%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP645+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:17 AM UTC 2025
% Result : Theorem 0.93s 1.11s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP645+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 16:36:41 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.93/1.11 % SZS status Theorem
% 0.93/1.11 % SZS output start Proof
% 0.93/1.11 tff(k3_xboole_0_type, type, (
% 0.93/1.11 k3_xboole_0: ( $i * $i ) > $i)).
% 0.93/1.11 tff(k1_funct_1_type, type, (
% 0.93/1.11 k1_funct_1: ( $i * $i ) > $i)).
% 0.93/1.11 tff(g1_group_1_type, type, (
% 0.93/1.11 g1_group_1: ( $i * $i ) > $i)).
% 0.93/1.11 tff(u1_group_1_type, type, (
% 0.93/1.11 u1_group_1: $i > $i)).
% 0.93/1.11 tff(tptp_fun_B_1_type, type, (
% 0.93/1.11 tptp_fun_B_1: $i)).
% 0.93/1.11 tff(u1_struct_0_type, type, (
% 0.93/1.11 u1_struct_0: $i > $i)).
% 0.93/1.11 tff(k1_latsubgr_type, type, (
% 0.93/1.11 k1_latsubgr: $i > $i)).
% 0.93/1.11 tff(tptp_fun_A_0_type, type, (
% 0.93/1.11 tptp_fun_A_0: $i)).
% 0.93/1.11 tff(tptp_fun_C_2_type, type, (
% 0.93/1.11 tptp_fun_C_2: $i)).
% 0.93/1.11 tff(k9_group_2_type, type, (
% 0.93/1.11 k9_group_2: ( $i * $i * $i ) > $i)).
% 0.93/1.11 tff(l1_group_1_type, type, (
% 0.93/1.11 l1_group_1: $i > $o)).
% 0.93/1.11 tff(v3_group_1_type, type, (
% 0.93/1.11 v3_group_1: $i > $o)).
% 0.93/1.11 tff(v3_struct_0_type, type, (
% 0.93/1.11 v3_struct_0: $i > $o)).
% 0.93/1.11 tff(m1_group_2_type, type, (
% 0.93/1.11 m1_group_2: ( $i * $i ) > $o)).
% 0.93/1.11 tff(v1_group_1_type, type, (
% 0.93/1.11 v1_group_1: $i > $o)).
% 0.93/1.11 tff(v4_group_1_type, type, (
% 0.93/1.11 v4_group_1: $i > $o)).
% 0.93/1.11 tff(k8_group_2_type, type, (
% 0.93/1.11 k8_group_2: ( $i * $i * $i ) > $i)).
% 0.93/1.11 tff(tptp_fun_C_3_type, type, (
% 0.93/1.11 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.93/1.11 tff(v1_funct_2_type, type, (
% 0.93/1.11 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.93/1.11 tff(k1_zfmisc_1_type, type, (
% 0.93/1.11 k1_zfmisc_1: $i > $i)).
% 0.93/1.11 tff(k1_group_3_type, type, (
% 0.93/1.11 k1_group_3: $i > $i)).
% 0.93/1.11 tff(m2_relset_1_type, type, (
% 0.93/1.11 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.93/1.11 tff(v1_funct_1_type, type, (
% 0.93/1.11 v1_funct_1: $i > $o)).
% 0.93/1.11 tff(1,plain,
% 0.93/1.11 (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(2,plain,
% 0.93/1.11 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[1])).
% 0.93/1.11 tff(3,plain,
% 0.93/1.11 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(4,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.93/1.11 tff(5,plain,
% 0.93/1.11 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.93/1.11 tff(6,plain,(
% 0.93/1.11 ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.93/1.11 inference(skolemize,[status(sab)],[5])).
% 0.93/1.11 tff(7,plain,
% 0.93/1.11 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.93/1.11 tff(8,plain,
% 0.93/1.11 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), B!1)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(9,plain,
% 0.93/1.11 (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), B!1))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.93/1.11 tff(10,plain,
% 0.93/1.11 (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))),
% 0.93/1.11 inference(symmetry,[status(thm)],[9])).
% 0.93/1.11 tff(11,plain,
% 0.93/1.11 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(12,plain,
% 0.93/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[11])).
% 0.93/1.11 tff(13,plain,
% 0.93/1.11 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(14,plain,
% 0.93/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[13])).
% 0.93/1.11 tff(15,plain,
% 0.93/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.93/1.11 inference(transitivity,[status(thm)],[14, 12])).
% 0.93/1.11 tff(16,plain,
% 0.93/1.11 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(17,plain,
% 0.93/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[16])).
% 0.93/1.11 tff(18,plain,
% 0.93/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(19,plain,
% 0.93/1.11 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> (m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), rewrite((m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), (![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(20,plain,
% 0.93/1.11 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[19])).
% 0.93/1.11 tff(21,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_group_2')).
% 0.93/1.11 tff(22,plain,
% 0.93/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.93/1.11 tff(23,plain,
% 0.93/1.11 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.93/1.11 tff(24,plain,(
% 0.93/1.11 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.93/1.11 inference(skolemize,[status(sab)],[23])).
% 0.93/1.11 tff(25,plain,
% 0.93/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.93/1.11 tff(26,plain,
% 0.93/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.93/1.11 tff(27,plain,
% 0.93/1.11 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(28,plain,
% 0.93/1.12 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(29,plain,
% 0.93/1.12 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))))))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[28])).
% 0.93/1.12 tff(30,plain,
% 0.93/1.12 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))),
% 0.93/1.12 inference(transitivity,[status(thm)],[29, 27])).
% 0.93/1.12 tff(31,plain,
% 0.93/1.12 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(32,plain,
% 0.93/1.12 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(33,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_latsubgr')).
% 0.93/1.12 tff(34,plain,
% 0.93/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.93/1.12 tff(35,plain,
% 0.93/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.93/1.12 tff(36,plain,
% 0.93/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.93/1.12 tff(37,plain,
% 0.93/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.93/1.12 tff(38,plain,
% 0.93/1.12 ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.93/1.12 tff(39,plain,
% 0.93/1.12 (l1_group_1(A!0)),
% 0.93/1.12 inference(and_elim,[status(thm)],[38])).
% 0.93/1.12 tff(40,plain,
% 0.93/1.12 (v3_group_1(A!0)),
% 0.93/1.12 inference(and_elim,[status(thm)],[38])).
% 0.93/1.12 tff(41,plain,
% 0.93/1.12 (~v3_struct_0(A!0)),
% 0.93/1.12 inference(and_elim,[status(thm)],[38])).
% 0.93/1.12 tff(42,plain,
% 0.93/1.12 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(43,plain,
% 0.93/1.12 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(44,plain,
% 0.93/1.12 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.93/1.12 tff(45,plain,
% 0.93/1.12 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[44, 41, 40, 39, 26])).
% 0.93/1.12 tff(46,plain,
% 0.93/1.12 (m1_group_2(B!1, A!0)),
% 0.93/1.12 inference(and_elim,[status(thm)],[38])).
% 0.93/1.12 tff(47,plain,
% 0.93/1.12 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(48,plain,
% 0.93/1.12 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(49,plain,
% 0.93/1.12 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.93/1.12 tff(50,plain,
% 0.93/1.12 (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[49, 46, 45])).
% 0.93/1.12 tff(51,plain,
% 0.93/1.12 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | l1_group_1(B!1)),
% 0.93/1.12 inference(tautology,[status(thm)],[])).
% 0.93/1.12 tff(52,plain,
% 0.93/1.12 (l1_group_1(B!1)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.93/1.12 tff(53,plain,
% 0.93/1.12 (^[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))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(54,plain,
% 0.93/1.12 (![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)))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[53])).
% 0.93/1.12 tff(55,plain,
% 0.93/1.12 (![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)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(56,plain,
% 0.93/1.12 (^[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)))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(57,plain,
% 0.93/1.12 (![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)))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[56])).
% 0.93/1.12 tff(58,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')).
% 0.93/1.12 tff(59,plain,
% 0.93/1.12 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.93/1.12 tff(60,plain,
% 0.93/1.12 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.93/1.12 tff(61,plain,(
% 0.93/1.12 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.93/1.12 inference(skolemize,[status(sab)],[60])).
% 0.93/1.12 tff(62,plain,
% 0.93/1.12 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.93/1.12 tff(63,plain,
% 0.93/1.12 (v1_group_1(B!1)),
% 0.93/1.12 inference(and_elim,[status(thm)],[38])).
% 0.93/1.12 tff(64,plain,
% 0.93/1.12 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(65,plain,
% 0.93/1.12 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(66,plain,
% 0.93/1.12 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.93/1.12 tff(67,plain,
% 0.93/1.12 ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(B!1))),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[66, 63, 62])).
% 0.93/1.12 tff(68,plain,
% 0.93/1.12 (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[67, 52])).
% 0.93/1.12 tff(69,plain,
% 0.93/1.12 (g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)) = B!1),
% 0.93/1.12 inference(symmetry,[status(thm)],[68])).
% 0.93/1.12 tff(70,plain,
% 0.93/1.12 (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k1_funct_1(k1_latsubgr(A!0), B!1)),
% 0.93/1.12 inference(monotonicity,[status(thm)],[69])).
% 0.93/1.12 tff(71,plain,
% 0.93/1.12 (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), B!1))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[70])).
% 0.93/1.12 tff(72,plain,
% 0.93/1.12 (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))),
% 0.93/1.12 inference(transitivity,[status(thm)],[71, 10])).
% 0.93/1.12 tff(73,plain,
% 0.93/1.12 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) <=> (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(74,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[73])).
% 0.93/1.12 tff(75,plain,
% 0.93/1.12 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) <=> (~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))))), rewrite((~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))))), rewrite(((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(76,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[75])).
% 0.93/1.12 tff(77,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(78,plain,
% 0.93/1.12 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(79,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[78])).
% 0.93/1.12 tff(80,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k9_group_2')).
% 0.93/1.12 tff(81,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.93/1.12 tff(82,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.93/1.12 tff(83,plain,(
% 0.93/1.12 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 0.93/1.12 inference(skolemize,[status(sab)],[82])).
% 0.93/1.12 tff(84,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.93/1.12 tff(85,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[84, 74])).
% 0.93/1.12 tff(86,plain,
% 0.93/1.12 (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))),
% 0.93/1.12 inference(and_elim,[status(thm)],[38])).
% 0.93/1.12 tff(87,plain,
% 0.93/1.12 (v1_group_1(C!2) & m1_group_2(C!2, A!0)),
% 0.93/1.12 inference(or_elim,[status(thm)],[86])).
% 0.93/1.12 tff(88,plain,
% 0.93/1.12 (m1_group_2(C!2, A!0)),
% 0.93/1.12 inference(and_elim,[status(thm)],[87])).
% 0.93/1.12 tff(89,plain,
% 0.93/1.12 (v4_group_1(A!0)),
% 0.93/1.12 inference(and_elim,[status(thm)],[38])).
% 0.93/1.12 tff(90,plain,
% 0.93/1.12 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(91,plain,
% 0.93/1.12 ((v3_struct_0(A!0) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(92,plain,
% 0.93/1.12 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0))))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[91])).
% 0.93/1.12 tff(93,plain,
% 0.93/1.12 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 0.93/1.12 inference(transitivity,[status(thm)],[92, 90])).
% 0.93/1.12 tff(94,plain,
% 0.93/1.12 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(95,plain,
% 0.93/1.12 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.93/1.12 tff(96,plain,
% 0.93/1.12 (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[95, 41, 40, 89, 39, 46, 88, 85])).
% 0.93/1.12 tff(97,plain,
% 0.93/1.12 (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[96])).
% 0.93/1.12 tff(98,plain,
% 0.93/1.12 (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2))),
% 0.93/1.12 inference(symmetry,[status(thm)],[97])).
% 0.93/1.12 tff(99,plain,
% 0.93/1.12 (k8_group_2(A!0, B!1, C!2) = k9_group_2(A!0, B!1, C!2)),
% 0.93/1.12 inference(symmetry,[status(thm)],[96])).
% 0.93/1.12 tff(100,plain,
% 0.93/1.12 (m1_group_2(k8_group_2(A!0, B!1, C!2), A!0) <=> m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)),
% 0.93/1.12 inference(monotonicity,[status(thm)],[99])).
% 0.93/1.12 tff(101,plain,
% 0.93/1.12 (m1_group_2(k9_group_2(A!0, B!1, C!2), A!0) <=> m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)),
% 0.93/1.12 inference(symmetry,[status(thm)],[100])).
% 0.93/1.12 tff(102,plain,
% 0.93/1.12 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(103,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[102])).
% 0.93/1.12 tff(104,plain,
% 0.93/1.12 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) <=> (~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))))), rewrite((~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), rewrite((v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)) <=> (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))))), rewrite(((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(105,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[104])).
% 0.93/1.12 tff(106,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(107,plain,
% 0.93/1.12 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(108,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[107])).
% 0.93/1.12 tff(109,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k9_group_2')).
% 0.93/1.12 tff(110,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.93/1.12 tff(111,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.93/1.12 tff(112,plain,(
% 0.93/1.12 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 0.93/1.12 inference(skolemize,[status(sab)],[111])).
% 0.93/1.12 tff(113,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.93/1.12 tff(114,plain,
% 0.93/1.12 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.93/1.12 tff(115,plain,
% 0.93/1.12 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(116,plain,
% 0.93/1.12 ((v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(117,plain,
% 0.93/1.12 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))))))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[116])).
% 0.93/1.12 tff(118,plain,
% 0.93/1.12 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))),
% 0.93/1.13 inference(transitivity,[status(thm)],[117, 115])).
% 0.93/1.13 tff(119,plain,
% 0.93/1.13 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(120,plain,
% 0.93/1.13 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.93/1.13 tff(121,plain,
% 0.93/1.13 (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[120, 41, 40, 89, 39, 46, 88, 114])).
% 0.93/1.13 tff(122,plain,
% 0.93/1.13 (((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))) | m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)),
% 0.93/1.13 inference(tautology,[status(thm)],[])).
% 0.93/1.13 tff(123,plain,
% 0.93/1.13 (m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.93/1.13 tff(124,plain,
% 0.93/1.13 (m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[123, 101])).
% 0.93/1.13 tff(125,plain,
% 0.93/1.13 (v1_group_1(k8_group_2(A!0, B!1, C!2)) <=> v1_group_1(k9_group_2(A!0, B!1, C!2))),
% 0.93/1.13 inference(monotonicity,[status(thm)],[99])).
% 0.93/1.13 tff(126,plain,
% 0.93/1.13 (v1_group_1(k9_group_2(A!0, B!1, C!2)) <=> v1_group_1(k8_group_2(A!0, B!1, C!2))),
% 0.93/1.13 inference(symmetry,[status(thm)],[125])).
% 0.93/1.13 tff(127,plain,
% 0.93/1.13 (((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))) | v1_group_1(k9_group_2(A!0, B!1, C!2))),
% 0.93/1.13 inference(tautology,[status(thm)],[])).
% 0.93/1.13 tff(128,plain,
% 0.93/1.13 (v1_group_1(k9_group_2(A!0, B!1, C!2))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[127, 121])).
% 0.93/1.13 tff(129,plain,
% 0.93/1.13 (v1_group_1(k8_group_2(A!0, B!1, C!2))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[128, 126])).
% 0.93/1.13 tff(130,plain,
% 0.93/1.13 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(131,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[130])).
% 0.93/1.13 tff(132,plain,
% 0.93/1.13 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(133,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[132])).
% 0.93/1.13 tff(134,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 0.93/1.13 inference(transitivity,[status(thm)],[133, 131])).
% 0.93/1.13 tff(135,plain,
% 0.93/1.13 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))), ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))), ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))), trans(monotonicity(rewrite(((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) <=> ((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))), trans(monotonicity(rewrite((~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))) <=> (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))), (((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))), rewrite(((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))), (((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))), ((((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))) <=> (((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A)))) & ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))), rewrite((((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A)))) & ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))) <=> (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))), ((((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))) <=> (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))))), (![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))))) <=> ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(136,plain,
% 0.93/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[135])).
% 0.93/1.13 tff(137,plain,
% 0.93/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(138,plain,
% 0.93/1.13 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) <=> (v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))), rewrite(((B = k1_latsubgr(A)) <=> ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(B, C) = u1_struct_0(C)))) <=> ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))), ((((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(B, C) = u1_struct_0(C))))) <=> ((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))))), ((((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(B, C) = u1_struct_0(C))))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))))))), (![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(B, C) = u1_struct_0(C))))) <=> ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(B, C) = u1_struct_0(C)))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(B, C) = u1_struct_0(C)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(139,plain,
% 0.93/1.13 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(B, C) = u1_struct_0(C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[138])).
% 0.93/1.13 tff(140,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) => ((B = k1_latsubgr(A)) <=> ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(B, C) = u1_struct_0(C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_latsubgr')).
% 0.93/1.13 tff(141,plain,
% 0.93/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.93/1.13 tff(142,plain,
% 0.93/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | ((B = k1_latsubgr(A)) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C))))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.93/1.13 tff(143,plain,(
% 0.93/1.13 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))))))),
% 0.93/1.13 inference(skolemize,[status(sab)],[142])).
% 0.93/1.13 tff(144,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.93/1.13 tff(145,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.93/1.13 tff(146,plain,
% 0.93/1.13 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0)))))))))))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(147,plain,
% 0.93/1.13 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0)))))))))))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(148,plain,
% 0.93/1.13 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))))),
% 0.93/1.13 inference(monotonicity,[status(thm)],[147])).
% 0.93/1.13 tff(149,plain,
% 0.93/1.13 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0)))))))))))),
% 0.93/1.13 inference(transitivity,[status(thm)],[148, 146])).
% 0.93/1.13 tff(150,plain,
% 0.93/1.13 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0))))))))))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(151,plain,
% 0.93/1.13 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.93/1.13 tff(152,plain,
% 0.93/1.13 (![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[151, 41, 40, 89, 39, 145])).
% 0.93/1.13 tff(153,plain,
% 0.93/1.13 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(154,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[153])).
% 0.93/1.13 tff(155,plain,
% 0.93/1.13 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), rewrite((v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(156,plain,
% 0.93/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[155])).
% 0.93/1.13 tff(157,plain,
% 0.93/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(158,plain,
% 0.93/1.13 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), rewrite(((v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) <=> (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(159,plain,
% 0.93/1.13 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[158])).
% 0.93/1.13 tff(160,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_latsubgr')).
% 0.93/1.13 tff(161,plain,
% 0.93/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.93/1.13 tff(162,plain,
% 0.93/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.93/1.13 tff(163,plain,(
% 0.93/1.13 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.93/1.13 inference(skolemize,[status(sab)],[162])).
% 0.93/1.13 tff(164,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.93/1.13 tff(165,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[164, 154])).
% 0.93/1.13 tff(166,plain,
% 0.93/1.13 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k1_latsubgr(A!0))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k1_latsubgr(A!0))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(167,plain,
% 0.93/1.13 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k1_latsubgr(A!0))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(168,plain,
% 0.93/1.13 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k1_latsubgr(A))) | (~v1_funct_2(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(k1_latsubgr(A), k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k1_latsubgr(A!0))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.93/1.13 tff(169,plain,
% 0.93/1.13 (~((~v1_funct_1(k1_latsubgr(A!0))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[168, 41, 40, 89, 39, 165])).
% 0.93/1.14 tff(170,plain,
% 0.93/1.14 (((~v1_funct_1(k1_latsubgr(A!0))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.93/1.14 inference(tautology,[status(thm)],[])).
% 0.93/1.14 tff(171,plain,
% 0.93/1.14 (m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.93/1.14 tff(172,plain,
% 0.93/1.14 (((~v1_funct_1(k1_latsubgr(A!0))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.93/1.14 inference(tautology,[status(thm)],[])).
% 0.93/1.14 tff(173,plain,
% 0.93/1.14 (v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[172, 169])).
% 0.93/1.14 tff(174,plain,
% 0.93/1.14 (((~v1_funct_1(k1_latsubgr(A!0))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | v1_funct_1(k1_latsubgr(A!0))),
% 0.93/1.14 inference(tautology,[status(thm)],[])).
% 0.93/1.14 tff(175,plain,
% 0.93/1.14 (v1_funct_1(k1_latsubgr(A!0))),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[174, 169])).
% 0.93/1.14 tff(176,plain,
% 0.93/1.14 (((~![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))) | ((~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))) | (~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(177,plain,
% 0.93/1.14 (((~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(k1_latsubgr(A!0) = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0)))))))))) <=> ((~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(178,plain,
% 0.93/1.14 (((~![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))) | ((~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(k1_latsubgr(A!0) = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))))))))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))) | ((~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[177])).
% 0.93/1.14 tff(179,plain,
% 0.93/1.14 (((~![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))) | ((~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(k1_latsubgr(A!0) = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))))))))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))) | (~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 0.93/1.14 inference(transitivity,[status(thm)],[178, 176])).
% 0.93/1.14 tff(180,plain,
% 0.93/1.14 ((~![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))) | ((~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(k1_latsubgr(A!0) = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))))))))))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(181,plain,
% 0.93/1.14 ((~![B: $i] : ((~v1_funct_1(B)) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((~m1_group_2(tptp_fun_C_3(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))))))))))) | (~v1_funct_1(k1_latsubgr(A!0))) | (~m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.93/1.14 tff(182,plain,
% 0.93/1.14 (![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[181, 175, 173, 171, 152])).
% 0.93/1.14 tff(183,plain,
% 0.93/1.14 (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | ((~v1_group_1(k8_group_2(A!0, B!1, C!2))) | (~m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)) | (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2))))) <=> ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | (~v1_group_1(k8_group_2(A!0, B!1, C!2))) | (~m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)) | (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(184,plain,
% 0.93/1.14 ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | ((~v1_group_1(k8_group_2(A!0, B!1, C!2))) | (~m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)) | (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2))))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(185,plain,
% 0.93/1.14 ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | (~v1_group_1(k8_group_2(A!0, B!1, C!2))) | (~m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)) | (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.93/1.14 tff(186,plain,
% 0.93/1.14 (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2))),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[185, 182, 129, 124])).
% 0.93/1.14 tff(187,plain,
% 0.93/1.14 (u1_struct_0(k8_group_2(A!0, B!1, C!2)) = k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2))),
% 0.93/1.14 inference(symmetry,[status(thm)],[186])).
% 0.93/1.14 tff(188,plain,
% 0.93/1.14 (^[A: $i, B: $i, C: $i] : refl(((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) <=> ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(189,plain,
% 0.93/1.14 (![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) <=> ![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[188])).
% 0.93/1.14 tff(190,plain,
% 0.93/1.14 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) <=> (~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))))), rewrite((~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))))), rewrite(((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(191,plain,
% 0.93/1.14 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[190])).
% 0.93/1.14 tff(192,plain,
% 0.93/1.14 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(193,plain,
% 0.93/1.14 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(194,plain,
% 0.93/1.14 (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[193])).
% 0.93/1.14 tff(195,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k9_group_2')).
% 0.93/1.14 tff(196,plain,
% 0.93/1.14 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.93/1.14 tff(197,plain,
% 0.93/1.14 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.93/1.14 tff(198,plain,(
% 0.93/1.14 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 0.93/1.14 inference(skolemize,[status(sab)],[197])).
% 0.93/1.14 tff(199,plain,
% 0.93/1.14 (![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.93/1.14 tff(200,plain,
% 0.93/1.14 (![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[199, 189])).
% 0.93/1.14 tff(201,plain,
% 0.93/1.14 (((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(202,plain,
% 0.93/1.14 (((k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)) | v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(203,plain,
% 0.93/1.14 (((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | ((k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)) | v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1))))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[202])).
% 0.93/1.14 tff(204,plain,
% 0.93/1.14 (((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | ((k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)) | v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)))),
% 0.93/1.14 inference(transitivity,[status(thm)],[203, 201])).
% 0.93/1.14 tff(205,plain,
% 0.93/1.14 ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | ((k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)) | v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(206,plain,
% 0.93/1.14 ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.93/1.14 tff(207,plain,
% 0.93/1.14 (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[206, 41, 40, 89, 39, 46, 88, 200])).
% 0.93/1.14 tff(208,plain,
% 0.93/1.14 (k9_group_2(A!0, C!2, B!1) = k9_group_2(A!0, B!1, C!2)),
% 0.93/1.14 inference(symmetry,[status(thm)],[207])).
% 0.93/1.14 tff(209,plain,
% 0.93/1.14 (k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k9_group_2(A!0, C!2, B!1)),
% 0.93/1.14 inference(monotonicity,[status(thm)],[69])).
% 0.93/1.14 tff(210,plain,
% 0.93/1.14 (k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k8_group_2(A!0, B!1, C!2)),
% 0.93/1.14 inference(transitivity,[status(thm)],[209, 208, 96])).
% 0.93/1.14 tff(211,plain,
% 0.93/1.14 (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = u1_struct_0(k8_group_2(A!0, B!1, C!2))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[210])).
% 0.93/1.14 tff(212,plain,
% 0.93/1.14 (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2))),
% 0.93/1.14 inference(transitivity,[status(thm)],[211, 187, 98])).
% 0.93/1.14 tff(213,plain,
% 0.93/1.14 ((u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) <=> (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[212, 72])).
% 0.93/1.14 tff(214,plain,
% 0.93/1.14 ((k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))) <=> (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 0.93/1.14 inference(symmetry,[status(thm)],[213])).
% 0.93/1.14 tff(215,plain,
% 0.93/1.14 ((~(k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))) <=> (~(u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[214])).
% 0.93/1.14 tff(216,plain,
% 0.93/1.14 (~(k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))),
% 0.93/1.14 inference(or_elim,[status(thm)],[86])).
% 0.93/1.14 tff(217,plain,
% 0.93/1.14 (~(u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.93/1.14 tff(218,plain,
% 0.93/1.14 (v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) <=> v1_group_1(B!1)),
% 0.93/1.14 inference(monotonicity,[status(thm)],[69])).
% 0.93/1.14 tff(219,plain,
% 0.93/1.14 (v1_group_1(B!1) <=> v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 0.93/1.14 inference(symmetry,[status(thm)],[218])).
% 0.93/1.14 tff(220,plain,
% 0.93/1.14 (v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[63, 219])).
% 0.93/1.14 tff(221,plain,
% 0.93/1.14 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0) <=> m1_group_2(B!1, A!0)),
% 0.93/1.14 inference(monotonicity,[status(thm)],[69])).
% 0.93/1.14 tff(222,plain,
% 0.93/1.14 (m1_group_2(B!1, A!0) <=> m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 0.93/1.14 inference(symmetry,[status(thm)],[221])).
% 0.93/1.14 tff(223,plain,
% 0.93/1.14 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[46, 222])).
% 0.93/1.14 tff(224,plain,
% 0.93/1.14 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(225,plain,
% 0.93/1.14 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[224])).
% 0.93/1.14 tff(226,plain,
% 0.93/1.14 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(227,plain,
% 0.93/1.14 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[226])).
% 0.93/1.14 tff(228,plain,
% 0.93/1.14 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 0.93/1.14 inference(transitivity,[status(thm)],[227, 225])).
% 0.93/1.14 tff(229,plain,
% 0.93/1.14 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_group_1(B) & m1_group_2(B, A)) <=> (~((~v1_group_1(B)) | (~m1_group_2(B, A))))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> (~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))))), rewrite((~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_group_1(C) & m1_group_2(C, A)) <=> (~((~v1_group_1(C)) | (~m1_group_2(C, A))))), ((~(v1_group_1(C) & m1_group_2(C, A))) <=> (~(~((~v1_group_1(C)) | (~m1_group_2(C, A))))))), rewrite((~(~((~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> ((~v1_group_1(C)) | (~m1_group_2(C, A)))), ((~(v1_group_1(C) & m1_group_2(C, A))) <=> ((~v1_group_1(C)) | (~m1_group_2(C, A))))), (((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> (((~v1_group_1(C)) | (~m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))), rewrite((((~v1_group_1(C)) | (~m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))), (((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))), (![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> (((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))), rewrite((((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))))), (![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(230,plain,
% 0.93/1.14 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[229])).
% 0.93/1.14 tff(231,plain,
% 0.93/1.14 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(232,plain,
% 0.93/1.14 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))), (![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), rewrite(((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))))), (![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(233,plain,
% 0.93/1.14 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.15 inference(quant_intro,[status(thm)],[232])).
% 0.93/1.15 tff(234,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_latsubgr')).
% 0.93/1.15 tff(235,plain,
% 0.93/1.15 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.93/1.15 tff(236,plain,
% 0.93/1.15 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.93/1.15 tff(237,plain,(
% 0.93/1.15 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 0.93/1.15 inference(skolemize,[status(sab)],[236])).
% 0.93/1.15 tff(238,plain,
% 0.93/1.15 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.93/1.15 tff(239,plain,
% 0.93/1.15 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[238, 228])).
% 0.93/1.15 tff(240,plain,
% 0.93/1.15 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0)))))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(241,plain,
% 0.93/1.15 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0)))))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(242,plain,
% 0.93/1.15 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[241])).
% 0.93/1.15 tff(243,plain,
% 0.93/1.15 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0)))))),
% 0.93/1.15 inference(transitivity,[status(thm)],[242, 240])).
% 0.93/1.15 tff(244,plain,
% 0.93/1.15 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A!0)))))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(245,plain,
% 0.93/1.15 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.93/1.15 tff(246,plain,
% 0.93/1.15 (![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[245, 41, 40, 89, 39, 239])).
% 0.93/1.15 tff(247,plain,
% 0.93/1.15 (v1_group_1(C!2)),
% 0.93/1.15 inference(and_elim,[status(thm)],[87])).
% 0.93/1.15 tff(248,plain,
% 0.93/1.15 (((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) | ((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C)))))) <=> ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) | (~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C)))))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(249,plain,
% 0.93/1.15 (((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0)))) <=> ((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C)))))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(250,plain,
% 0.93/1.15 (((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) | ((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) <=> ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) | ((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[249])).
% 0.93/1.15 tff(251,plain,
% 0.93/1.15 (((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) | ((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) <=> ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) | (~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C)))))),
% 0.93/1.15 inference(transitivity,[status(thm)],[250, 248])).
% 0.93/1.15 tff(252,plain,
% 0.93/1.15 ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) | ((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(253,plain,
% 0.93/1.15 ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~m1_group_2(C, A!0))))) | (~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.93/1.15 tff(254,plain,
% 0.93/1.15 (![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[253, 247, 88, 246])).
% 0.93/1.15 tff(255,plain,
% 0.93/1.15 (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))) | ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))) <=> ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))) | (~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(256,plain,
% 0.93/1.15 ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))) | ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(257,plain,
% 0.93/1.15 ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))) | (~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.93/1.15 tff(258,plain,
% 0.93/1.15 ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[257, 254])).
% 0.93/1.16 tff(259,plain,
% 0.93/1.16 ($false),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[258, 223, 220, 217])).
% 0.93/1.16 % SZS output end Proof
% 0.93/1.16 % E exiting
%------------------------------------------------------------------------------