%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU110+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:26:54 AM UTC 2025
% Result : Theorem 0.22s 0.47s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU110+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 06:04:10 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47 % SZS output start Proof
% 0.22/0.47 tff(subset_type, type, (
% 0.22/0.47 subset: ( $i * $i ) > $o)).
% 0.22/0.47 tff(tptp_fun_B_11_type, type, (
% 0.22/0.47 tptp_fun_B_11: $i)).
% 0.22/0.47 tff(tptp_fun_C_0_type, type, (
% 0.22/0.47 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.22/0.47 tff(finite_subsets_type, type, (
% 0.22/0.47 finite_subsets: $i > $i)).
% 0.22/0.47 tff(tptp_fun_A_12_type, type, (
% 0.22/0.47 tptp_fun_A_12: $i)).
% 0.22/0.47 tff(finite_type, type, (
% 0.22/0.47 finite: $i > $o)).
% 0.22/0.47 tff(in_type, type, (
% 0.22/0.47 in: ( $i * $i ) > $o)).
% 0.22/0.47 tff(preboolean_type, type, (
% 0.22/0.47 preboolean: $i > $o)).
% 0.22/0.47 tff(tptp_fun_C_1_type, type, (
% 0.22/0.47 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.22/0.47 tff(element_type, type, (
% 0.22/0.47 element: ( $i * $i ) > $o)).
% 0.22/0.47 tff(1,plain,
% 0.22/0.47 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(2,plain,
% 0.22/0.47 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.47 tff(3,plain,
% 0.22/0.47 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(4,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.22/0.47 tff(5,plain,
% 0.22/0.47 (![A: $i] : preboolean(finite_subsets(A))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.47 tff(6,plain,(
% 0.22/0.47 ![A: $i] : preboolean(finite_subsets(A))),
% 0.22/0.47 inference(skolemize,[status(sab)],[5])).
% 0.22/0.47 tff(7,plain,
% 0.22/0.47 (![A: $i] : preboolean(finite_subsets(A))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.47 tff(8,plain,
% 0.22/0.47 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(B!11))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(9,plain,
% 0.22/0.47 (preboolean(finite_subsets(B!11))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.47 tff(10,plain,
% 0.22/0.47 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B)))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(11,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.47 tff(12,plain,
% 0.22/0.47 (^[A: $i, B: $i] : refl(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(13,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.47 tff(14,plain,
% 0.22/0.47 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(15,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.22/0.47 tff(16,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[15, 13])).
% 0.22/0.47 tff(17,plain,
% 0.22/0.47 (^[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] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(18,plain,
% 0.22/0.47 (![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] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[17])).
% 0.22/0.47 tff(19,plain,
% 0.22/0.47 (![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)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(20,plain,
% 0.22/0.47 (^[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)))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(21,plain,
% 0.22/0.47 (![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)))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.47 tff(22,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')).
% 0.22/0.47 tff(23,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.22/0.47 tff(24,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.22/0.47 tff(25,plain,(
% 0.22/0.47 ![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))))))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[24])).
% 0.22/0.47 tff(26,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.22/0.47 tff(27,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.22/0.47 tff(28,plain,
% 0.22/0.47 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[27, 11])).
% 0.22/0.47 tff(29,plain,
% 0.22/0.47 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11)))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(30,plain,
% 0.22/0.47 (((~preboolean(finite_subsets(B!11))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_1(finite_subsets(B!11), B!11), finite_subsets(B!11))))) | (~((~(finite_subsets(B!11) = finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11))))))))) <=> ((~preboolean(finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(31,plain,
% 0.22/0.47 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(B!11))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_1(finite_subsets(B!11), B!11), finite_subsets(B!11))))) | (~((~(finite_subsets(B!11) = finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11)))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[30])).
% 0.22/0.47 tff(32,plain,
% 0.22/0.47 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(B!11))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_1(finite_subsets(B!11), B!11), finite_subsets(B!11))))) | (~((~(finite_subsets(B!11) = finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11)))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11)))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[31, 29])).
% 0.22/0.47 tff(33,plain,
% 0.22/0.47 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(B!11))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_1(finite_subsets(B!11), B!11), finite_subsets(B!11))))) | (~((~(finite_subsets(B!11) = finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11)))))))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(34,plain,
% 0.22/0.47 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(B!11))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.47 tff(35,plain,
% 0.22/0.47 (![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, finite_subsets(B!11))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[34, 28, 9])).
% 0.22/0.47 tff(36,plain,
% 0.22/0.47 ((~![C: $i] : (~(((~finite(C)) | (~subset(C, B!11))) <=> in(C, 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))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(37,plain,
% 0.22/0.48 (~(((~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))) <=> in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.22/0.48 tff(38,plain,
% 0.22/0.48 (^[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))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(39,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.48 tff(40,plain,
% 0.22/0.48 (^[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))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(41,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.48 tff(42,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[41, 39])).
% 0.22/0.48 tff(43,plain,
% 0.22/0.48 (^[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)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(44,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.48 tff(45,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(46,plain,
% 0.22/0.48 (^[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))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(47,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.48 tff(48,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')).
% 0.22/0.48 tff(49,plain,
% 0.22/0.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.22/0.48 tff(50,plain,
% 0.22/0.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.22/0.48 tff(51,plain,(
% 0.22/0.48 ![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)))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[50])).
% 0.22/0.48 tff(52,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.22/0.48 tff(53,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.22/0.48 tff(54,plain,
% 0.22/0.48 ((~![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))))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(55,plain,
% 0.22/0.48 (~((~((~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)))))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.22/0.48 tff(56,plain,
% 0.22/0.48 (((~((~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)))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(57,plain,
% 0.22/0.48 (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))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.22/0.48 tff(58,plain,
% 0.22/0.48 ((~![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))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(59,plain,
% 0.22/0.48 ((~![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))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(60,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')).
% 0.22/0.48 tff(61,plain,
% 0.22/0.48 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.48 tff(62,plain,
% 0.22/0.48 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.22/0.48 tff(63,plain,
% 0.22/0.48 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.22/0.48 tff(64,plain,
% 0.22/0.48 (~![A: $i, B: $i] : ((~subset(A, B)) | subset(finite_subsets(A), finite_subsets(B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.22/0.48 tff(65,plain,(
% 0.22/0.48 ~((~subset(A!12, B!11)) | subset(finite_subsets(A!12), finite_subsets(B!11)))),
% 0.22/0.48 inference(skolemize,[status(sab)],[64])).
% 0.22/0.48 tff(66,plain,
% 0.22/0.48 (~subset(finite_subsets(A!12), finite_subsets(B!11))),
% 0.22/0.48 inference(or_elim,[status(thm)],[65])).
% 0.22/0.48 tff(67,plain,
% 0.22/0.48 ((~(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))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(68,plain,
% 0.22/0.48 ((~(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))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.22/0.48 tff(69,plain,
% 0.22/0.48 (~((~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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[68, 57])).
% 0.22/0.48 tff(70,plain,
% 0.22/0.48 (((~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)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(71,plain,
% 0.22/0.48 (~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(B!11))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.22/0.48 tff(72,plain,
% 0.22/0.48 ((((~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))) <=> 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))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(73,plain,
% 0.22/0.48 ((((~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))) <=> 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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.22/0.48 tff(74,plain,
% 0.22/0.48 ((~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))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[73, 37])).
% 0.22/0.48 tff(75,plain,
% 0.22/0.48 (((~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))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(76,plain,
% 0.22/0.48 (in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[75, 69])).
% 0.22/0.48 tff(77,plain,
% 0.22/0.48 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(78,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[77])).
% 0.22/0.48 tff(79,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(80,plain,
% 0.22/0.48 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(81,plain,
% 0.22/0.48 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[80])).
% 0.22/0.48 tff(82,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.22/0.48 tff(83,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.22/0.48 tff(84,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.22/0.48 tff(85,plain,(
% 0.22/0.48 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.22/0.48 inference(skolemize,[status(sab)],[84])).
% 0.22/0.48 tff(86,plain,
% 0.22/0.48 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.22/0.48 tff(87,plain,
% 0.22/0.48 (((~![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)))) <=> ((~![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)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(88,plain,
% 0.22/0.48 ((~![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)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(89,plain,
% 0.22/0.48 ((~![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))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.22/0.48 tff(90,plain,
% 0.22/0.48 (element(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[89, 86, 76])).
% 0.22/0.48 tff(91,plain,
% 0.22/0.48 (^[A: $i, B: $i] : refl((finite(B) | (~element(B, finite_subsets(A)))) <=> (finite(B) | (~element(B, finite_subsets(A)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(92,plain,
% 0.22/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A)))) <=> ![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[91])).
% 0.22/0.48 tff(93,plain,
% 0.22/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A)))) <=> ![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(94,plain,
% 0.22/0.48 (^[A: $i, B: $i] : rewrite((element(B, finite_subsets(A)) => finite(B)) <=> (finite(B) | (~element(B, finite_subsets(A)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(95,plain,
% 0.22/0.48 (![A: $i, B: $i] : (element(B, finite_subsets(A)) => finite(B)) <=> ![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[94])).
% 0.22/0.48 tff(96,axiom,(![A: $i, B: $i] : (element(B, finite_subsets(A)) => finite(B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc3_finsub_1')).
% 0.22/0.48 tff(97,plain,
% 0.22/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.22/0.48 tff(98,plain,
% 0.22/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.22/0.48 tff(99,plain,(
% 0.22/0.48 ![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[98])).
% 0.22/0.48 tff(100,plain,
% 0.22/0.48 (![A: $i, B: $i] : (finite(B) | (~element(B, finite_subsets(A))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.22/0.48 tff(101,plain,
% 0.22/0.48 (((~![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))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(102,plain,
% 0.22/0.48 ((~![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))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(103,plain,
% 0.22/0.48 ((~![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)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.22/0.48 tff(104,plain,
% 0.22/0.48 (finite(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[103, 100, 90])).
% 0.22/0.48 tff(105,plain,
% 0.22/0.48 ((~((~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))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(106,plain,
% 0.22/0.48 ((~((~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))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.22/0.48 tff(107,plain,
% 0.22/0.48 (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[106, 74])).
% 0.22/0.48 tff(108,plain,
% 0.22/0.48 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!12))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(109,plain,
% 0.22/0.48 (preboolean(finite_subsets(A!12))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[108, 7])).
% 0.22/0.48 tff(110,plain,
% 0.22/0.48 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12)))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(111,plain,
% 0.22/0.48 (((~preboolean(finite_subsets(A!12))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_1(finite_subsets(A!12), A!12), finite_subsets(A!12))))) | (~((~(finite_subsets(A!12) = finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12))))))))) <=> ((~preboolean(finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(112,plain,
% 0.22/0.49 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!12))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_1(finite_subsets(A!12), A!12), finite_subsets(A!12))))) | (~((~(finite_subsets(A!12) = finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12)))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12))))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[111])).
% 0.22/0.49 tff(113,plain,
% 0.22/0.49 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!12))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_1(finite_subsets(A!12), A!12), finite_subsets(A!12))))) | (~((~(finite_subsets(A!12) = finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12)))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12)))))),
% 0.22/0.49 inference(transitivity,[status(thm)],[112, 110])).
% 0.22/0.49 tff(114,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!12))) | (~((~((finite_subsets(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)))) <=> in(tptp_fun_C_1(finite_subsets(A!12), A!12), finite_subsets(A!12))))) | (~((~(finite_subsets(A!12) = finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12)))))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(115,plain,
% 0.22/0.49 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_1(B, A), A)) | (~finite(tptp_fun_C_1(B, A)))) <=> in(tptp_fun_C_1(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!12))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.22/0.49 tff(116,plain,
% 0.22/0.49 (![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, finite_subsets(A!12))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[115, 28, 109])).
% 0.22/0.49 tff(117,plain,
% 0.22/0.49 ((~![C: $i] : (~(((~finite(C)) | (~subset(C, A!12))) <=> in(C, 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))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(118,plain,
% 0.22/0.49 (~(((~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)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.22/0.49 tff(119,plain,
% 0.22/0.49 ((((~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)))) | (~in(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), finite_subsets(A!12)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(120,plain,
% 0.22/0.49 ((((~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))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[119, 76])).
% 0.22/0.49 tff(121,plain,
% 0.22/0.49 (~((~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)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[120, 118])).
% 0.22/0.49 tff(122,plain,
% 0.22/0.49 (((~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)),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(123,plain,
% 0.22/0.49 (subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.22/0.49 tff(124,plain,
% 0.22/0.49 (subset(A!12, B!11)),
% 0.22/0.49 inference(or_elim,[status(thm)],[65])).
% 0.22/0.49 tff(125,plain,
% 0.22/0.49 (![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)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(126,plain,
% 0.22/0.49 (^[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)))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(127,plain,
% 0.22/0.49 (![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)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[126])).
% 0.22/0.49 tff(128,plain,
% 0.22/0.49 (![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))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(129,plain,
% 0.22/0.49 (^[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)))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(130,plain,
% 0.22/0.49 (![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))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[129])).
% 0.22/0.49 tff(131,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')).
% 0.22/0.49 tff(132,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.22/0.49 tff(133,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.22/0.49 tff(134,plain,(
% 0.22/0.49 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.22/0.49 inference(skolemize,[status(sab)],[133])).
% 0.22/0.49 tff(135,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.22/0.49 tff(136,plain,
% 0.22/0.49 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.22/0.49 tff(137,plain,
% 0.22/0.49 (((~![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))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(138,plain,
% 0.22/0.49 ((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))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(139,plain,
% 0.22/0.49 (((~![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)))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[138])).
% 0.22/0.49 tff(140,plain,
% 0.22/0.49 (((~![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))),
% 0.22/0.49 inference(transitivity,[status(thm)],[139, 137])).
% 0.22/0.49 tff(141,plain,
% 0.22/0.49 ((~![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)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(142,plain,
% 0.22/0.49 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!12, B!11)) | (~subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), A!12)) | subset(tptp_fun_C_0(finite_subsets(B!11), finite_subsets(A!12)), B!11)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.22/0.49 tff(143,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[142, 136, 124, 123, 107])).
% 0.22/0.49 % SZS output end Proof
% 0.22/0.49 % E exiting
%------------------------------------------------------------------------------