%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP642+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:08:16 AM UTC 2025
% Result : Theorem 0.97s 1.15s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP642+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:36:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.97/1.15 % SZS status Theorem
% 0.97/1.15 % SZS output start Proof
% 0.97/1.15 tff(v1_xboole_0_type, type, (
% 0.97/1.15 v1_xboole_0: $i > $o)).
% 0.97/1.15 tff(u1_struct_0_type, type, (
% 0.97/1.15 u1_struct_0: $i > $i)).
% 0.97/1.15 tff(g1_group_1_type, type, (
% 0.97/1.15 g1_group_1: ( $i * $i ) > $i)).
% 0.97/1.15 tff(u1_group_1_type, type, (
% 0.97/1.15 u1_group_1: $i > $i)).
% 0.97/1.15 tff(tptp_fun_B_1_type, type, (
% 0.97/1.15 tptp_fun_B_1: $i)).
% 0.97/1.15 tff(k1_xboole_0_type, type, (
% 0.97/1.15 k1_xboole_0: $i)).
% 0.97/1.15 tff(k1_funct_1_type, type, (
% 0.97/1.15 k1_funct_1: ( $i * $i ) > $i)).
% 0.97/1.15 tff(k1_latsubgr_type, type, (
% 0.97/1.15 k1_latsubgr: $i > $i)).
% 0.97/1.15 tff(tptp_fun_A_0_type, type, (
% 0.97/1.15 tptp_fun_A_0: $i)).
% 0.97/1.15 tff(m1_group_2_type, type, (
% 0.97/1.15 m1_group_2: ( $i * $i ) > $o)).
% 0.97/1.15 tff(v1_group_1_type, type, (
% 0.97/1.15 v1_group_1: $i > $o)).
% 0.97/1.15 tff(l1_group_1_type, type, (
% 0.97/1.15 l1_group_1: $i > $o)).
% 0.97/1.15 tff(v4_group_1_type, type, (
% 0.97/1.15 v4_group_1: $i > $o)).
% 0.97/1.15 tff(v3_group_1_type, type, (
% 0.97/1.15 v3_group_1: $i > $o)).
% 0.97/1.15 tff(v3_struct_0_type, type, (
% 0.97/1.15 v3_struct_0: $i > $o)).
% 0.97/1.15 tff(tptp_fun_C_2_type, type, (
% 0.97/1.15 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.97/1.15 tff(v1_funct_2_type, type, (
% 0.97/1.15 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.97/1.15 tff(k1_zfmisc_1_type, type, (
% 0.97/1.15 k1_zfmisc_1: $i > $i)).
% 0.97/1.15 tff(k1_group_3_type, type, (
% 0.97/1.15 k1_group_3: $i > $i)).
% 0.97/1.15 tff(m2_relset_1_type, type, (
% 0.97/1.15 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.97/1.15 tff(v1_funct_1_type, type, (
% 0.97/1.15 v1_funct_1: $i > $o)).
% 0.97/1.15 tff(l1_struct_0_type, type, (
% 0.97/1.15 l1_struct_0: $i > $o)).
% 0.97/1.15 tff(1,plain,
% 0.97/1.15 ((((~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))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0))))) <=> ((~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))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(2,plain,
% 0.97/1.15 ((~![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))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))) <=> (~![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))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(3,plain,
% 0.97/1.15 ((~![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)) => (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))) <=> (~![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))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4,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)) => (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_latsubgr')).
% 0.97/1.15 tff(5,plain,
% 0.97/1.15 (~![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))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.97/1.15 tff(6,plain,
% 0.97/1.15 (~![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))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.97/1.15 tff(7,plain,
% 0.97/1.15 (~![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))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.97/1.15 tff(8,plain,
% 0.97/1.15 (~![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))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.97/1.15 tff(9,plain,
% 0.97/1.15 ((~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))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.97/1.15 tff(10,plain,
% 0.97/1.15 (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0)))),
% 0.97/1.15 inference(and_elim,[status(thm)],[9])).
% 0.97/1.15 tff(11,plain,
% 0.97/1.15 (k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0),
% 0.97/1.15 inference(or_elim,[status(thm)],[10])).
% 0.97/1.15 tff(12,plain,
% 0.97/1.15 (^[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)))))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(13,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[12])).
% 0.97/1.15 tff(14,plain,
% 0.97/1.15 (^[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)))))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(15,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[14])).
% 0.97/1.15 tff(16,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[15, 13])).
% 0.97/1.15 tff(17,plain,
% 0.97/1.15 (^[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))))))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(18,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[17])).
% 0.97/1.15 tff(19,plain,
% 0.97/1.15 (![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))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(20,plain,
% 0.97/1.15 (^[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))))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(21,plain,
% 0.97/1.15 (![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))))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[20])).
% 0.97/1.15 tff(22,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')).
% 0.97/1.15 tff(23,plain,
% 0.97/1.15 (![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))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.97/1.15 tff(24,plain,
% 0.97/1.15 (![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))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.97/1.15 tff(25,plain,(
% 0.97/1.15 ![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))))),
% 0.97/1.15 inference(skolemize,[status(sab)],[24])).
% 0.97/1.15 tff(26,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.97/1.15 tff(27,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.97/1.15 tff(28,plain,
% 0.97/1.15 (l1_group_1(A!0)),
% 0.97/1.15 inference(and_elim,[status(thm)],[9])).
% 0.97/1.15 tff(29,plain,
% 0.97/1.15 (v3_group_1(A!0)),
% 0.97/1.15 inference(and_elim,[status(thm)],[9])).
% 0.97/1.15 tff(30,plain,
% 0.97/1.15 (~v3_struct_0(A!0)),
% 0.97/1.15 inference(and_elim,[status(thm)],[9])).
% 0.97/1.15 tff(31,plain,
% 0.97/1.15 (((~![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))))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(32,plain,
% 0.97/1.15 ((~![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))))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(33,plain,
% 0.97/1.15 ((~![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)))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.97/1.15 tff(34,plain,
% 0.97/1.15 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[33, 30, 29, 28, 27])).
% 0.97/1.15 tff(35,plain,
% 0.97/1.15 (v1_group_1(B!1) & m1_group_2(B!1, A!0)),
% 0.97/1.15 inference(or_elim,[status(thm)],[10])).
% 0.97/1.15 tff(36,plain,
% 0.97/1.15 (m1_group_2(B!1, A!0)),
% 0.97/1.15 inference(and_elim,[status(thm)],[35])).
% 0.97/1.15 tff(37,plain,
% 0.97/1.15 (((~![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)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(38,plain,
% 0.97/1.15 ((~![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)))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(39,plain,
% 0.97/1.15 ((~![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))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.97/1.15 tff(40,plain,
% 0.97/1.15 (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[39, 36, 34])).
% 0.97/1.15 tff(41,plain,
% 0.97/1.15 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | l1_group_1(B!1)),
% 0.97/1.15 inference(tautology,[status(thm)],[])).
% 0.97/1.15 tff(42,plain,
% 0.97/1.15 (l1_group_1(B!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.97/1.15 tff(43,plain,
% 0.97/1.15 (^[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))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(44,plain,
% 0.97/1.15 (![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)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[43])).
% 0.97/1.15 tff(45,plain,
% 0.97/1.15 (![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)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(46,plain,
% 0.97/1.15 (^[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)))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(47,plain,
% 0.97/1.15 (![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)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[46])).
% 0.97/1.15 tff(48,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')).
% 0.97/1.15 tff(49,plain,
% 0.97/1.15 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.97/1.15 tff(50,plain,
% 0.97/1.15 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.97/1.15 tff(51,plain,(
% 0.97/1.15 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.97/1.15 inference(skolemize,[status(sab)],[50])).
% 0.97/1.15 tff(52,plain,
% 0.97/1.15 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.97/1.15 tff(53,plain,
% 0.97/1.15 (v1_group_1(B!1)),
% 0.97/1.15 inference(and_elim,[status(thm)],[35])).
% 0.97/1.15 tff(54,plain,
% 0.97/1.15 (((~![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)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(55,plain,
% 0.97/1.15 ((~![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)))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(56,plain,
% 0.97/1.15 ((~![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))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.97/1.15 tff(57,plain,
% 0.97/1.15 ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(B!1))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 0.97/1.15 tff(58,plain,
% 0.97/1.15 (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[57, 42])).
% 0.97/1.15 tff(59,plain,
% 0.97/1.15 (g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)) = B!1),
% 0.97/1.15 inference(symmetry,[status(thm)],[58])).
% 0.97/1.15 tff(60,plain,
% 0.97/1.15 (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)),
% 0.97/1.15 inference(monotonicity,[status(thm)],[59])).
% 0.97/1.15 tff(61,plain,
% 0.97/1.15 (v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) <=> v1_group_1(B!1)),
% 0.97/1.15 inference(monotonicity,[status(thm)],[59])).
% 0.97/1.15 tff(62,plain,
% 0.97/1.15 (v1_group_1(B!1) <=> v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 0.97/1.15 inference(symmetry,[status(thm)],[61])).
% 0.97/1.15 tff(63,plain,
% 0.97/1.15 (v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[53, 62])).
% 0.97/1.15 tff(64,plain,
% 0.97/1.15 (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)),
% 0.97/1.15 inference(monotonicity,[status(thm)],[59])).
% 0.97/1.15 tff(65,plain,
% 0.97/1.15 (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)),
% 0.97/1.15 inference(symmetry,[status(thm)],[64])).
% 0.97/1.15 tff(66,plain,
% 0.97/1.15 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[36, 65])).
% 0.97/1.15 tff(67,plain,
% 0.97/1.15 (^[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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(68,plain,
% 0.97/1.15 (![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[67])).
% 0.97/1.15 tff(69,plain,
% 0.97/1.15 (^[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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(70,plain,
% 0.97/1.15 (![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[69])).
% 0.97/1.15 tff(71,plain,
% 0.97/1.15 (![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[70, 68])).
% 0.97/1.15 tff(72,plain,
% 0.97/1.15 (^[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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))))) <=> (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))), (((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))), rewrite(((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))), (((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(73,plain,
% 0.97/1.15 (![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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[72])).
% 0.97/1.15 tff(74,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(75,plain,
% 0.97/1.15 (^[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))))))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(76,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[75])).
% 0.97/1.15 tff(77,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')).
% 0.97/1.15 tff(78,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.97/1.15 tff(79,plain,
% 0.97/1.15 (![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))))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.97/1.15 tff(80,plain,(
% 0.97/1.15 ![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_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))))))),
% 0.97/1.15 inference(skolemize,[status(sab)],[79])).
% 0.97/1.15 tff(81,plain,
% 0.97/1.15 (![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.97/1.15 tff(82,plain,
% 0.97/1.15 (![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.97/1.15 tff(83,plain,
% 0.97/1.15 (v4_group_1(A!0)),
% 0.97/1.15 inference(and_elim,[status(thm)],[9])).
% 0.97/1.15 tff(84,plain,
% 0.97/1.15 (((~![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0)))))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(85,plain,
% 0.97/1.16 ((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_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0)))))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(86,plain,
% 0.97/1.16 (((~![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))))))))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[85])).
% 0.97/1.16 tff(87,plain,
% 0.97/1.16 (((~![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0)))))))))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[86, 84])).
% 0.97/1.16 tff(88,plain,
% 0.97/1.16 ((~![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0))))))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(89,plain,
% 0.97/1.16 ((~![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_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))))))))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.97/1.16 tff(90,plain,
% 0.97/1.16 (![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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))))))))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[89, 30, 29, 83, 28, 82])).
% 0.97/1.16 tff(91,plain,
% 0.97/1.16 (^[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))))))))),
% 0.97/1.16 inference(bind,[status(th)],[])).
% 0.97/1.16 tff(92,plain,
% 0.97/1.16 (![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)))))))),
% 0.97/1.16 inference(quant_intro,[status(thm)],[91])).
% 0.97/1.16 tff(93,plain,
% 0.97/1.16 (^[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)))))))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(94,plain,
% 1.00/1.16 (![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)))))))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[93])).
% 1.00/1.16 tff(95,plain,
% 1.00/1.16 (![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)))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(96,plain,
% 1.00/1.16 (^[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)))))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(97,plain,
% 1.00/1.16 (![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)))))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[96])).
% 1.00/1.16 tff(98,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')).
% 1.00/1.16 tff(99,plain,
% 1.00/1.16 (![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)))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.00/1.16 tff(100,plain,
% 1.00/1.16 (![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)))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[99, 95])).
% 1.00/1.16 tff(101,plain,(
% 1.00/1.16 ![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)))))),
% 1.00/1.16 inference(skolemize,[status(sab)],[100])).
% 1.00/1.16 tff(102,plain,
% 1.00/1.16 (![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)))))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[101, 94])).
% 1.00/1.16 tff(103,plain,
% 1.00/1.16 (![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)))))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[102, 92])).
% 1.00/1.16 tff(104,plain,
% 1.00/1.16 (((~![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)))))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(105,plain,
% 1.00/1.16 ((~![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)))))))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(106,plain,
% 1.00/1.16 ((~![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))))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.00/1.16 tff(107,plain,
% 1.00/1.16 (~((~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)))))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[106, 30, 29, 83, 28, 103])).
% 1.00/1.16 tff(108,plain,
% 1.00/1.16 (((~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)))),
% 1.00/1.16 inference(tautology,[status(thm)],[])).
% 1.00/1.16 tff(109,plain,
% 1.00/1.16 (m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[108, 107])).
% 1.00/1.16 tff(110,plain,
% 1.00/1.16 (((~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)))),
% 1.00/1.16 inference(tautology,[status(thm)],[])).
% 1.00/1.16 tff(111,plain,
% 1.00/1.16 (v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[110, 107])).
% 1.00/1.16 tff(112,plain,
% 1.00/1.16 (((~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))),
% 1.00/1.16 inference(tautology,[status(thm)],[])).
% 1.00/1.16 tff(113,plain,
% 1.00/1.16 (v1_funct_1(k1_latsubgr(A!0))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[112, 107])).
% 1.00/1.16 tff(114,plain,
% 1.00/1.16 (((~![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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(115,plain,
% 1.00/1.16 (((~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_2(k1_latsubgr(A!0), A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(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))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(116,plain,
% 1.00/1.16 (((~![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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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_2(k1_latsubgr(A!0), A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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)))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[115])).
% 1.00/1.16 tff(117,plain,
% 1.00/1.16 (((~![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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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_2(k1_latsubgr(A!0), A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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))))),
% 1.00/1.16 inference(transitivity,[status(thm)],[116, 114])).
% 1.00/1.16 tff(118,plain,
% 1.00/1.16 ((~![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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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_2(k1_latsubgr(A!0), A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))))))))))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(119,plain,
% 1.00/1.16 ((~![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_2(B, A!0), A!0)) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(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)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.00/1.16 tff(120,plain,
% 1.00/1.16 (![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[119, 113, 111, 109, 90])).
% 1.00/1.16 tff(121,plain,
% 1.00/1.16 (((~![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(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)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_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)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_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)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(122,plain,
% 1.00/1.16 ((~![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(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)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(123,plain,
% 1.00/1.16 ((~![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(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)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.00/1.16 tff(124,plain,
% 1.00/1.16 ((~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)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[123, 120])).
% 1.00/1.16 tff(125,plain,
% 1.00/1.16 (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[124, 66, 63])).
% 1.00/1.16 tff(126,plain,
% 1.00/1.16 (u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.00/1.16 inference(symmetry,[status(thm)],[125])).
% 1.00/1.16 tff(127,plain,
% 1.00/1.16 (u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k1_xboole_0),
% 1.00/1.16 inference(transitivity,[status(thm)],[126, 60, 11])).
% 1.00/1.16 tff(128,plain,
% 1.00/1.16 (v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) <=> v1_xboole_0(k1_xboole_0)),
% 1.00/1.16 inference(monotonicity,[status(thm)],[127])).
% 1.00/1.16 tff(129,plain,
% 1.00/1.16 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 1.00/1.16 inference(symmetry,[status(thm)],[128])).
% 1.00/1.16 tff(130,plain,
% 1.00/1.16 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(131,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 1.00/1.16 tff(132,plain,
% 1.00/1.16 (v1_xboole_0(k1_xboole_0)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.00/1.16 tff(133,plain,
% 1.00/1.16 (v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[132, 129])).
% 1.00/1.16 tff(134,plain,
% 1.00/1.16 (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) <=> v3_struct_0(B!1)),
% 1.00/1.16 inference(monotonicity,[status(thm)],[59])).
% 1.00/1.16 tff(135,plain,
% 1.00/1.16 (v3_struct_0(B!1) <=> v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.00/1.16 inference(symmetry,[status(thm)],[134])).
% 1.00/1.16 tff(136,plain,
% 1.00/1.16 ((~v3_struct_0(B!1)) <=> (~v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[135])).
% 1.00/1.16 tff(137,plain,
% 1.00/1.16 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | (~v3_struct_0(B!1))),
% 1.00/1.16 inference(tautology,[status(thm)],[])).
% 1.00/1.16 tff(138,plain,
% 1.00/1.16 (~v3_struct_0(B!1)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[137, 40])).
% 1.00/1.16 tff(139,plain,
% 1.00/1.16 (~v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[138, 136])).
% 1.00/1.16 tff(140,plain,
% 1.00/1.16 (l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) <=> l1_group_1(B!1)),
% 1.00/1.16 inference(monotonicity,[status(thm)],[59])).
% 1.00/1.16 tff(141,plain,
% 1.00/1.16 (l1_group_1(B!1) <=> l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.00/1.16 inference(symmetry,[status(thm)],[140])).
% 1.00/1.16 tff(142,plain,
% 1.00/1.16 (l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[42, 141])).
% 1.00/1.16 tff(143,plain,
% 1.00/1.16 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(144,plain,
% 1.00/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[143])).
% 1.00/1.16 tff(145,plain,
% 1.00/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(146,plain,
% 1.00/1.16 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(147,plain,
% 1.00/1.16 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[146])).
% 1.00/1.16 tff(148,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 1.00/1.16 tff(149,plain,
% 1.00/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.00/1.16 tff(150,plain,
% 1.00/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[149, 145])).
% 1.00/1.16 tff(151,plain,(
% 1.00/1.16 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.00/1.16 inference(skolemize,[status(sab)],[150])).
% 1.00/1.16 tff(152,plain,
% 1.00/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[151, 144])).
% 1.00/1.16 tff(153,plain,
% 1.00/1.16 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(154,plain,
% 1.00/1.16 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(155,plain,
% 1.00/1.16 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.00/1.16 tff(156,plain,
% 1.00/1.16 (l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[155, 152])).
% 1.00/1.16 tff(157,plain,
% 1.00/1.16 (l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[156, 142])).
% 1.00/1.16 tff(158,plain,
% 1.00/1.16 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(159,plain,
% 1.00/1.16 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[158])).
% 1.00/1.16 tff(160,plain,
% 1.00/1.16 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(161,plain,
% 1.00/1.16 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[160])).
% 1.00/1.16 tff(162,plain,
% 1.00/1.16 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(163,plain,
% 1.00/1.16 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(164,plain,
% 1.00/1.16 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[163])).
% 1.00/1.16 tff(165,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 1.00/1.16 tff(166,plain,
% 1.00/1.16 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.00/1.16 tff(167,plain,
% 1.00/1.16 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[166, 162])).
% 1.00/1.16 tff(168,plain,(
% 1.00/1.16 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.00/1.16 inference(skolemize,[status(sab)],[167])).
% 1.00/1.16 tff(169,plain,
% 1.00/1.16 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[168, 161])).
% 1.00/1.16 tff(170,plain,
% 1.00/1.16 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[169, 159])).
% 1.00/1.16 tff(171,plain,
% 1.00/1.16 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(172,plain,
% 1.00/1.16 ((v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) <=> (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(173,plain,
% 1.00/1.16 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[172])).
% 1.00/1.17 tff(174,plain,
% 1.00/1.17 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 1.00/1.17 inference(transitivity,[status(thm)],[173, 171])).
% 1.00/1.17 tff(175,plain,
% 1.00/1.17 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(176,plain,
% 1.00/1.17 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.00/1.17 tff(177,plain,
% 1.00/1.17 (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[176, 170])).
% 1.00/1.17 tff(178,plain,
% 1.00/1.17 (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[177, 157, 139])).
% 1.00/1.17 tff(179,plain,
% 1.00/1.17 ($false),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[178, 133])).
% 1.00/1.17 % SZS output end Proof
% 1.00/1.17 % E exiting
%------------------------------------------------------------------------------