%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP632+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 05:08:14 AM UTC 2025
% Result : Theorem 0.70s 0.87s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP632+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:31:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.70/0.87 % SZS status Theorem
% 0.70/0.87 % SZS output start Proof
% 0.70/0.87 tff(tptp_fun_B_1_type, type, (
% 0.70/0.87 tptp_fun_B_1: $i)).
% 0.70/0.87 tff(k7_funct_2_type, type, (
% 0.70/0.87 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.70/0.87 tff(k6_autgroup_type, type, (
% 0.70/0.87 k6_autgroup: ( $i * $i ) > $i)).
% 0.70/0.87 tff(k2_group_1_type, type, (
% 0.70/0.87 k2_group_1: $i > $i)).
% 0.70/0.87 tff(tptp_fun_A_0_type, type, (
% 0.70/0.87 tptp_fun_A_0: $i)).
% 0.70/0.87 tff(u1_struct_0_type, type, (
% 0.70/0.87 u1_struct_0: $i > $i)).
% 0.70/0.87 tff(k7_relset_1_type, type, (
% 0.70/0.87 k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.70/0.87 tff(k6_partfun1_type, type, (
% 0.70/0.87 k6_partfun1: $i > $i)).
% 0.70/0.87 tff(m2_relset_1_type, type, (
% 0.70/0.87 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.70/0.87 tff(v1_funct_2_type, type, (
% 0.70/0.87 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.70/0.87 tff(v1_funct_1_type, type, (
% 0.70/0.87 v1_funct_1: $i > $o)).
% 0.70/0.87 tff(m2_fraenkel_type, type, (
% 0.70/0.87 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 0.70/0.87 tff(k4_autgroup_type, type, (
% 0.70/0.87 k4_autgroup: $i > $i)).
% 0.70/0.87 tff(m1_fraenkel_type, type, (
% 0.70/0.87 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 0.70/0.87 tff(v4_group_1_type, type, (
% 0.70/0.87 v4_group_1: $i > $o)).
% 0.70/0.87 tff(v3_group_1_type, type, (
% 0.70/0.87 v3_group_1: $i > $o)).
% 0.70/0.87 tff(l1_group_1_type, type, (
% 0.70/0.87 l1_group_1: $i > $o)).
% 0.70/0.87 tff(v1_group_1_type, type, (
% 0.70/0.87 v1_group_1: $i > $o)).
% 0.70/0.87 tff(v3_struct_0_type, type, (
% 0.70/0.87 v3_struct_0: $i > $o)).
% 0.70/0.87 tff(v1_xboole_0_type, type, (
% 0.70/0.87 v1_xboole_0: $i > $o)).
% 0.70/0.87 tff(l1_struct_0_type, type, (
% 0.70/0.87 l1_struct_0: $i > $o)).
% 0.70/0.87 tff(k5_relat_1_type, type, (
% 0.70/0.87 k5_relat_1: ( $i * $i ) > $i)).
% 0.70/0.87 tff(m1_relset_1_type, type, (
% 0.70/0.87 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.70/0.87 tff(v1_partfun1_type, type, (
% 0.70/0.87 v1_partfun1: ( $i * $i * $i ) > $o)).
% 0.70/0.87 tff(g1_group_1_type, type, (
% 0.70/0.87 g1_group_1: ( $i * $i ) > $i)).
% 0.70/0.87 tff(u1_group_1_type, type, (
% 0.70/0.87 u1_group_1: $i > $i)).
% 0.70/0.87 tff(m1_subset_1_type, type, (
% 0.70/0.87 m1_subset_1: ( $i * $i ) > $o)).
% 0.70/0.87 tff(k6_relat_1_type, type, (
% 0.70/0.87 k6_relat_1: $i > $i)).
% 0.70/0.87 tff(v8_relat_2_type, type, (
% 0.70/0.87 v8_relat_2: $i > $o)).
% 0.70/0.87 tff(v4_relat_2_type, type, (
% 0.70/0.87 v4_relat_2: $i > $o)).
% 0.70/0.87 tff(v3_relat_2_type, type, (
% 0.70/0.87 v3_relat_2: $i > $o)).
% 0.70/0.87 tff(v1_relat_2_type, type, (
% 0.70/0.87 v1_relat_2: $i > $o)).
% 0.70/0.87 tff(v1_relat_1_type, type, (
% 0.70/0.87 v1_relat_1: $i > $o)).
% 0.70/0.87 tff(1,plain,
% 0.70/0.87 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(2,plain,
% 0.70/0.87 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[1])).
% 0.70/0.87 tff(3,plain,
% 0.70/0.87 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(4,plain,
% 0.70/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[3])).
% 0.70/0.87 tff(5,plain,
% 0.70/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(6,plain,
% 0.70/0.87 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(7,plain,
% 0.70/0.87 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[6])).
% 0.70/0.87 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_autgroup')).
% 0.70/0.87 tff(9,plain,
% 0.70/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.70/0.87 tff(10,plain,
% 0.70/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.70/0.87 tff(11,plain,(
% 0.70/0.87 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[10])).
% 0.70/0.87 tff(12,plain,
% 0.70/0.87 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.70/0.87 tff(13,plain,
% 0.70/0.87 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.70/0.87 tff(14,plain,
% 0.70/0.87 ((((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (~((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1) & (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1))))) <=> ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1) & (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1)))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(15,plain,
% 0.70/0.87 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B)))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(16,plain,
% 0.70/0.87 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B)))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(17,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_autgroup')).
% 0.70/0.87 tff(18,plain,
% 0.70/0.87 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B))))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.70/0.87 tff(19,plain,
% 0.70/0.87 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B))))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.70/0.87 tff(20,plain,
% 0.70/0.87 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B))))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.70/0.87 tff(21,plain,
% 0.70/0.87 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B) & (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, k6_autgroup(A, k2_group_1(A))) = B))))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.70/0.87 tff(22,plain,
% 0.70/0.87 ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1) & (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1))))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.70/0.87 tff(23,plain,
% 0.70/0.87 (l1_group_1(A!0)),
% 0.70/0.87 inference(and_elim,[status(thm)],[22])).
% 0.70/0.87 tff(24,plain,
% 0.70/0.87 (v4_group_1(A!0)),
% 0.70/0.87 inference(and_elim,[status(thm)],[22])).
% 0.70/0.87 tff(25,plain,
% 0.70/0.87 (v3_group_1(A!0)),
% 0.70/0.87 inference(and_elim,[status(thm)],[22])).
% 0.70/0.87 tff(26,plain,
% 0.70/0.87 (v1_group_1(A!0)),
% 0.70/0.87 inference(and_elim,[status(thm)],[22])).
% 0.70/0.87 tff(27,plain,
% 0.70/0.87 (~v3_struct_0(A!0)),
% 0.70/0.87 inference(and_elim,[status(thm)],[22])).
% 0.70/0.87 tff(28,plain,
% 0.70/0.87 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(29,plain,
% 0.70/0.87 ((v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(30,plain,
% 0.70/0.87 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[29])).
% 0.70/0.87 tff(31,plain,
% 0.70/0.87 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[30, 28])).
% 0.70/0.87 tff(32,plain,
% 0.70/0.87 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(33,plain,
% 0.70/0.87 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.70/0.87 tff(34,plain,
% 0.70/0.87 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[33, 27, 26, 25, 24, 23, 13])).
% 0.70/0.87 tff(35,plain,
% 0.70/0.87 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(36,plain,
% 0.70/0.87 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[35])).
% 0.70/0.87 tff(37,plain,
% 0.70/0.87 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(38,plain,
% 0.70/0.87 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(39,plain,
% 0.70/0.87 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[38])).
% 0.70/0.87 tff(40,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 0.70/0.87 tff(41,plain,
% 0.70/0.87 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.70/0.87 tff(42,plain,
% 0.70/0.87 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.70/0.87 tff(43,plain,(
% 0.70/0.87 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[42])).
% 0.70/0.87 tff(44,plain,
% 0.70/0.87 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.70/0.87 tff(45,plain,
% 0.70/0.87 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(46,plain,
% 0.70/0.87 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(47,plain,
% 0.70/0.87 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.70/0.87 tff(48,plain,
% 0.70/0.87 (l1_struct_0(A!0)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[47, 23, 44])).
% 0.70/0.87 tff(49,plain,
% 0.70/0.87 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(50,plain,
% 0.70/0.87 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[49])).
% 0.70/0.87 tff(51,plain,
% 0.70/0.87 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(52,plain,
% 0.70/0.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[51])).
% 0.70/0.87 tff(53,plain,
% 0.70/0.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(54,plain,
% 0.70/0.87 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(55,plain,
% 0.70/0.87 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[54])).
% 0.70/0.87 tff(56,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.70/0.87 tff(57,plain,
% 0.70/0.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.70/0.87 tff(58,plain,
% 0.70/0.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.70/0.87 tff(59,plain,(
% 0.70/0.87 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.70/0.87 inference(skolemize,[status(sab)],[58])).
% 0.70/0.87 tff(60,plain,
% 0.70/0.87 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.70/0.87 tff(61,plain,
% 0.70/0.87 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.70/0.87 tff(62,plain,
% 0.70/0.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(63,plain,
% 0.70/0.87 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(64,plain,
% 0.70/0.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[63])).
% 0.70/0.87 tff(65,plain,
% 0.70/0.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.70/0.87 inference(transitivity,[status(thm)],[64, 62])).
% 0.70/0.87 tff(66,plain,
% 0.70/0.87 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(67,plain,
% 0.70/0.87 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.70/0.87 tff(68,plain,
% 0.70/0.87 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[67, 27, 61])).
% 0.70/0.87 tff(69,plain,
% 0.70/0.87 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[68, 48])).
% 0.70/0.87 tff(70,plain,
% 0.70/0.87 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(71,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[70])).
% 0.70/0.87 tff(72,plain,
% 0.70/0.87 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(73,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[72])).
% 0.70/0.87 tff(74,plain,
% 0.70/0.87 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.70/0.87 inference(transitivity,[status(thm)],[73, 71])).
% 0.70/0.87 tff(75,plain,
% 0.70/0.87 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), quant_intro(proof_bind(^[D: $i] : rewrite(((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(76,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[75])).
% 0.70/0.88 tff(77,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(78,plain,
% 0.70/0.88 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> (m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), rewrite((m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), (![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(79,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[78])).
% 0.70/0.88 tff(80,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_fraenkel')).
% 0.70/0.88 tff(81,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.70/0.88 tff(82,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.70/0.88 tff(83,plain,(
% 0.70/0.88 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.70/0.88 inference(skolemize,[status(sab)],[82])).
% 0.70/0.88 tff(84,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.70/0.88 tff(85,plain,
% 0.70/0.88 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[84, 74])).
% 0.70/0.88 tff(86,plain,
% 0.70/0.88 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(87,plain,
% 0.70/0.88 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(88,plain,
% 0.72/0.88 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.72/0.88 tff(89,plain,
% 0.72/0.88 (![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[88, 85, 69, 34])).
% 0.72/0.88 tff(90,plain,
% 0.72/0.88 (~((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1) & (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1)))),
% 0.72/0.88 inference(and_elim,[status(thm)],[22])).
% 0.72/0.88 tff(91,plain,
% 0.72/0.88 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.72/0.88 inference(or_elim,[status(thm)],[90])).
% 0.72/0.88 tff(92,plain,
% 0.72/0.88 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(93,plain,
% 0.72/0.88 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(94,plain,
% 0.72/0.88 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.72/0.88 tff(95,plain,
% 0.72/0.88 (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[94, 91, 89])).
% 0.72/0.88 tff(96,plain,
% 0.72/0.88 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(97,plain,
% 0.72/0.88 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.72/0.88 tff(98,plain,
% 0.72/0.88 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))) <=> ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(99,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[98])).
% 0.72/0.88 tff(100,plain,
% 0.72/0.88 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(101,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[100])).
% 0.72/0.88 tff(102,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(103,plain,
% 0.72/0.88 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(104,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[103])).
% 0.72/0.88 tff(105,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_2')).
% 0.72/0.88 tff(106,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.72/0.88 tff(107,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.72/0.88 tff(108,plain,(
% 0.72/0.88 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[107])).
% 0.72/0.88 tff(109,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.72/0.88 tff(110,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.72/0.88 tff(111,plain,
% 0.72/0.88 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | ((~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1)) | (~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1)) | (~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1)))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(112,plain,
% 0.72/0.88 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | ((~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1)) | (~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1)))))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(113,plain,
% 0.72/0.88 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1)) | (~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.72/0.88 tff(114,plain,
% 0.72/0.88 (~((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1)) | (~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1)))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[113, 110, 97])).
% 0.72/0.88 tff(115,plain,
% 0.72/0.88 (((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1)) | (~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1)),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(116,plain,
% 0.72/0.88 (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.72/0.88 tff(117,plain,
% 0.72/0.88 (^[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)))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(118,plain,
% 0.72/0.88 (![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))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[117])).
% 0.72/0.88 tff(119,plain,
% 0.72/0.88 (![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))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(120,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')).
% 0.72/0.88 tff(121,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.72/0.88 tff(122,plain,(
% 0.72/0.88 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.72/0.88 inference(skolemize,[status(sab)],[121])).
% 0.72/0.88 tff(123,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.72/0.88 tff(124,plain,
% 0.72/0.88 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(125,plain,
% 0.72/0.88 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.72/0.88 tff(126,plain,
% 0.72/0.88 ((~(m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(127,plain,
% 0.72/0.88 ((~(m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[126, 97])).
% 0.72/0.88 tff(128,plain,
% 0.72/0.88 (m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[127, 125])).
% 0.72/0.88 tff(129,plain,
% 0.72/0.88 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(130,plain,
% 0.72/0.88 (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[129, 123])).
% 0.72/0.88 tff(131,plain,
% 0.72/0.88 (^[A: $i] : refl((~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))) <=> (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(132,plain,
% 0.72/0.88 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))) <=> ![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[131])).
% 0.72/0.88 tff(133,plain,
% 0.72/0.88 (^[A: $i] : rewrite((v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(134,plain,
% 0.72/0.88 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> ![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[133])).
% 0.72/0.88 tff(135,plain,
% 0.72/0.88 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(136,axiom,(![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_partfun1')).
% 0.72/0.88 tff(137,plain,
% 0.72/0.88 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.72/0.88 tff(138,plain,(
% 0.72/0.88 ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.72/0.88 inference(skolemize,[status(sab)],[137])).
% 0.72/0.88 tff(139,plain,
% 0.72/0.88 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.72/0.88 tff(140,plain,
% 0.72/0.88 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.72/0.88 tff(141,plain,
% 0.72/0.88 ((~![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))) | (~((~v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(142,plain,
% 0.72/0.88 (~((~v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.72/0.88 tff(143,plain,
% 0.72/0.88 (((~v1_partfun1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(144,plain,
% 0.72/0.88 (m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.72/0.88 tff(145,plain,
% 0.72/0.88 ((~(m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(146,plain,
% 0.72/0.88 ((~(m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.72/0.88 tff(147,plain,
% 0.72/0.88 (m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[146, 130])).
% 0.72/0.88 tff(148,plain,
% 0.72/0.88 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl(((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(149,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[148])).
% 0.72/0.88 tff(150,plain,
% 0.72/0.88 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) <=> (~((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))), ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) <=> (~(~((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))))), rewrite((~(~((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))) <=> ((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))), ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) <=> ((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))))), (((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> (((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))))), rewrite((((~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))), (((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(151,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[150])).
% 0.72/0.88 tff(152,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(153,plain,
% 0.72/0.88 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : rewrite(((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(154,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[153])).
% 0.72/0.88 tff(155,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k7_relset_1')).
% 0.72/0.88 tff(156,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.72/0.88 tff(157,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.72/0.88 tff(158,plain,(
% 0.72/0.88 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[157])).
% 0.72/0.88 tff(159,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.72/0.88 tff(160,plain,
% 0.72/0.88 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[159, 149])).
% 0.72/0.88 tff(161,plain,
% 0.72/0.88 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(162,plain,
% 0.72/0.88 (((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(163,plain,
% 0.72/0.88 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1))))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[162])).
% 0.72/0.88 tff(164,plain,
% 0.72/0.88 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)))),
% 0.72/0.88 inference(transitivity,[status(thm)],[163, 161])).
% 0.72/0.88 tff(165,plain,
% 0.72/0.88 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(166,plain,
% 0.72/0.88 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.72/0.88 tff(167,plain,
% 0.72/0.88 (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[166, 160, 147, 128])).
% 0.72/0.88 tff(168,plain,
% 0.72/0.88 (k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1) = k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1)),
% 0.72/0.88 inference(symmetry,[status(thm)],[167])).
% 0.72/0.88 tff(169,plain,
% 0.72/0.88 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(170,plain,
% 0.72/0.88 (v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[169, 95])).
% 0.72/0.88 tff(171,plain,
% 0.72/0.88 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(B!1)),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(172,plain,
% 0.72/0.88 (v1_funct_1(B!1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[171, 95])).
% 0.72/0.88 tff(173,plain,
% 0.72/0.88 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(174,plain,
% 0.72/0.88 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[173])).
% 0.72/0.89 tff(175,plain,
% 0.72/0.89 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(176,plain,
% 0.72/0.89 (^[A: $i] : trans(monotonicity(rewrite((v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))) <=> ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> (l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))))), rewrite((l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(177,plain,
% 0.72/0.89 (![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[176])).
% 0.72/0.89 tff(178,axiom,(![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 0.72/0.89 tff(179,plain,
% 0.72/0.89 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.72/0.89 tff(180,plain,
% 0.72/0.89 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.72/0.89 tff(181,plain,(
% 0.72/0.89 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[180])).
% 0.72/0.89 tff(182,plain,
% 0.72/0.89 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.72/0.89 tff(183,plain,
% 0.72/0.89 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(184,plain,
% 0.72/0.89 (((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0))) <=> ((~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(185,plain,
% 0.72/0.89 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[184])).
% 0.72/0.89 tff(186,plain,
% 0.72/0.89 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.72/0.89 inference(transitivity,[status(thm)],[185, 183])).
% 0.72/0.89 tff(187,plain,
% 0.72/0.89 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(188,plain,
% 0.72/0.89 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.72/0.89 tff(189,plain,
% 0.72/0.89 (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[188, 26, 23, 182])).
% 0.72/0.89 tff(190,plain,
% 0.72/0.89 (g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)) = A!0),
% 0.72/0.89 inference(symmetry,[status(thm)],[189])).
% 0.72/0.89 tff(191,plain,
% 0.72/0.89 (k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) = k4_autgroup(A!0)),
% 0.72/0.89 inference(monotonicity,[status(thm)],[190])).
% 0.72/0.89 tff(192,plain,
% 0.72/0.89 (k4_autgroup(A!0) = k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(symmetry,[status(thm)],[191])).
% 0.72/0.89 tff(193,plain,
% 0.72/0.89 (u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) = u1_struct_0(A!0)),
% 0.72/0.89 inference(monotonicity,[status(thm)],[190])).
% 0.72/0.89 tff(194,plain,
% 0.72/0.89 (u1_struct_0(A!0) = u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(symmetry,[status(thm)],[193])).
% 0.72/0.89 tff(195,plain,
% 0.72/0.89 (k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[190])).
% 0.72/0.89 tff(196,plain,
% 0.72/0.89 (k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0))),
% 0.72/0.89 inference(symmetry,[status(thm)],[195])).
% 0.72/0.89 tff(197,plain,
% 0.72/0.89 (^[A: $i] : refl((v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(198,plain,
% 0.72/0.89 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[197])).
% 0.72/0.89 tff(199,plain,
% 0.72/0.89 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(200,plain,
% 0.72/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[199])).
% 0.72/0.89 tff(201,plain,
% 0.72/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(202,plain,
% 0.72/0.89 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(203,plain,
% 0.72/0.89 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[202])).
% 0.72/0.89 tff(204,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_autgroup')).
% 0.72/0.89 tff(205,plain,
% 0.72/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.72/0.89 tff(206,plain,
% 0.72/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.72/0.89 tff(207,plain,(
% 0.72/0.89 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))))),
% 0.72/0.89 inference(skolemize,[status(sab)],[206])).
% 0.72/0.89 tff(208,plain,
% 0.72/0.89 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.72/0.89 tff(209,plain,
% 0.72/0.89 (![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[208, 198])).
% 0.72/0.89 tff(210,plain,
% 0.72/0.89 (((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(211,plain,
% 0.72/0.89 ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(212,plain,
% 0.72/0.89 ((~![A: $i] : (v3_struct_0(A) | (k6_autgroup(A, k2_group_1(A)) = k6_partfun1(u1_struct_0(A))) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.72/0.89 tff(213,plain,
% 0.72/0.89 (k6_autgroup(A!0, k2_group_1(A!0)) = k6_partfun1(u1_struct_0(A!0))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[212, 27, 26, 25, 24, 23, 209])).
% 0.72/0.89 tff(214,plain,
% 0.72/0.89 (k6_partfun1(u1_struct_0(A!0)) = k6_autgroup(A!0, k2_group_1(A!0))),
% 0.72/0.89 inference(symmetry,[status(thm)],[213])).
% 0.72/0.89 tff(215,plain,
% 0.72/0.89 (k6_partfun1(u1_struct_0(A!0)) = k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0))),
% 0.72/0.89 inference(transitivity,[status(thm)],[214, 196])).
% 0.72/0.89 tff(216,plain,
% 0.72/0.89 (m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[215, 194, 194, 192])).
% 0.72/0.89 tff(217,plain,
% 0.72/0.89 (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.72/0.89 inference(symmetry,[status(thm)],[216])).
% 0.72/0.89 tff(218,plain,
% 0.72/0.89 (m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[193])).
% 0.72/0.89 tff(219,plain,
% 0.72/0.89 (m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) <=> m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.72/0.89 inference(symmetry,[status(thm)],[218])).
% 0.72/0.89 tff(220,plain,
% 0.72/0.89 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(221,plain,
% 0.72/0.89 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[220])).
% 0.72/0.89 tff(222,plain,
% 0.72/0.89 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(223,plain,
% 0.72/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[222])).
% 0.72/0.89 tff(224,plain,
% 0.72/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(225,plain,
% 0.72/0.89 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(226,plain,
% 0.72/0.89 (![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[225])).
% 0.72/0.89 tff(227,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_group_1')).
% 0.72/0.89 tff(228,plain,
% 0.72/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.72/0.89 tff(229,plain,
% 0.72/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.72/0.89 tff(230,plain,(
% 0.72/0.89 ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[229])).
% 0.72/0.89 tff(231,plain,
% 0.72/0.89 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[230, 223])).
% 0.72/0.89 tff(232,plain,
% 0.72/0.89 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[231, 221])).
% 0.72/0.89 tff(233,plain,
% 0.72/0.89 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(234,plain,
% 0.72/0.89 ((v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(235,plain,
% 0.72/0.89 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[234])).
% 0.72/0.89 tff(236,plain,
% 0.72/0.89 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[235, 233])).
% 0.72/0.89 tff(237,plain,
% 0.72/0.89 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(238,plain,
% 0.72/0.89 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.72/0.89 tff(239,plain,
% 0.72/0.89 (m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[238, 27, 23, 232])).
% 0.72/0.89 tff(240,plain,
% 0.72/0.89 (m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[239, 219])).
% 0.72/0.89 tff(241,plain,
% 0.72/0.89 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> l1_group_1(A!0)),
% 0.72/0.89 inference(monotonicity,[status(thm)],[190])).
% 0.72/0.89 tff(242,plain,
% 0.72/0.89 (l1_group_1(A!0) <=> l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(symmetry,[status(thm)],[241])).
% 0.72/0.89 tff(243,plain,
% 0.72/0.89 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[23, 242])).
% 0.72/0.89 tff(244,plain,
% 0.72/0.89 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_1(A!0)),
% 0.72/0.89 inference(monotonicity,[status(thm)],[190])).
% 0.72/0.89 tff(245,plain,
% 0.72/0.89 (v4_group_1(A!0) <=> v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(symmetry,[status(thm)],[244])).
% 0.72/0.89 tff(246,plain,
% 0.72/0.89 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[24, 245])).
% 0.72/0.89 tff(247,plain,
% 0.72/0.89 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_group_1(A!0)),
% 0.72/0.89 inference(monotonicity,[status(thm)],[190])).
% 0.72/0.89 tff(248,plain,
% 0.72/0.89 (v3_group_1(A!0) <=> v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(symmetry,[status(thm)],[247])).
% 0.72/0.89 tff(249,plain,
% 0.72/0.89 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[25, 248])).
% 0.72/0.89 tff(250,plain,
% 0.72/0.89 (v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_1(A!0)),
% 0.72/0.89 inference(monotonicity,[status(thm)],[190])).
% 0.72/0.89 tff(251,plain,
% 0.72/0.89 (v1_group_1(A!0) <=> v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(symmetry,[status(thm)],[250])).
% 0.72/0.89 tff(252,plain,
% 0.72/0.89 (v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[26, 251])).
% 0.72/0.89 tff(253,plain,
% 0.72/0.89 (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_struct_0(A!0)),
% 0.72/0.89 inference(monotonicity,[status(thm)],[190])).
% 0.72/0.89 tff(254,plain,
% 0.72/0.89 (v3_struct_0(A!0) <=> v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(symmetry,[status(thm)],[253])).
% 0.72/0.89 tff(255,plain,
% 0.72/0.89 ((~v3_struct_0(A!0)) <=> (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[254])).
% 0.72/0.89 tff(256,plain,
% 0.72/0.89 (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[27, 255])).
% 0.72/0.89 tff(257,plain,
% 0.72/0.89 (^[A: $i, B: $i] : refl((m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(258,plain,
% 0.72/0.89 (![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[257])).
% 0.72/0.89 tff(259,plain,
% 0.72/0.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(260,plain,
% 0.72/0.89 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[259])).
% 0.72/0.89 tff(261,plain,
% 0.72/0.89 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(262,plain,
% 0.72/0.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), ((((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(263,plain,
% 0.72/0.89 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[262])).
% 0.72/0.89 tff(264,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_autgroup')).
% 0.72/0.89 tff(265,plain,
% 0.72/0.89 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.72/0.89 tff(266,plain,
% 0.72/0.89 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[265, 261])).
% 0.72/0.89 tff(267,plain,(
% 0.72/0.89 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[266])).
% 0.72/0.89 tff(268,plain,
% 0.72/0.89 (![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[267, 260])).
% 0.72/0.89 tff(269,plain,
% 0.72/0.89 (![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[268, 258])).
% 0.72/0.89 tff(270,plain,
% 0.72/0.89 (((~![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(271,plain,
% 0.72/0.89 ((~![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(272,plain,
% 0.72/0.89 ((~![A: $i, B: $i] : (m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | v3_struct_0(A) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.72/0.89 tff(273,plain,
% 0.72/0.89 (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[272, 269])).
% 0.72/0.89 tff(274,plain,
% 0.72/0.89 (m2_fraenkel(k6_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), k4_autgroup(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[273, 256, 252, 249, 246, 243, 240])).
% 0.72/0.89 tff(275,plain,
% 0.72/0.89 (m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[274, 217])).
% 0.72/0.89 tff(276,plain,
% 0.72/0.89 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(277,plain,
% 0.72/0.89 (((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(278,plain,
% 0.72/0.89 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[277])).
% 0.72/0.89 tff(279,plain,
% 0.72/0.89 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.72/0.89 inference(transitivity,[status(thm)],[278, 276])).
% 0.72/0.89 tff(280,plain,
% 0.72/0.89 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(281,plain,
% 0.72/0.89 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.72/0.89 tff(282,plain,
% 0.72/0.89 (~((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[281, 89, 275])).
% 0.72/0.89 tff(283,plain,
% 0.72/0.89 (((~m2_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.89 inference(tautology,[status(thm)],[])).
% 0.72/0.89 tff(284,plain,
% 0.72/0.89 (v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.72/0.89 tff(285,plain,
% 0.72/0.89 (^[A: $i] : refl((k6_partfun1(A) = k6_relat_1(A)) <=> (k6_partfun1(A) = k6_relat_1(A)))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(286,plain,
% 0.72/0.89 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[285])).
% 0.72/0.89 tff(287,plain,
% 0.72/0.89 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(288,axiom,(![A: $i] : (k6_partfun1(A) = k6_relat_1(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 0.72/0.89 tff(289,plain,
% 0.72/0.89 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.72/0.89 tff(290,plain,(
% 0.72/0.89 ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.72/0.89 inference(skolemize,[status(sab)],[289])).
% 0.72/0.89 tff(291,plain,
% 0.72/0.89 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.72/0.89 tff(292,plain,
% 0.72/0.89 ((~![A: $i] : (k6_partfun1(A) = k6_relat_1(A))) | (k6_partfun1(u1_struct_0(A!0)) = k6_relat_1(u1_struct_0(A!0)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(293,plain,
% 0.72/0.89 (k6_partfun1(u1_struct_0(A!0)) = k6_relat_1(u1_struct_0(A!0))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[292, 291])).
% 0.72/0.89 tff(294,plain,
% 0.72/0.89 (k6_relat_1(u1_struct_0(A!0)) = k6_partfun1(u1_struct_0(A!0))),
% 0.72/0.89 inference(symmetry,[status(thm)],[293])).
% 0.72/0.89 tff(295,plain,
% 0.72/0.89 (v1_funct_1(k6_relat_1(u1_struct_0(A!0))) <=> v1_funct_1(k6_partfun1(u1_struct_0(A!0)))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[294])).
% 0.72/0.89 tff(296,plain,
% 0.72/0.89 (^[A: $i] : refl((~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A))))) <=> (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A))))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(297,plain,
% 0.72/0.89 (![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A))))) <=> ![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[296])).
% 0.72/0.89 tff(298,plain,
% 0.72/0.89 (^[A: $i] : rewrite((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A))) <=> (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A))))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(299,plain,
% 0.72/0.89 (![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A))) <=> ![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[298])).
% 0.72/0.89 tff(300,plain,
% 0.72/0.89 (![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A))) <=> ![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(301,plain,
% 0.72/0.89 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)))), ((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) <=> ((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))))), rewrite(((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))), ((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A))))), (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) <=> ((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))))), rewrite(((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)))), (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A))))), ((((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))) <=> ((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))))), rewrite(((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))), ((((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))) <=> (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(302,plain,
% 0.72/0.90 (![A: $i] : (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A))) <=> ![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[301])).
% 0.72/0.90 tff(303,axiom,(![A: $i] : (((((v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A))) & v1_relat_2(k6_relat_1(A))) & v3_relat_2(k6_relat_1(A))) & v4_relat_2(k6_relat_1(A))) & v8_relat_2(k6_relat_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_partfun1')).
% 0.72/0.90 tff(304,plain,
% 0.72/0.90 (![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.72/0.90 tff(305,plain,
% 0.72/0.90 (![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[304, 300])).
% 0.72/0.90 tff(306,plain,(
% 0.72/0.90 ![A: $i] : (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))),
% 0.72/0.90 inference(skolemize,[status(sab)],[305])).
% 0.72/0.90 tff(307,plain,
% 0.72/0.90 (![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[306, 299])).
% 0.72/0.90 tff(308,plain,
% 0.72/0.90 (![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[307, 297])).
% 0.72/0.90 tff(309,plain,
% 0.72/0.90 ((~![A: $i] : (~((~v1_relat_1(k6_relat_1(A))) | (~v1_funct_1(k6_relat_1(A))) | (~v1_relat_2(k6_relat_1(A))) | (~v3_relat_2(k6_relat_1(A))) | (~v4_relat_2(k6_relat_1(A))) | (~v8_relat_2(k6_relat_1(A)))))) | (~((~v1_relat_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v3_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v4_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v8_relat_2(k6_relat_1(u1_struct_0(A!0))))))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(310,plain,
% 0.72/0.90 (~((~v1_relat_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v3_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v4_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v8_relat_2(k6_relat_1(u1_struct_0(A!0)))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[309, 308])).
% 0.72/0.90 tff(311,plain,
% 0.72/0.90 (((~v1_relat_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_relat_1(u1_struct_0(A!0)))) | (~v1_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v3_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v4_relat_2(k6_relat_1(u1_struct_0(A!0)))) | (~v8_relat_2(k6_relat_1(u1_struct_0(A!0))))) | v1_funct_1(k6_relat_1(u1_struct_0(A!0)))),
% 0.72/0.90 inference(tautology,[status(thm)],[])).
% 0.72/0.90 tff(312,plain,
% 0.72/0.90 (v1_funct_1(k6_relat_1(u1_struct_0(A!0)))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[311, 310])).
% 0.72/0.90 tff(313,plain,
% 0.72/0.90 (v1_funct_1(k6_partfun1(u1_struct_0(A!0)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[312, 295])).
% 0.72/0.90 tff(314,plain,
% 0.72/0.90 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(315,plain,
% 0.72/0.90 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[314])).
% 0.72/0.90 tff(316,plain,
% 0.72/0.90 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(317,plain,
% 0.72/0.90 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[316])).
% 0.72/0.90 tff(318,plain,
% 0.72/0.90 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(319,plain,
% 0.72/0.90 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(320,plain,
% 0.72/0.90 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[319])).
% 0.72/0.90 tff(321,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k7_funct_2')).
% 0.72/0.90 tff(322,plain,
% 0.72/0.90 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.72/0.90 tff(323,plain,
% 0.72/0.90 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[322, 318])).
% 0.72/0.90 tff(324,plain,(
% 0.72/0.90 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.72/0.90 inference(skolemize,[status(sab)],[323])).
% 0.72/0.90 tff(325,plain,
% 0.72/0.90 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[324, 317])).
% 0.72/0.90 tff(326,plain,
% 0.72/0.90 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[325, 315])).
% 0.72/0.90 tff(327,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(328,plain,
% 0.72/0.90 ((v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(329,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[328])).
% 0.72/0.90 tff(330,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[329, 327])).
% 0.72/0.90 tff(331,plain,
% 0.72/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(332,plain,
% 0.72/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.72/0.90 tff(333,plain,
% 0.72/0.90 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = k5_relat_1(k6_partfun1(u1_struct_0(A!0)), B!1)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[332, 326, 69, 313, 284, 147, 172, 170, 128])).
% 0.72/0.90 tff(334,plain,
% 0.72/0.90 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1)),
% 0.72/0.90 inference(monotonicity,[status(thm)],[213])).
% 0.72/0.90 tff(335,plain,
% 0.72/0.90 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1),
% 0.72/0.90 inference(transitivity,[status(thm)],[334, 333, 168, 116])).
% 0.72/0.90 tff(336,plain,
% 0.72/0.90 (((~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_partfun1(u1_struct_0(A!0)), B!1) = B!1)) | (~(k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1)),
% 0.72/0.90 inference(tautology,[status(thm)],[])).
% 0.72/0.90 tff(337,plain,
% 0.72/0.90 (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = B!1),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[336, 114])).
% 0.72/0.90 tff(338,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(339,plain,
% 0.72/0.90 (((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(340,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0))))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[339])).
% 0.72/0.90 tff(341,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))))),
% 0.72/0.90 inference(transitivity,[status(thm)],[340, 338])).
% 0.72/0.90 tff(342,plain,
% 0.72/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | ((k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(343,plain,
% 0.72/0.90 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(F, C, D)) | (~m1_relset_1(E, A, B)))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.72/0.90 tff(344,plain,
% 0.72/0.90 (k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[343, 160, 147, 128])).
% 0.72/0.90 tff(345,plain,
% 0.72/0.90 (k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0))) = k7_relset_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0)))),
% 0.72/0.90 inference(symmetry,[status(thm)],[344])).
% 0.72/0.90 tff(346,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(347,plain,
% 0.72/0.90 ((v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(348,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0))))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[347])).
% 0.72/0.90 tff(349,plain,
% 0.72/0.90 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))))),
% 0.72/0.91 inference(transitivity,[status(thm)],[348, 346])).
% 0.72/0.91 tff(350,plain,
% 0.72/0.91 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(351,plain,
% 0.72/0.91 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_partfun1(u1_struct_0(A!0)))) | (~v1_funct_2(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_partfun1(u1_struct_0(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0))))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.72/0.91 tff(352,plain,
% 0.72/0.91 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0))) = k5_relat_1(B!1, k6_partfun1(u1_struct_0(A!0)))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[351, 326, 69, 313, 284, 147, 172, 170, 128])).
% 0.72/0.91 tff(353,plain,
% 0.72/0.91 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_partfun1(u1_struct_0(A!0)))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[213])).
% 0.72/0.91 tff(354,plain,
% 0.72/0.91 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1),
% 0.72/0.91 inference(transitivity,[status(thm)],[353, 352, 345, 337])).
% 0.72/0.91 tff(355,assumption,(~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1)), introduced(assumption)).
% 0.72/0.91 tff(356,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[355, 354])).
% 0.72/0.91 tff(357,plain,(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(358,plain,
% 0.72/0.91 ((~(~((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1)) | (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1))))) <=> ((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1)) | (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(359,plain,
% 0.72/0.91 (((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1) & (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1)) <=> (~((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1)) | (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1))))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(360,plain,
% 0.72/0.91 ((~((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1) & (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1))) <=> (~(~((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1)) | (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1)))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[359])).
% 0.72/0.91 tff(361,plain,
% 0.72/0.91 ((~((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1) & (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1))) <=> ((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1)) | (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[360, 358])).
% 0.72/0.91 tff(362,plain,
% 0.72/0.91 (~((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1) & (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1))),
% 0.72/0.91 inference(or_elim,[status(thm)],[90])).
% 0.72/0.91 tff(363,plain,
% 0.72/0.91 ((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1)) | (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), B!1, k6_autgroup(A!0, k2_group_1(A!0))) = B!1))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.72/0.91 tff(364,plain,
% 0.72/0.91 (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B!1) = B!1)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[363, 357])).
% 0.72/0.91 tff(365,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[364, 335])).
% 0.72/0.91 % SZS output end Proof
% 0.75/0.92 % E exiting
%------------------------------------------------------------------------------