%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU425+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:27:54 AM UTC 2025
% Result : Theorem 2.44s 2.63s
% Output : Proof 2.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SEU425+1 : TPTP v9.0.0. Released v3.4.0.
% 0.09/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 07:13:50 EDT 2025
% 0.13/0.33 % CPUTime :
% 2.44/2.63 % SZS status Theorem
% 2.44/2.63 % SZS output start Proof
% 2.44/2.63 tff(v1_xboole_0_type, type, (
% 2.44/2.63 v1_xboole_0: $i > $o)).
% 2.44/2.63 tff(k1_zfmisc_1_type, type, (
% 2.44/2.63 k1_zfmisc_1: $i > $i)).
% 2.44/2.63 tff(k2_relat_1_type, type, (
% 2.44/2.63 k2_relat_1: $i > $i)).
% 2.44/2.63 tff(tptp_fun_C_0_type, type, (
% 2.44/2.63 tptp_fun_C_0: $i)).
% 2.44/2.63 tff(k1_xboole_0_type, type, (
% 2.44/2.63 k1_xboole_0: $i)).
% 2.44/2.63 tff(tptp_fun_A_2_type, type, (
% 2.44/2.63 tptp_fun_A_2: $i)).
% 2.44/2.63 tff(k4_relset_1_type, type, (
% 2.44/2.63 k4_relset_1: ( $i * $i * $i ) > $i)).
% 2.44/2.63 tff(k5_relset_2_type, type, (
% 2.44/2.63 k5_relset_2: ( $i * $i ) > $i)).
% 2.44/2.63 tff(v1_funct_2_type, type, (
% 2.44/2.63 v1_funct_2: ( $i * $i * $i ) > $o)).
% 2.44/2.63 tff(m2_relset_1_type, type, (
% 2.44/2.63 m2_relset_1: ( $i * $i * $i ) > $o)).
% 2.44/2.63 tff(r1_tarski_type, type, (
% 2.44/2.63 r1_tarski: ( $i * $i ) > $o)).
% 2.44/2.63 tff(k1_relat_1_type, type, (
% 2.44/2.63 k1_relat_1: $i > $i)).
% 2.44/2.63 tff(k9_relat_1_type, type, (
% 2.44/2.63 k9_relat_1: ( $i * $i ) > $i)).
% 2.44/2.63 tff(k1_funct_1_type, type, (
% 2.44/2.63 k1_funct_1: ( $i * $i ) > $i)).
% 2.44/2.63 tff(tptp_fun_D_3_type, type, (
% 2.44/2.63 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 2.44/2.63 tff(v1_funct_1_type, type, (
% 2.44/2.63 v1_funct_1: $i > $o)).
% 2.44/2.63 tff(v1_relat_1_type, type, (
% 2.44/2.63 v1_relat_1: $i > $o)).
% 2.44/2.63 tff(m1_subset_1_type, type, (
% 2.44/2.63 m1_subset_1: ( $i * $i ) > $o)).
% 2.44/2.63 tff(k2_zfmisc_1_type, type, (
% 2.44/2.63 k2_zfmisc_1: ( $i * $i ) > $i)).
% 2.44/2.63 tff(tptp_fun_B_1_type, type, (
% 2.44/2.63 tptp_fun_B_1: $i)).
% 2.44/2.63 tff(m1_relset_1_type, type, (
% 2.44/2.63 m1_relset_1: ( $i * $i * $i ) > $o)).
% 2.44/2.63 tff(v3_relat_1_type, type, (
% 2.44/2.63 v3_relat_1: $i > $o)).
% 2.44/2.63 tff(1,plain,
% 2.44/2.63 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))))) <=> ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(2,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[1])).
% 2.44/2.63 tff(3,plain,
% 2.44/2.63 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))) <=> ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(4,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[3])).
% 2.44/2.63 tff(5,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(6,plain,
% 2.44/2.63 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((((B = k1_xboole_0) => (A = k1_xboole_0)) => (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((B = k1_xboole_0) => ((A = k1_xboole_0) | (v1_funct_2(C, A, B) <=> (C = k1_xboole_0))))) <=> (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))), ((m2_relset_1(C, A, B) => ((((B = k1_xboole_0) => (A = k1_xboole_0)) => (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((B = k1_xboole_0) => ((A = k1_xboole_0) | (v1_funct_2(C, A, B) <=> (C = k1_xboole_0)))))) <=> (m2_relset_1(C, A, B) => (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))))), rewrite((m2_relset_1(C, A, B) => (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0))))) <=> ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))), ((m2_relset_1(C, A, B) => ((((B = k1_xboole_0) => (A = k1_xboole_0)) => (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((B = k1_xboole_0) => ((A = k1_xboole_0) | (v1_funct_2(C, A, B) <=> (C = k1_xboole_0)))))) <=> ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(7,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((((B = k1_xboole_0) => (A = k1_xboole_0)) => (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((B = k1_xboole_0) => ((A = k1_xboole_0) | (v1_funct_2(C, A, B) <=> (C = k1_xboole_0)))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[6])).
% 2.44/2.63 tff(8,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((((B = k1_xboole_0) => (A = k1_xboole_0)) => (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((B = k1_xboole_0) => ((A = k1_xboole_0) | (v1_funct_2(C, A, B) <=> (C = k1_xboole_0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_funct_2')).
% 2.44/2.63 tff(9,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[8, 7])).
% 2.44/2.63 tff(10,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[9, 5])).
% 2.44/2.63 tff(11,plain,(
% 2.44/2.63 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C)))) & ((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))),
% 2.44/2.63 inference(skolemize,[status(sab)],[10])).
% 2.44/2.63 tff(12,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11, 4])).
% 2.44/2.63 tff(13,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12, 2])).
% 2.44/2.63 tff(14,plain,
% 2.44/2.63 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(15,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[14])).
% 2.44/2.63 tff(16,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(17,plain,
% 2.44/2.63 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(18,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[17])).
% 2.44/2.63 tff(19,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 2.44/2.63 tff(20,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.44/2.63 tff(21,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[20, 16])).
% 2.44/2.63 tff(22,plain,(
% 2.44/2.63 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.44/2.63 inference(skolemize,[status(sab)],[21])).
% 2.44/2.63 tff(23,plain,
% 2.44/2.63 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[22, 15])).
% 2.44/2.63 tff(24,plain,
% 2.44/2.63 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(25,plain,
% 2.44/2.63 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => ((v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(26,axiom,(~![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => ((v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_relset_2')).
% 2.44/2.63 tff(27,plain,
% 2.44/2.63 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[26, 25])).
% 2.44/2.63 tff(28,plain,
% 2.44/2.63 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[27, 24])).
% 2.44/2.63 tff(29,plain,
% 2.44/2.63 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.44/2.63 tff(30,plain,
% 2.44/2.63 (~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (v1_funct_1(k5_relset_2(A, C)) & v1_funct_2(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C))) & m2_relset_1(k5_relset_2(A, C), k1_zfmisc_1(A), k1_zfmisc_1(k2_relat_1(C)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[29, 24])).
% 2.44/2.63 tff(31,plain,(
% 2.44/2.63 ~((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (v1_funct_1(k5_relset_2(A!2, C!0)) & v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) & m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))))),
% 2.44/2.63 inference(skolemize,[status(sab)],[30])).
% 2.44/2.63 tff(32,plain,
% 2.44/2.63 (m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 2.44/2.63 inference(or_elim,[status(thm)],[31])).
% 2.44/2.63 tff(33,plain,
% 2.44/2.63 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(C!0) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(C!0) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(34,plain,
% 2.44/2.63 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(C!0) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(35,plain,
% 2.44/2.63 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(C!0) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.44/2.63 tff(36,plain,
% 2.44/2.63 (v1_relat_1(C!0)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[35, 32, 23])).
% 2.44/2.63 tff(37,plain,
% 2.44/2.63 (^[A: $i, B: $i] : rewrite(((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(38,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[37])).
% 2.44/2.63 tff(39,plain,
% 2.44/2.63 (^[A: $i, B: $i] : refl(((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(40,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[39])).
% 2.44/2.63 tff(41,plain,
% 2.44/2.63 (^[A: $i, B: $i] : rewrite(((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(42,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[41])).
% 2.44/2.63 tff(43,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[42, 40])).
% 2.44/2.63 tff(44,plain,
% 2.44/2.63 (^[A: $i, B: $i] : rewrite(((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | (((~(C = k5_relset_2(A, B))) | ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))) & ((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(45,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | (((~(C = k5_relset_2(A, B))) | ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))) & ((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[44])).
% 2.44/2.63 tff(46,plain,
% 2.44/2.63 (^[A: $i, B: $i] : rewrite(((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | (((~(C = k5_relset_2(A, B))) | ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))) & ((C = k5_relset_2(A, B)) | ((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | (((~(C = k5_relset_2(A, B))) | ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))) & ((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(47,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | (((~(C = k5_relset_2(A, B))) | ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))) & ((C = k5_relset_2(A, B)) | ((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | (((~(C = k5_relset_2(A, B))) | ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))) & ((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[46])).
% 2.44/2.63 tff(48,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(49,plain,
% 2.44/2.63 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : (r1_tarski(D, A) => (k1_funct_1(C, D) = k9_relat_1(B, D))))) <=> ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))), (((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : (r1_tarski(D, A) => (k1_funct_1(C, D) = k9_relat_1(B, D)))))) <=> ((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))), rewrite(((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))) <=> ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))), (((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : (r1_tarski(D, A) => (k1_funct_1(C, D) = k9_relat_1(B, D)))))) <=> ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))), (![C: $i] : ((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : (r1_tarski(D, A) => (k1_funct_1(C, D) = k9_relat_1(B, D)))))) <=> ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))), ((v1_relat_1(B) => ![C: $i] : ((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : (r1_tarski(D, A) => (k1_funct_1(C, D) = k9_relat_1(B, D))))))) <=> (v1_relat_1(B) => ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))), rewrite((v1_relat_1(B) => ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))), ((v1_relat_1(B) => ![C: $i] : ((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : (r1_tarski(D, A) => (k1_funct_1(C, D) = k9_relat_1(B, D))))))) <=> ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))))),
% 2.44/2.63 inference(bind,[status(th)],[])).
% 2.44/2.63 tff(50,plain,
% 2.44/2.63 (![A: $i, B: $i] : (v1_relat_1(B) => ![C: $i] : ((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : (r1_tarski(D, A) => (k1_funct_1(C, D) = k9_relat_1(B, D))))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))),
% 2.44/2.63 inference(quant_intro,[status(thm)],[49])).
% 2.44/2.63 tff(51,axiom,(![A: $i, B: $i] : (v1_relat_1(B) => ![C: $i] : ((v1_relat_1(C) & v1_funct_1(C)) => ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : (r1_tarski(D, A) => (k1_funct_1(C, D) = k9_relat_1(B, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_relset_2')).
% 2.44/2.63 tff(52,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.44/2.63 tff(53,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | ((C = k5_relset_2(A, B)) <=> ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[52, 48])).
% 2.44/2.63 tff(54,plain,(
% 2.44/2.63 ![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | (((~(C = k5_relset_2(A, B))) | ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))) & ((C = k5_relset_2(A, B)) | ((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))))))),
% 2.44/2.63 inference(skolemize,[status(sab)],[53])).
% 2.44/2.63 tff(55,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~(v1_relat_1(C) & v1_funct_1(C))) | (((~(C = k5_relset_2(A, B))) | ((k1_relat_1(C) = k1_zfmisc_1(A)) & ![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))) & ((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[54, 47])).
% 2.44/2.63 tff(56,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[55, 45])).
% 2.44/2.63 tff(57,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D)))))))) | (~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A)))))))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[56, 43])).
% 2.44/2.63 tff(58,plain,
% 2.44/2.63 (![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[57, 38])).
% 2.44/2.64 tff(59,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))) | ((~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D))))))))))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))) | (~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D))))))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(60,plain,
% 2.44/2.64 (((~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A!2, C!0)) | (~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) <=> ((~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D))))))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(61,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))) | ((~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A!2, C!0)) | (~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D))))))))))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))) | ((~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[60])).
% 2.44/2.64 tff(62,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))) | ((~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A!2, C!0)) | (~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D))))))))))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))) | (~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D))))))))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[61, 59])).
% 2.44/2.64 tff(63,plain,
% 2.44/2.64 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))) | ((~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A!2, C!0)) | (~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D))))))))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(64,plain,
% 2.44/2.64 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((C = k5_relset_2(A, B)) | (~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~((~r1_tarski(tptp_fun_D_3(C, B, A), A)) | (k1_funct_1(C, tptp_fun_D_3(C, B, A)) = k9_relat_1(B, tptp_fun_D_3(C, B, A))))))) | (~((~(C = k5_relset_2(A, B))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A))) | (~![D: $i] : ((~r1_tarski(D, A)) | (k1_funct_1(C, D) = k9_relat_1(B, D))))))))))))) | (~v1_relat_1(C!0)) | ![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.44/2.64 tff(65,plain,
% 2.44/2.64 (![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[64, 58, 36])).
% 2.44/2.64 tff(66,plain,
% 2.44/2.64 (^[A: $i, B: $i] : refl(((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B)))))) <=> ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B)))))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(67,plain,
% 2.44/2.64 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B)))))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[66])).
% 2.44/2.64 tff(68,plain,
% 2.44/2.64 (^[A: $i, B: $i] : rewrite(((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B)))))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(69,plain,
% 2.44/2.64 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[68])).
% 2.44/2.64 tff(70,plain,
% 2.44/2.64 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(71,plain,
% 2.44/2.64 (^[A: $i, B: $i] : rewrite((v1_relat_1(B) => (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(72,plain,
% 2.44/2.64 (![A: $i, B: $i] : (v1_relat_1(B) => (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B)))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[71])).
% 2.44/2.64 tff(73,axiom,(![A: $i, B: $i] : (v1_relat_1(B) => (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_relset_2')).
% 2.44/2.64 tff(74,plain,
% 2.44/2.64 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.44/2.64 tff(75,plain,
% 2.44/2.64 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[74, 70])).
% 2.44/2.64 tff(76,plain,(
% 2.44/2.64 ![A: $i, B: $i] : ((~v1_relat_1(B)) | (v1_relat_1(k5_relset_2(A, B)) & v1_funct_1(k5_relset_2(A, B))))),
% 2.44/2.64 inference(skolemize,[status(sab)],[75])).
% 2.44/2.64 tff(77,plain,
% 2.44/2.64 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[76, 69])).
% 2.44/2.64 tff(78,plain,
% 2.44/2.64 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[77, 67])).
% 2.44/2.64 tff(79,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | ((~v1_relat_1(C!0)) | (~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | (~v1_relat_1(C!0)) | (~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(80,plain,
% 2.44/2.64 (((~v1_relat_1(C!0)) | (~((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0)))))) <=> ((~v1_relat_1(C!0)) | (~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(81,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | ((~v1_relat_1(C!0)) | (~((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | ((~v1_relat_1(C!0)) | (~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0)))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[80])).
% 2.44/2.64 tff(82,plain,
% 2.44/2.64 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | ((~v1_relat_1(C!0)) | (~((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | (~v1_relat_1(C!0)) | (~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[81, 79])).
% 2.44/2.64 tff(83,plain,
% 2.44/2.64 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | ((~v1_relat_1(C!0)) | (~((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(84,plain,
% 2.44/2.64 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (~((~v1_relat_1(k5_relset_2(A, B))) | (~v1_funct_1(k5_relset_2(A, B))))))) | (~v1_relat_1(C!0)) | (~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0)))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.44/2.64 tff(85,plain,
% 2.44/2.64 (~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[84, 78, 36])).
% 2.44/2.64 tff(86,plain,
% 2.44/2.64 (((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0)))) | v1_relat_1(k5_relset_2(A!2, C!0))),
% 2.44/2.64 inference(tautology,[status(thm)],[])).
% 2.44/2.64 tff(87,plain,
% 2.44/2.64 (v1_relat_1(k5_relset_2(A!2, C!0))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[86, 85])).
% 2.44/2.64 tff(88,plain,
% 2.44/2.64 (((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0)))) | v1_funct_1(k5_relset_2(A!2, C!0))),
% 2.44/2.64 inference(tautology,[status(thm)],[])).
% 2.44/2.64 tff(89,plain,
% 2.44/2.64 (v1_funct_1(k5_relset_2(A!2, C!0))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[88, 85])).
% 2.44/2.64 tff(90,plain,
% 2.44/2.64 (((~![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) | ((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(91,plain,
% 2.44/2.64 (((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2)))))) <=> ((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(92,plain,
% 2.44/2.64 ((~((~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2), A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2))))))) | (~((~(k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))))))))) <=> (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(93,plain,
% 2.44/2.64 (((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~((~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2), A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2))))))) | (~((~(k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D))))))))))) <=> ((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[92])).
% 2.44/2.64 tff(94,plain,
% 2.44/2.64 (((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~((~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2), A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2))))))) | (~((~(k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D))))))))))) <=> ((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[93, 91])).
% 2.44/2.64 tff(95,plain,
% 2.44/2.64 (((~![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) | ((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~((~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2), A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2))))))) | (~((~(k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) | ((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2)))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[94])).
% 2.44/2.64 tff(96,plain,
% 2.44/2.64 (((~![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) | ((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~((~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2), A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2))))))) | (~((~(k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))))))))))) <=> ((~![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[95, 90])).
% 2.44/2.64 tff(97,plain,
% 2.44/2.64 ((~![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) | ((~v1_relat_1(k5_relset_2(A!2, C!0))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~((~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2), A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(k5_relset_2(A!2, C!0), C!0, A!2))))))) | (~((~(k5_relset_2(A!2, C!0) = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))))))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(98,plain,
% 2.44/2.64 ((~![C: $i] : ((~v1_relat_1(C)) | (~v1_funct_1(C)) | (~((~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (C = k5_relset_2(A!2, C!0)) | (~((~r1_tarski(tptp_fun_D_3(C, C!0, A!2), A!2)) | (k1_funct_1(C, tptp_fun_D_3(C, C!0, A!2)) = k9_relat_1(C!0, tptp_fun_D_3(C, C!0, A!2))))))) | (~((~(C = k5_relset_2(A!2, C!0))) | (~((~(k1_relat_1(C) = k1_zfmisc_1(A!2))) | (~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(C, D) = k9_relat_1(C!0, D)))))))))))) | (~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2)))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[97, 96])).
% 2.44/2.64 tff(99,plain,
% 2.44/2.64 (~((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[98, 89, 87, 65])).
% 2.44/2.64 tff(100,plain,
% 2.44/2.64 (((~![D: $i] : ((~r1_tarski(D, A!2)) | (k1_funct_1(k5_relset_2(A!2, C!0), D) = k9_relat_1(C!0, D)))) | (~(k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2)))) | (k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2))),
% 2.44/2.64 inference(tautology,[status(thm)],[])).
% 2.44/2.64 tff(101,plain,
% 2.44/2.64 (k1_relat_1(k5_relset_2(A!2, C!0)) = k1_zfmisc_1(A!2)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[100, 99])).
% 2.44/2.64 tff(102,plain,
% 2.44/2.64 (k1_zfmisc_1(A!2) = k1_relat_1(k5_relset_2(A!2, C!0))),
% 2.44/2.64 inference(symmetry,[status(thm)],[101])).
% 2.44/2.64 tff(103,plain,
% 2.44/2.64 (r1_tarski(k1_zfmisc_1(A!2), k1_zfmisc_1(A!2)) <=> r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[102])).
% 2.44/2.64 tff(104,plain,
% 2.44/2.64 (r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2)) <=> r1_tarski(k1_zfmisc_1(A!2), k1_zfmisc_1(A!2))),
% 2.44/2.64 inference(symmetry,[status(thm)],[103])).
% 2.44/2.64 tff(105,plain,
% 2.44/2.64 ((~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))) <=> (~r1_tarski(k1_zfmisc_1(A!2), k1_zfmisc_1(A!2)))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[104])).
% 2.44/2.64 tff(106,assumption,(~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))), introduced(assumption)).
% 2.44/2.64 tff(107,plain,
% 2.44/2.64 (~r1_tarski(k1_zfmisc_1(A!2), k1_zfmisc_1(A!2))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[106, 105])).
% 2.44/2.64 tff(108,plain,
% 2.44/2.64 (^[A: $i] : refl(r1_tarski(A, A) <=> r1_tarski(A, A))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(109,plain,
% 2.44/2.64 (![A: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 2.44/2.64 inference(quant_intro,[status(thm)],[108])).
% 2.44/2.64 tff(110,plain,
% 2.44/2.64 (![A: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(111,plain,
% 2.44/2.64 (![A: $i, B: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 2.44/2.64 inference(elim_unused_vars,[status(thm)],[])).
% 2.44/2.64 tff(112,axiom,(![A: $i, B: $i] : r1_tarski(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 2.44/2.64 tff(113,plain,
% 2.44/2.64 (![A: $i] : r1_tarski(A, A)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.44/2.64 tff(114,plain,
% 2.44/2.64 (![A: $i] : r1_tarski(A, A)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[113, 110])).
% 2.44/2.64 tff(115,plain,(
% 2.44/2.64 ![A: $i] : r1_tarski(A, A)),
% 2.44/2.64 inference(skolemize,[status(sab)],[114])).
% 2.44/2.64 tff(116,plain,
% 2.44/2.64 (![A: $i] : r1_tarski(A, A)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[115, 109])).
% 2.44/2.64 tff(117,plain,
% 2.44/2.64 ((~![A: $i] : r1_tarski(A, A)) | r1_tarski(k1_zfmisc_1(A!2), k1_zfmisc_1(A!2))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(118,plain,
% 2.44/2.64 (r1_tarski(k1_zfmisc_1(A!2), k1_zfmisc_1(A!2))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[117, 116])).
% 2.44/2.64 tff(119,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[118, 107])).
% 2.44/2.64 tff(120,plain,(r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(121,plain,
% 2.44/2.64 (^[A: $i, B: $i, C: $i] : refl(((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C)))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(122,plain,
% 2.44/2.64 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C)))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[121])).
% 2.44/2.64 tff(123,plain,
% 2.44/2.64 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C)))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(124,plain,
% 2.44/2.64 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C)))))),
% 2.44/2.64 inference(bind,[status(th)],[])).
% 2.44/2.64 tff(125,plain,
% 2.44/2.64 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C)))) <=> ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))),
% 2.44/2.64 inference(quant_intro,[status(thm)],[124])).
% 2.44/2.64 tff(126,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_relset_2')).
% 2.44/2.64 tff(127,plain,
% 2.44/2.64 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[126, 125])).
% 2.44/2.64 tff(128,plain,
% 2.44/2.64 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[127, 123])).
% 2.44/2.64 tff(129,plain,(
% 2.44/2.64 ![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))),
% 2.44/2.64 inference(skolemize,[status(sab)],[128])).
% 2.44/2.64 tff(130,plain,
% 2.44/2.64 (![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[129, 122])).
% 2.44/2.64 tff(131,plain,
% 2.44/2.64 (((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(132,plain,
% 2.44/2.64 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(133,plain,
% 2.44/2.65 ((~![A: $i, B: $i, C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | r1_tarski(k2_relat_1(k5_relset_2(A, C)), k1_zfmisc_1(k2_relat_1(C))))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[132, 131])).
% 2.44/2.65 tff(134,plain,
% 2.44/2.65 (r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[133, 32, 130])).
% 2.44/2.65 tff(135,plain,
% 2.44/2.65 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B))) <=> (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B))))),
% 2.44/2.65 inference(bind,[status(th)],[])).
% 2.44/2.65 tff(136,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B))) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))),
% 2.44/2.65 inference(quant_intro,[status(thm)],[135])).
% 2.44/2.65 tff(137,plain,
% 2.44/2.65 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)) <=> (~((~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B))))), ((~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))) <=> (~(~((~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B))))))), rewrite((~(~((~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B))))) <=> ((~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))), ((~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))) <=> ((~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B))))), ((m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)))) <=> (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | ((~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))))), rewrite((m2_relset_1(C, A, B) | (~v1_relat_1(C)) | ((~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) <=> (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))), ((m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)))) <=> (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))))),
% 2.44/2.65 inference(bind,[status(th)],[])).
% 2.44/2.65 tff(138,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)))) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))),
% 2.44/2.65 inference(quant_intro,[status(thm)],[137])).
% 2.44/2.65 tff(139,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)))) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(140,plain,
% 2.44/2.65 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)) => m2_relset_1(C, A, B)) <=> ((~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))) | m2_relset_1(C, A, B))), ((v1_relat_1(C) => ((r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)) => m2_relset_1(C, A, B))) <=> (v1_relat_1(C) => ((~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))) | m2_relset_1(C, A, B))))), rewrite((v1_relat_1(C) => ((~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))) | m2_relset_1(C, A, B))) <=> (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))))), ((v1_relat_1(C) => ((r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)) => m2_relset_1(C, A, B))) <=> (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))))))),
% 2.44/2.65 inference(bind,[status(th)],[])).
% 2.44/2.65 tff(141,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) => ((r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)) => m2_relset_1(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))))),
% 2.44/2.65 inference(quant_intro,[status(thm)],[140])).
% 2.44/2.65 tff(142,axiom,(![A: $i, B: $i, C: $i] : (v1_relat_1(C) => ((r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B)) => m2_relset_1(C, A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t11_relset_1')).
% 2.44/2.65 tff(143,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[142, 141])).
% 2.44/2.65 tff(144,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[143, 139])).
% 2.44/2.65 tff(145,plain,(
% 2.44/2.65 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~(r1_tarski(k1_relat_1(C), A) & r1_tarski(k2_relat_1(C), B))))),
% 2.44/2.65 inference(skolemize,[status(sab)],[144])).
% 2.44/2.65 tff(146,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[145, 138])).
% 2.44/2.65 tff(147,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[146, 136])).
% 2.44/2.65 tff(148,assumption,(~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))), introduced(assumption)).
% 2.44/2.65 tff(149,plain,
% 2.44/2.65 (((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) | (m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))))) <=> ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) | m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(150,plain,
% 2.44/2.65 ((m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0))))) <=> (m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(151,plain,
% 2.44/2.65 (((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) | (m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) | (m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[150])).
% 2.44/2.65 tff(152,plain,
% 2.44/2.65 (((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) | (m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) | m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[151, 149])).
% 2.44/2.65 tff(153,plain,
% 2.44/2.65 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) | (m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(154,plain,
% 2.44/2.65 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) | (~v1_relat_1(C)) | (~r1_tarski(k1_relat_1(C), A)) | (~r1_tarski(k2_relat_1(C), B)))) | m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~v1_relat_1(k5_relset_2(A!2, C!0))) | (~r1_tarski(k2_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(k2_relat_1(C!0)))) | (~r1_tarski(k1_relat_1(k5_relset_2(A!2, C!0)), k1_zfmisc_1(A!2)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[153, 152])).
% 2.44/2.65 tff(155,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[154, 148, 147, 134, 87, 120])).
% 2.44/2.65 tff(156,plain,(m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(157,plain,
% 2.44/2.65 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))) | ((~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(158,plain,
% 2.44/2.65 (((~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0))))))) <=> ((~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(159,plain,
% 2.44/2.65 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))) | ((~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))) | ((~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0))))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[158])).
% 2.44/2.65 tff(160,plain,
% 2.44/2.65 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))) | ((~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[159, 157])).
% 2.44/2.65 tff(161,plain,
% 2.44/2.65 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))) | ((~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(162,plain,
% 2.44/2.65 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~((~((~(B = k1_xboole_0)) | (A = k1_xboole_0))) | (v1_funct_2(C, A, B) <=> (A = k4_relset_1(A, B, C))))) | (~((v1_funct_2(C, A, B) <=> (C = k1_xboole_0)) | (A = k1_xboole_0) | (~(B = k1_xboole_0)))))))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0))))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[161, 160])).
% 2.44/2.65 tff(163,plain,
% 2.44/2.65 (~((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[162, 156, 13])).
% 2.44/2.65 tff(164,plain,
% 2.44/2.65 (((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k5_relset_2(A!2, C!0) = k1_xboole_0))))) | ((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))),
% 2.44/2.65 inference(tautology,[status(thm)],[])).
% 2.44/2.65 tff(165,plain,
% 2.44/2.65 ((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[164, 163])).
% 2.44/2.65 tff(166,plain,
% 2.44/2.65 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 2.44/2.65 inference(bind,[status(th)],[])).
% 2.44/2.65 tff(167,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.44/2.65 inference(quant_intro,[status(thm)],[166])).
% 2.44/2.65 tff(168,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(169,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 2.44/2.65 tff(170,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[169, 168])).
% 2.44/2.65 tff(171,plain,(
% 2.44/2.65 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.44/2.65 inference(skolemize,[status(sab)],[170])).
% 2.44/2.65 tff(172,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[171, 167])).
% 2.44/2.65 tff(173,plain,
% 2.44/2.65 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(174,plain,
% 2.44/2.65 (m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[173, 172])).
% 2.44/2.65 tff(175,plain,
% 2.44/2.65 ((~(m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.65 inference(tautology,[status(thm)],[])).
% 2.44/2.65 tff(176,plain,
% 2.44/2.65 ((~(m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))) | m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[175, 156])).
% 2.44/2.65 tff(177,plain,
% 2.44/2.65 (m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[176, 174])).
% 2.44/2.65 tff(178,plain,
% 2.44/2.65 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))))),
% 2.44/2.65 inference(bind,[status(th)],[])).
% 2.44/2.65 tff(179,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 2.44/2.65 inference(quant_intro,[status(thm)],[178])).
% 2.44/2.65 tff(180,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(181,plain,
% 2.44/2.65 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))))),
% 2.44/2.65 inference(bind,[status(th)],[])).
% 2.44/2.65 tff(182,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 2.44/2.65 inference(quant_intro,[status(thm)],[181])).
% 2.44/2.65 tff(183,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k4_relset_1(A, B, C) = k1_relat_1(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_relset_1')).
% 2.44/2.65 tff(184,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[183, 182])).
% 2.44/2.65 tff(185,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[184, 180])).
% 2.44/2.65 tff(186,plain,(
% 2.44/2.65 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 2.44/2.65 inference(skolemize,[status(sab)],[185])).
% 2.44/2.65 tff(187,plain,
% 2.44/2.65 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[186, 179])).
% 2.44/2.65 tff(188,plain,
% 2.44/2.65 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | ((~m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)) = k1_relat_1(k5_relset_2(A!2, C!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | (~m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)) = k1_relat_1(k5_relset_2(A!2, C!0))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(189,plain,
% 2.44/2.65 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | ((~m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)) = k1_relat_1(k5_relset_2(A!2, C!0))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(190,plain,
% 2.44/2.65 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | (~m1_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)) = k1_relat_1(k5_relset_2(A!2, C!0)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[189, 188])).
% 2.44/2.65 tff(191,plain,
% 2.44/2.65 (k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)) = k1_relat_1(k5_relset_2(A!2, C!0))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[190, 187, 177])).
% 2.44/2.65 tff(192,plain,
% 2.44/2.65 (k1_relat_1(k5_relset_2(A!2, C!0)) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))),
% 2.44/2.65 inference(symmetry,[status(thm)],[191])).
% 2.44/2.65 tff(193,plain,
% 2.44/2.65 (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))),
% 2.44/2.65 inference(transitivity,[status(thm)],[102, 192])).
% 2.44/2.65 tff(194,plain,
% 2.44/2.65 ((~(~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))))) <=> ((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(195,plain,
% 2.44/2.65 ((v1_funct_1(k5_relset_2(A!2, C!0)) & v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) & m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) <=> (~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(196,plain,
% 2.44/2.65 ((~(v1_funct_1(k5_relset_2(A!2, C!0)) & v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) & m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))) <=> (~(~((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[195])).
% 2.44/2.65 tff(197,plain,
% 2.44/2.65 ((~(v1_funct_1(k5_relset_2(A!2, C!0)) & v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) & m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))) <=> ((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[196, 194])).
% 2.44/2.65 tff(198,plain,
% 2.44/2.65 (~(v1_funct_1(k5_relset_2(A!2, C!0)) & v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) & m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))),
% 2.44/2.65 inference(or_elim,[status(thm)],[31])).
% 2.44/2.65 tff(199,plain,
% 2.44/2.65 ((~v1_funct_1(k5_relset_2(A!2, C!0))) | (~v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[198, 197])).
% 2.44/2.65 tff(200,plain,
% 2.44/2.65 ((~v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))) | (~m2_relset_1(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[199, 89])).
% 2.44/2.65 tff(201,plain,
% 2.44/2.65 (~v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[200, 156])).
% 2.44/2.65 tff(202,plain,
% 2.44/2.65 ((~(v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))))) | v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) | (~(k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))))),
% 2.44/2.65 inference(tautology,[status(thm)],[])).
% 2.44/2.65 tff(203,plain,
% 2.44/2.65 ((~(v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))))) | (~(k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[202, 201])).
% 2.44/2.65 tff(204,plain,
% 2.44/2.65 (~(v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[203, 193])).
% 2.44/2.65 tff(205,plain,
% 2.44/2.65 ((~((~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0)))))) | (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))) | (v1_funct_2(k5_relset_2(A!2, C!0), k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0))) <=> (k1_zfmisc_1(A!2) = k4_relset_1(k1_zfmisc_1(A!2), k1_zfmisc_1(k2_relat_1(C!0)), k5_relset_2(A!2, C!0))))),
% 2.44/2.65 inference(tautology,[status(thm)],[])).
% 2.44/2.65 tff(206,plain,
% 2.44/2.65 (~((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[205, 204, 165])).
% 2.44/2.65 tff(207,plain,
% 2.44/2.65 (((~(k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)) | (k1_zfmisc_1(A!2) = k1_xboole_0)) | (k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0)),
% 2.44/2.67 inference(tautology,[status(thm)],[])).
% 2.44/2.67 tff(208,plain,
% 2.44/2.67 (k1_zfmisc_1(k2_relat_1(C!0)) = k1_xboole_0),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[207, 206])).
% 2.44/2.67 tff(209,plain,
% 2.44/2.67 (v1_xboole_0(k1_zfmisc_1(k2_relat_1(C!0))) <=> v1_xboole_0(k1_xboole_0)),
% 2.44/2.67 inference(monotonicity,[status(thm)],[208])).
% 2.44/2.67 tff(210,plain,
% 2.44/2.67 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.67 inference(symmetry,[status(thm)],[209])).
% 2.44/2.67 tff(211,plain,
% 2.44/2.67 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(212,axiom,((v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0)) & v3_relat_1(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_relat_1')).
% 2.44/2.67 tff(213,plain,
% 2.44/2.67 (v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0)),
% 2.44/2.67 inference(and_elim,[status(thm)],[212])).
% 2.44/2.67 tff(214,plain,
% 2.44/2.67 (v1_xboole_0(k1_xboole_0)),
% 2.44/2.67 inference(and_elim,[status(thm)],[213])).
% 2.44/2.67 tff(215,plain,
% 2.44/2.67 (v1_xboole_0(k1_xboole_0)),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[214, 211])).
% 2.44/2.67 tff(216,plain,
% 2.44/2.67 (v1_xboole_0(k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[215, 210])).
% 2.44/2.67 tff(217,plain,
% 2.44/2.67 (^[A: $i] : refl((~v1_xboole_0(k1_zfmisc_1(A))) <=> (~v1_xboole_0(k1_zfmisc_1(A))))),
% 2.44/2.67 inference(bind,[status(th)],[])).
% 2.44/2.67 tff(218,plain,
% 2.44/2.67 (![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A))) <=> ![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 2.44/2.67 inference(quant_intro,[status(thm)],[217])).
% 2.44/2.67 tff(219,plain,
% 2.44/2.67 (![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A))) <=> ![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(220,axiom,(![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_subset_1')).
% 2.44/2.67 tff(221,plain,
% 2.44/2.67 (![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[220, 219])).
% 2.44/2.67 tff(222,plain,(
% 2.44/2.67 ![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 2.44/2.67 inference(skolemize,[status(sab)],[221])).
% 2.44/2.67 tff(223,plain,
% 2.44/2.67 (![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[222, 218])).
% 2.44/2.67 tff(224,plain,
% 2.44/2.67 ((~![A: $i] : (~v1_xboole_0(k1_zfmisc_1(A)))) | (~v1_xboole_0(k1_zfmisc_1(k2_relat_1(C!0))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(225,plain,
% 2.44/2.67 (~v1_xboole_0(k1_zfmisc_1(k2_relat_1(C!0)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[224, 223])).
% 2.44/2.67 tff(226,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[225, 216])).
% 2.44/2.67 % SZS output end Proof
% 2.44/2.67 % E exiting
%------------------------------------------------------------------------------