsets(B!11))))) | (~(subset(finite_subsets(A!12), finite_subsets(B!11)) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))))))) | (subset(finite_subsets(A!12), finite_subsets(B!11)) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 (subset(finite_subsets(A!12), finite_subsets(B!11)) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.47 tff(61,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(62,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : (subset(A, B) => subset(finite_subsets(A), finite_subsets(B)))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(63,axiom,(~![A: $i, B: $i] : (subset(A, B) => subset(finite_subsets(A), finite_subsets(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_finsub_1')).
% 0.21/0.47 tff(64,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.47 tff(65,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.21/0.47 tff(66,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[66, 61])).
% 0.21/0.47 tff(68,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[67, 61])).
% 0.21/0.47 tff(69,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[69, 61])).
% 0.21/0.47 tff(71,plain,(
% 0.21/0.47 ~((~subset(A!12, B!11)) | subset(finite_subsets(A!12), finite_subsets(B!11)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[70])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 (~subset(finite_subsets(A!12), finite_subsets(B!11))),
% 0.21/0.47 inference(or_elim,[status(thm)],[71])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 ((~(subset(finite_subsets(A!12), finite_subsets(B!11)) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)))))) | subset(finite_subsets(A!12), finite_subsets(B!11)) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 ((~(subset(finite_subsets(A!12), finite_subsets(B!11)) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)))))) | (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 (~((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[74, 60])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 (((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))) | (~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(77,plain,
% 0.21/0.47 (~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 ((~(in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)))))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)) | ((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(79,plain,
% 0.21/0.47 ((~(in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)))))) | ((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.47 tff(80,plain,
% 0.21/0.47 ((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[79, 40])).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 (((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))) | in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 (in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.47 tff(88,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.47 tff(90,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.47 tff(91,plain,(
% 0.21/0.47 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.47 inference(skolemize,[status(sab)],[90])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.21/0.47 tff(93,plain,
% 0.21/0.47 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 (element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[95, 92, 82])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (^[A: $i, B: $i] : refl((finite(B) | (~element(B, finite_subsets(A)))) <=> (finite(B) | (~element(B, finite_subsets(A)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A)))) <=> ![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A)))) <=> ![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 (^[A: $i, B: $i] : rewrite((element(B, finite_subsets(A)) => finite(B)) <=> (finite(B) | (~element(B, finite_subsets(A)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 (![A: $i, B: $i] : (element(B, finite_subsets(A)) => finite(B)) <=> ![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.48 tff(102,axiom,(![A: $i, B: $i] : (element(B, finite_subsets(A)) => finite(B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc3_finsub_1')).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.21/0.48 tff(105,plain,(
% 0.21/0.48 ![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[104])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))) | (finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12))) | (~element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))))) <=> ((~![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))) | finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12))) | (~element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))) | (finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12))) | (~element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))) | finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12))) | (~element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 (finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[109, 106, 96])).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 ((~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)))) | (~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 ((~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[112, 80])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!12))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (preboolean(finite_subsets(A!12))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[114, 7])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (((~![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!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12))))))) <=> ((~![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!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 (((~preboolean(finite_subsets(A!12))) | (~((~((finite_subsets(A!12) = finite_subsets(A!12)) | (in(tptp_fun_C_1(finite_subsets(A!12), A!12), finite_subsets(A!12)) <=> ((~subset(tptp_fun_C_1(finite_subsets(A!12), A!12), A!12)) | (~finite(tptp_fun_C_1(finite_subsets(A!12), A!12))))))) | (~((~(finite_subsets(A!12) = finite_subsets(A!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12)))))))))) <=> ((~preboolean(finite_subsets(A!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 (((~![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!12))) | (~((~((finite_subsets(A!12) = finite_subsets(A!12)) | (in(tptp_fun_C_1(finite_subsets(A!12), A!12), finite_subsets(A!12)) <=> ((~subset(tptp_fun_C_1(finite_subsets(A!12), A!12), A!12)) | (~finite(tptp_fun_C_1(finite_subsets(A!12), A!12))))))) | (~((~(finite_subsets(A!12) = finite_subsets(A!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12))))))))))) <=> ((~![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!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12)))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (((~![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!12))) | (~((~((finite_subsets(A!12) = finite_subsets(A!12)) | (in(tptp_fun_C_1(finite_subsets(A!12), A!12), finite_subsets(A!12)) <=> ((~subset(tptp_fun_C_1(finite_subsets(A!12), A!12), A!12)) | (~finite(tptp_fun_C_1(finite_subsets(A!12), A!12))))))) | (~((~(finite_subsets(A!12) = finite_subsets(A!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12))))))))))) <=> ((~![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!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 ((~![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!12))) | (~((~((finite_subsets(A!12) = finite_subsets(A!12)) | (in(tptp_fun_C_1(finite_subsets(A!12), A!12), finite_subsets(A!12)) <=> ((~subset(tptp_fun_C_1(finite_subsets(A!12), A!12), A!12)) | (~finite(tptp_fun_C_1(finite_subsets(A!12), A!12))))))) | (~((~(finite_subsets(A!12) = finite_subsets(A!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12))))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 ((~![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!12))) | ![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 (![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[121, 31, 115])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 ((~![C: $i] : (in(C, finite_subsets(A!12)) <=> (~((~finite(C)) | (~subset(C, A!12)))))) | (in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 (in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 ((~(in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)))))) | (~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))) | (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 ((~(in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)) <=> (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)))))) | (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[125, 82])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 (~((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[126, 124])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (((~finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12))) | subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 (subset(A!12, B!11)),
% 0.21/0.48 inference(or_elim,[status(thm)],[71])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(B, C)) | (~subset(A, B))))))), rewrite((~(~((~subset(B, C)) | (~subset(A, B))))) <=> ((~subset(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(B, C)) | (~subset(A, B))) | subset(A, C)))), rewrite((((~subset(B, C)) | (~subset(A, B))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.48 tff(137,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.21/0.48 tff(140,plain,(
% 0.21/0.48 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.21/0.48 inference(skolemize,[status(sab)],[139])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)) | subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)) | subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 ((subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11) | (~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12))) <=> ((~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)) | subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11) | (~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)) | subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[144])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11) | (~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)) | subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11))),
% 0.21/0.48 inference(transitivity,[status(thm)],[145, 143])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11) | (~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)) | subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[148, 142, 130, 129, 113])).
% 0.21/0.48 % SZS output end Proof
%------------------------------------------------------------------------------