%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT291+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:11 AM UTC 2025
% Result : Theorem 0.48s 0.65s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : LAT291+1 : TPTP v9.0.0. Released v3.4.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n012.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Jun 19 20:02:11 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.48/0.65 % SZS status Theorem
% 0.48/0.65 % SZS output start Proof
% 0.48/0.65 tff(k7_lopclset_type, type, (
% 0.48/0.65 k7_lopclset: $i > $i)).
% 0.48/0.65 tff(tptp_fun_A_0_type, type, (
% 0.48/0.65 tptp_fun_A_0: $i)).
% 0.48/0.65 tff(k8_funct_2_type, type, (
% 0.48/0.65 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 0.48/0.65 tff(k6_lattices_type, type, (
% 0.48/0.65 k6_lattices: $i > $i)).
% 0.48/0.65 tff(k9_lopclset_type, type, (
% 0.48/0.65 k9_lopclset: $i > $i)).
% 0.48/0.65 tff(k1_zfmisc_1_type, type, (
% 0.48/0.65 k1_zfmisc_1: $i > $i)).
% 0.48/0.65 tff(u1_struct_0_type, type, (
% 0.48/0.65 u1_struct_0: $i > $i)).
% 0.48/0.65 tff(a_1_1_lopclset_type, type, (
% 0.48/0.65 a_1_1_lopclset: $i > $i)).
% 0.48/0.65 tff(v17_lattices_type, type, (
% 0.48/0.65 v17_lattices: $i > $o)).
% 0.48/0.65 tff(v10_lattices_type, type, (
% 0.48/0.65 v10_lattices: $i > $o)).
% 0.48/0.65 tff(l3_lattices_type, type, (
% 0.48/0.65 l3_lattices: $i > $o)).
% 0.48/0.65 tff(v3_struct_0_type, type, (
% 0.48/0.65 v3_struct_0: $i > $o)).
% 0.48/0.65 tff(v3_realset2_type, type, (
% 0.48/0.65 v3_realset2: $i > $o)).
% 0.48/0.65 tff(k4_xboole_0_type, type, (
% 0.48/0.65 k4_xboole_0: ( $i * $i ) > $i)).
% 0.48/0.65 tff(k1_xboole_0_type, type, (
% 0.48/0.65 k1_xboole_0: $i)).
% 0.48/0.65 tff(k5_lattices_type, type, (
% 0.48/0.65 k5_lattices: $i > $i)).
% 0.48/0.65 tff(k7_lattices_type, type, (
% 0.48/0.65 k7_lattices: ( $i * $i ) > $i)).
% 0.48/0.65 tff(m1_subset_1_type, type, (
% 0.48/0.65 m1_subset_1: ( $i * $i ) > $o)).
% 0.48/0.65 tff(l1_lattices_type, type, (
% 0.48/0.65 l1_lattices: $i > $o)).
% 0.48/0.65 tff(l2_lattices_type, type, (
% 0.48/0.65 l2_lattices: $i > $o)).
% 0.48/0.65 tff(1,plain,
% 0.48/0.65 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(2,plain,
% 0.48/0.65 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[1])).
% 0.48/0.65 tff(3,plain,
% 0.48/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(4,plain,
% 0.48/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[3])).
% 0.48/0.65 tff(5,plain,
% 0.48/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(6,plain,
% 0.48/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(7,plain,
% 0.48/0.65 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[6])).
% 0.48/0.65 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_lopclset')).
% 0.48/0.65 tff(9,plain,
% 0.48/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.48/0.65 tff(10,plain,
% 0.48/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.48/0.65 tff(11,plain,(
% 0.48/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[10])).
% 0.48/0.65 tff(12,plain,
% 0.48/0.65 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.48/0.65 tff(13,plain,
% 0.48/0.65 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.48/0.65 tff(14,plain,
% 0.48/0.65 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A)))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(15,plain,
% 0.48/0.65 ((~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A)))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(16,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_lopclset')).
% 0.48/0.65 tff(17,plain,
% 0.48/0.65 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.48/0.65 tff(18,plain,
% 0.48/0.65 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.48/0.65 tff(19,plain,
% 0.48/0.65 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.48/0.65 tff(20,plain,
% 0.48/0.65 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k6_lattices(A)) = k7_lopclset(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.48/0.65 tff(21,plain,(
% 0.48/0.65 ~((~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k6_lattices(A!0)) = k7_lopclset(A!0)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[20])).
% 0.48/0.65 tff(22,plain,
% 0.48/0.65 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)),
% 0.48/0.65 inference(or_elim,[status(thm)],[21])).
% 0.48/0.65 tff(23,plain,
% 0.48/0.65 (l3_lattices(A!0)),
% 0.48/0.65 inference(and_elim,[status(thm)],[22])).
% 0.48/0.65 tff(24,plain,
% 0.48/0.65 (~v3_realset2(A!0)),
% 0.48/0.65 inference(and_elim,[status(thm)],[22])).
% 0.48/0.65 tff(25,plain,
% 0.48/0.65 (v17_lattices(A!0)),
% 0.48/0.65 inference(and_elim,[status(thm)],[22])).
% 0.48/0.65 tff(26,plain,
% 0.48/0.65 (v10_lattices(A!0)),
% 0.48/0.65 inference(and_elim,[status(thm)],[22])).
% 0.48/0.65 tff(27,plain,
% 0.48/0.65 (~v3_struct_0(A!0)),
% 0.48/0.65 inference(and_elim,[status(thm)],[22])).
% 0.48/0.65 tff(28,plain,
% 0.48/0.65 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(29,plain,
% 0.48/0.65 ((v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))) <=> (v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(30,plain,
% 0.48/0.65 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[29])).
% 0.48/0.65 tff(31,plain,
% 0.48/0.65 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[30, 28])).
% 0.48/0.65 tff(32,plain,
% 0.48/0.65 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(33,plain,
% 0.48/0.65 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.48/0.65 tff(34,plain,
% 0.48/0.65 (k7_lopclset(A!0) = a_1_1_lopclset(A!0)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[33, 27, 26, 25, 24, 23, 13])).
% 0.48/0.65 tff(35,plain,
% 0.48/0.65 (a_1_1_lopclset(A!0) = k7_lopclset(A!0)),
% 0.48/0.65 inference(symmetry,[status(thm)],[34])).
% 0.48/0.65 tff(36,plain,
% 0.48/0.65 (^[A: $i] : refl((k4_xboole_0(A, k1_xboole_0) = A) <=> (k4_xboole_0(A, k1_xboole_0) = A))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(37,plain,
% 0.48/0.65 (![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A) <=> ![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A)),
% 0.48/0.65 inference(quant_intro,[status(thm)],[36])).
% 0.48/0.65 tff(38,plain,
% 0.48/0.65 (![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A) <=> ![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A)),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(39,axiom,(![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_boole')).
% 0.48/0.65 tff(40,plain,
% 0.48/0.65 (![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.48/0.65 tff(41,plain,(
% 0.48/0.65 ![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A)),
% 0.48/0.65 inference(skolemize,[status(sab)],[40])).
% 0.48/0.65 tff(42,plain,
% 0.48/0.65 (![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.48/0.65 tff(43,plain,
% 0.48/0.65 ((~![A: $i] : (k4_xboole_0(A, k1_xboole_0) = A)) | (k4_xboole_0(a_1_1_lopclset(A!0), k1_xboole_0) = a_1_1_lopclset(A!0))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(44,plain,
% 0.48/0.65 (k4_xboole_0(a_1_1_lopclset(A!0), k1_xboole_0) = a_1_1_lopclset(A!0)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.48/0.65 tff(45,plain,
% 0.48/0.65 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(46,plain,
% 0.48/0.65 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[45])).
% 0.48/0.65 tff(47,plain,
% 0.48/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(48,plain,
% 0.48/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[47])).
% 0.48/0.65 tff(49,plain,
% 0.48/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(50,plain,
% 0.48/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(51,plain,
% 0.48/0.65 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[50])).
% 0.48/0.65 tff(52,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t36_lopclset')).
% 0.48/0.65 tff(53,plain,
% 0.48/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.48/0.65 tff(54,plain,
% 0.48/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.48/0.65 tff(55,plain,(
% 0.48/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0))),
% 0.48/0.65 inference(skolemize,[status(sab)],[54])).
% 0.48/0.65 tff(56,plain,
% 0.48/0.65 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.48/0.65 tff(57,plain,
% 0.48/0.65 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.48/0.65 tff(58,plain,
% 0.48/0.65 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(59,plain,
% 0.48/0.65 ((v3_realset2(A!0) | v3_struct_0(A!0) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))) <=> (v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(60,plain,
% 0.48/0.65 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[59])).
% 0.48/0.65 tff(61,plain,
% 0.48/0.65 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0))),
% 0.48/0.65 inference(transitivity,[status(thm)],[60, 58])).
% 0.48/0.65 tff(62,plain,
% 0.48/0.65 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(63,plain,
% 0.48/0.65 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k5_lattices(A)) = k1_xboole_0) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_struct_0(A!0) | v3_realset2(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.48/0.65 tff(64,plain,
% 0.48/0.65 (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)) = k1_xboole_0),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[63, 27, 26, 25, 24, 23, 57])).
% 0.48/0.65 tff(65,plain,
% 0.48/0.65 (k1_xboole_0 = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0))),
% 0.48/0.65 inference(symmetry,[status(thm)],[64])).
% 0.48/0.65 tff(66,plain,
% 0.48/0.65 (k4_xboole_0(a_1_1_lopclset(A!0), k1_xboole_0) = k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[35, 65])).
% 0.48/0.65 tff(67,plain,
% 0.48/0.65 (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0))) = k4_xboole_0(a_1_1_lopclset(A!0), k1_xboole_0)),
% 0.48/0.65 inference(symmetry,[status(thm)],[66])).
% 0.48/0.65 tff(68,plain,
% 0.48/0.65 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(69,plain,
% 0.48/0.65 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[68])).
% 0.48/0.65 tff(70,plain,
% 0.48/0.65 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(71,plain,
% 0.48/0.65 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[70])).
% 0.48/0.65 tff(72,plain,
% 0.48/0.65 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(73,plain,
% 0.48/0.65 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(74,plain,
% 0.48/0.65 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[73])).
% 0.48/0.65 tff(75,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.48/0.65 tff(76,plain,
% 0.48/0.65 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.48/0.65 tff(77,plain,
% 0.48/0.65 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.48/0.65 tff(78,plain,(
% 0.48/0.65 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[77])).
% 0.48/0.65 tff(79,plain,
% 0.48/0.65 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.48/0.66 tff(80,plain,
% 0.48/0.66 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.48/0.66 tff(81,plain,
% 0.48/0.66 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(82,plain,
% 0.48/0.66 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(83,plain,
% 0.48/0.66 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.48/0.66 tff(84,plain,
% 0.48/0.66 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[83, 23, 80])).
% 0.48/0.66 tff(85,plain,
% 0.48/0.66 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(86,plain,
% 0.48/0.66 (l1_lattices(A!0)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.48/0.66 tff(87,plain,
% 0.48/0.66 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(88,plain,
% 0.48/0.66 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[87])).
% 0.48/0.66 tff(89,plain,
% 0.48/0.66 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(90,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[89])).
% 0.48/0.66 tff(91,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(92,plain,
% 0.48/0.66 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(93,plain,
% 0.48/0.66 (![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[92])).
% 0.48/0.66 tff(94,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_lattices')).
% 0.48/0.66 tff(95,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.48/0.66 tff(96,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.48/0.66 tff(97,plain,(
% 0.48/0.66 ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.48/0.66 inference(skolemize,[status(sab)],[96])).
% 0.48/0.66 tff(98,plain,
% 0.48/0.66 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.48/0.66 tff(99,plain,
% 0.48/0.66 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.48/0.66 tff(100,plain,
% 0.48/0.66 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(101,plain,
% 0.48/0.66 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(102,plain,
% 0.48/0.66 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.48/0.66 tff(103,plain,
% 0.48/0.66 (m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[102, 27, 99])).
% 0.48/0.66 tff(104,plain,
% 0.48/0.66 (m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[103, 86])).
% 0.48/0.66 tff(105,plain,
% 0.48/0.66 (^[A: $i] : rewrite((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(106,plain,
% 0.48/0.66 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[105])).
% 0.48/0.66 tff(107,plain,
% 0.48/0.66 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(108,plain,
% 0.48/0.66 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[107])).
% 0.48/0.66 tff(109,plain,
% 0.48/0.66 (^[A: $i] : rewrite((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(110,plain,
% 0.48/0.66 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[109])).
% 0.48/0.66 tff(111,plain,
% 0.48/0.66 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.66 inference(transitivity,[status(thm)],[110, 108])).
% 0.48/0.66 tff(112,plain,
% 0.48/0.66 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(113,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[112])).
% 0.48/0.66 tff(114,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(115,plain,
% 0.48/0.66 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(116,plain,
% 0.48/0.66 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[115])).
% 0.48/0.66 tff(117,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t28_lopclset')).
% 0.48/0.66 tff(118,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.48/0.66 tff(119,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.48/0.66 tff(120,plain,(
% 0.48/0.66 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))),
% 0.48/0.66 inference(skolemize,[status(sab)],[119])).
% 0.48/0.66 tff(121,plain,
% 0.48/0.66 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.48/0.66 tff(122,plain,
% 0.48/0.66 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.48/0.66 tff(123,plain,
% 0.48/0.66 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[122, 106])).
% 0.48/0.66 tff(124,plain,
% 0.48/0.66 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B)))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(125,plain,
% 0.48/0.66 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B)))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(126,plain,
% 0.48/0.66 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k4_xboole_0(k7_lopclset(A), k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)) = k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), k7_lattices(A, B)))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.48/0.66 tff(127,plain,
% 0.48/0.66 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[126, 27, 26, 25, 24, 23, 123])).
% 0.48/0.66 tff(128,plain,
% 0.48/0.66 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0))) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, k5_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B))))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0))) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, k5_lattices(A!0)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(129,plain,
% 0.48/0.66 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0))) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, k5_lattices(A!0)))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(130,plain,
% 0.48/0.66 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, B))))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0))) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, k5_lattices(A!0))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.48/0.66 tff(131,plain,
% 0.48/0.66 (k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0))) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, k5_lattices(A!0)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[130, 127, 104])).
% 0.48/0.66 tff(132,plain,
% 0.48/0.66 (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, k5_lattices(A!0))) = k4_xboole_0(k7_lopclset(A!0), k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k5_lattices(A!0)))),
% 0.48/0.66 inference(symmetry,[status(thm)],[131])).
% 0.48/0.66 tff(133,plain,
% 0.48/0.66 (^[A: $i] : refl((v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(134,plain,
% 0.48/0.66 (![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[133])).
% 0.48/0.66 tff(135,plain,
% 0.48/0.66 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(136,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[135])).
% 0.48/0.66 tff(137,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(138,plain,
% 0.48/0.66 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(139,plain,
% 0.48/0.66 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => (k7_lattices(A, k5_lattices(A)) = k6_lattices(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[138])).
% 0.48/0.66 tff(140,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_lattice4')).
% 0.48/0.66 tff(141,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.48/0.66 tff(142,plain,
% 0.48/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.48/0.67 tff(143,plain,(
% 0.48/0.67 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)))),
% 0.48/0.67 inference(skolemize,[status(sab)],[142])).
% 0.48/0.67 tff(144,plain,
% 0.48/0.67 (![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.48/0.67 tff(145,plain,
% 0.48/0.67 (![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.48/0.67 tff(146,plain,
% 0.48/0.67 (((~![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | (k7_lattices(A!0, k5_lattices(A!0)) = k6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_struct_0(A!0) | (k7_lattices(A!0, k5_lattices(A!0)) = k6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(147,plain,
% 0.48/0.67 ((~![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | (k7_lattices(A!0, k5_lattices(A!0)) = k6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(148,plain,
% 0.48/0.67 ((~![A: $i] : (v3_struct_0(A) | (k7_lattices(A, k5_lattices(A)) = k6_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_struct_0(A!0) | (k7_lattices(A!0, k5_lattices(A!0)) = k6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.48/0.67 tff(149,plain,
% 0.48/0.67 (k7_lattices(A!0, k5_lattices(A!0)) = k6_lattices(A!0)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[148, 27, 26, 25, 23, 145])).
% 0.48/0.67 tff(150,plain,
% 0.48/0.67 (k6_lattices(A!0) = k7_lattices(A!0, k5_lattices(A!0))),
% 0.48/0.67 inference(symmetry,[status(thm)],[149])).
% 0.48/0.67 tff(151,plain,
% 0.48/0.67 (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k6_lattices(A!0)) = k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k7_lattices(A!0, k5_lattices(A!0)))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[150])).
% 0.48/0.67 tff(152,plain,
% 0.48/0.67 (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k6_lattices(A!0)) = k7_lopclset(A!0)),
% 0.48/0.67 inference(transitivity,[status(thm)],[151, 132, 67, 44, 35])).
% 0.48/0.67 tff(153,plain,
% 0.48/0.67 (~(k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), k6_lattices(A!0)) = k7_lopclset(A!0))),
% 0.48/0.67 inference(or_elim,[status(thm)],[21])).
% 0.48/0.67 tff(154,plain,
% 0.48/0.67 ($false),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.48/0.67 % SZS output end Proof
% 0.48/0.67 % E exiting
%------------------------------------------------------------------------------