TSTP Solution File: GRP645+1 by Z3---4.8.9.0

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GRP645+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n008.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 : Fri Sep 16 22:29:07 EDT 2022

% Result   : Theorem 1.32s 1.09s
% Output   : Proof 1.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP645+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n008.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Aug 31 19:05:25 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 1.32/1.09  % SZS status Theorem
% 1.32/1.09  % SZS output start Proof
% 1.32/1.09  tff(k3_xboole_0_type, type, (
% 1.32/1.09     k3_xboole_0: ( $i * $i ) > $i)).
% 1.32/1.09  tff(k1_funct_1_type, type, (
% 1.32/1.09     k1_funct_1: ( $i * $i ) > $i)).
% 1.32/1.09  tff(g1_group_1_type, type, (
% 1.32/1.09     g1_group_1: ( $i * $i ) > $i)).
% 1.32/1.09  tff(u1_group_1_type, type, (
% 1.32/1.09     u1_group_1: $i > $i)).
% 1.32/1.09  tff(tptp_fun_B_1_type, type, (
% 1.32/1.09     tptp_fun_B_1: $i)).
% 1.32/1.09  tff(u1_struct_0_type, type, (
% 1.32/1.09     u1_struct_0: $i > $i)).
% 1.32/1.09  tff(k1_latsubgr_type, type, (
% 1.32/1.09     k1_latsubgr: $i > $i)).
% 1.32/1.09  tff(tptp_fun_A_0_type, type, (
% 1.32/1.09     tptp_fun_A_0: $i)).
% 1.32/1.09  tff(tptp_fun_C_2_type, type, (
% 1.32/1.09     tptp_fun_C_2: $i)).
% 1.32/1.09  tff(k9_group_2_type, type, (
% 1.32/1.09     k9_group_2: ( $i * $i * $i ) > $i)).
% 1.32/1.09  tff(l1_group_1_type, type, (
% 1.32/1.09     l1_group_1: $i > $o)).
% 1.32/1.09  tff(v3_group_1_type, type, (
% 1.32/1.09     v3_group_1: $i > $o)).
% 1.32/1.09  tff(v3_struct_0_type, type, (
% 1.32/1.09     v3_struct_0: $i > $o)).
% 1.32/1.09  tff(m1_group_2_type, type, (
% 1.32/1.09     m1_group_2: ( $i * $i ) > $o)).
% 1.32/1.09  tff(v1_group_1_type, type, (
% 1.32/1.09     v1_group_1: $i > $o)).
% 1.32/1.09  tff(v4_group_1_type, type, (
% 1.32/1.09     v4_group_1: $i > $o)).
% 1.32/1.09  tff(k8_group_2_type, type, (
% 1.32/1.09     k8_group_2: ( $i * $i * $i ) > $i)).
% 1.32/1.09  tff(tptp_fun_C_3_type, type, (
% 1.32/1.09     tptp_fun_C_3: ( $i * $i ) > $i)).
% 1.32/1.09  tff(m2_relset_1_type, type, (
% 1.32/1.09     m2_relset_1: ( $i * $i * $i ) > $o)).
% 1.32/1.09  tff(k1_zfmisc_1_type, type, (
% 1.32/1.09     k1_zfmisc_1: $i > $i)).
% 1.32/1.09  tff(k1_group_3_type, type, (
% 1.32/1.09     k1_group_3: $i > $i)).
% 1.32/1.09  tff(v1_funct_2_type, type, (
% 1.32/1.09     v1_funct_2: ( $i * $i * $i ) > $o)).
% 1.32/1.09  tff(v1_funct_1_type, type, (
% 1.32/1.09     v1_funct_1: $i > $o)).
% 1.32/1.09  tff(1,plain,
% 1.32/1.09      (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 1.32/1.09      inference(bind,[status(th)],[])).
% 1.32/1.09  tff(2,plain,
% 1.32/1.09      (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.32/1.09      inference(quant_intro,[status(thm)],[1])).
% 1.32/1.09  tff(3,plain,
% 1.32/1.09      (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.32/1.09      inference(rewrite,[status(thm)],[])).
% 1.32/1.09  tff(4,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 1.32/1.09  tff(5,plain,
% 1.32/1.09      (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.32/1.09      inference(modus_ponens,[status(thm)],[4, 3])).
% 1.32/1.09  tff(6,plain,(
% 1.32/1.09      ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.32/1.09      inference(skolemize,[status(sab)],[5])).
% 1.32/1.09  tff(7,plain,
% 1.32/1.09      (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.32/1.09      inference(modus_ponens,[status(thm)],[6, 2])).
% 1.32/1.09  tff(8,plain,
% 1.32/1.09      ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), B!1)))),
% 1.32/1.09      inference(quant_inst,[status(thm)],[])).
% 1.32/1.09  tff(9,plain,
% 1.32/1.09      (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), B!1))),
% 1.32/1.09      inference(unit_resolution,[status(thm)],[8, 7])).
% 1.32/1.09  tff(10,plain,
% 1.32/1.09      (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))),
% 1.32/1.09      inference(symmetry,[status(thm)],[9])).
% 1.32/1.09  tff(11,plain,
% 1.32/1.09      (^[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)))))))),
% 1.32/1.09      inference(bind,[status(th)],[])).
% 1.32/1.09  tff(12,plain,
% 1.32/1.09      (![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))))))),
% 1.32/1.09      inference(quant_intro,[status(thm)],[11])).
% 1.32/1.09  tff(13,plain,
% 1.32/1.09      (^[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)))))))),
% 1.32/1.09      inference(bind,[status(th)],[])).
% 1.32/1.09  tff(14,plain,
% 1.32/1.09      (![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))))))),
% 1.32/1.09      inference(quant_intro,[status(thm)],[13])).
% 1.32/1.09  tff(15,plain,
% 1.32/1.09      (![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))))))),
% 1.32/1.09      inference(transitivity,[status(thm)],[14, 12])).
% 1.32/1.09  tff(16,plain,
% 1.32/1.09      (^[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))))))))),
% 1.32/1.09      inference(bind,[status(th)],[])).
% 1.32/1.09  tff(17,plain,
% 1.32/1.09      (![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))))))),
% 1.32/1.09      inference(quant_intro,[status(thm)],[16])).
% 1.32/1.09  tff(18,plain,
% 1.32/1.09      (![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))))),
% 1.32/1.09      inference(rewrite,[status(thm)],[])).
% 1.32/1.09  tff(19,plain,
% 1.32/1.09      (^[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))))))),
% 1.32/1.09      inference(bind,[status(th)],[])).
% 1.32/1.09  tff(20,plain,
% 1.32/1.09      (![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))))),
% 1.32/1.09      inference(quant_intro,[status(thm)],[19])).
% 1.32/1.09  tff(21,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_group_2')).
% 1.32/1.09  tff(22,plain,
% 1.32/1.09      (![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))))),
% 1.32/1.09      inference(modus_ponens,[status(thm)],[21, 20])).
% 1.32/1.09  tff(23,plain,
% 1.32/1.09      (![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))))),
% 1.32/1.09      inference(modus_ponens,[status(thm)],[22, 18])).
% 1.32/1.09  tff(24,plain,(
% 1.32/1.09      ![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))))),
% 1.32/1.09      inference(skolemize,[status(sab)],[23])).
% 1.32/1.09  tff(25,plain,
% 1.32/1.09      (![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))))))),
% 1.32/1.09      inference(modus_ponens,[status(thm)],[24, 17])).
% 1.32/1.09  tff(26,plain,
% 1.32/1.09      (![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))))))),
% 1.32/1.09      inference(modus_ponens,[status(thm)],[25, 15])).
% 1.32/1.09  tff(27,plain,
% 1.32/1.09      ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(28,plain,
% 1.32/1.10      (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(29,plain,
% 1.32/1.10      ((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(30,plain,
% 1.32/1.10      (((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))))) <=> ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))),
% 1.32/1.10      inference(monotonicity,[status(thm)],[29])).
% 1.32/1.10  tff(31,plain,
% 1.32/1.10      (((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))),
% 1.32/1.10      inference(transitivity,[status(thm)],[30, 28])).
% 1.32/1.10  tff(32,plain,
% 1.32/1.10      ((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(33,plain,
% 1.32/1.10      (((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) & ((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))))))),
% 1.32/1.10      inference(monotonicity,[status(thm)],[32, 31])).
% 1.32/1.10  tff(34,plain,
% 1.32/1.10      (((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) & ((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))))),
% 1.32/1.10      inference(transitivity,[status(thm)],[33, 27])).
% 1.32/1.10  tff(35,plain,
% 1.32/1.10      ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(36,plain,
% 1.32/1.10      ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(37,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_latsubgr')).
% 1.32/1.10  tff(38,plain,
% 1.32/1.10      (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[37, 36])).
% 1.32/1.10  tff(39,plain,
% 1.32/1.10      (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[38, 35])).
% 1.32/1.10  tff(40,plain,
% 1.32/1.10      (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[39, 35])).
% 1.32/1.10  tff(41,plain,
% 1.32/1.10      (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[40, 35])).
% 1.32/1.10  tff(42,plain,
% 1.32/1.10      (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[41, 35])).
% 1.32/1.10  tff(43,plain,
% 1.32/1.10      (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[42, 35])).
% 1.32/1.10  tff(44,plain,
% 1.32/1.10      (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(k1_latsubgr(A), k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[43, 35])).
% 1.32/1.10  tff(45,plain,
% 1.32/1.10      ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[44, 34])).
% 1.32/1.10  tff(46,plain,
% 1.32/1.10      (l1_group_1(A!0)),
% 1.32/1.10      inference(and_elim,[status(thm)],[45])).
% 1.32/1.10  tff(47,plain,
% 1.32/1.10      (v3_group_1(A!0)),
% 1.32/1.10      inference(and_elim,[status(thm)],[45])).
% 1.32/1.10  tff(48,plain,
% 1.32/1.10      (~v3_struct_0(A!0)),
% 1.32/1.10      inference(and_elim,[status(thm)],[45])).
% 1.32/1.10  tff(49,plain,
% 1.32/1.10      (((~![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))))))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(50,plain,
% 1.32/1.10      ((~![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))))))),
% 1.32/1.10      inference(quant_inst,[status(thm)],[])).
% 1.32/1.10  tff(51,plain,
% 1.32/1.10      ((~![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)))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[50, 49])).
% 1.32/1.10  tff(52,plain,
% 1.32/1.10      (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[51, 48, 47, 46, 26])).
% 1.32/1.10  tff(53,plain,
% 1.32/1.10      (m1_group_2(B!1, A!0)),
% 1.32/1.10      inference(and_elim,[status(thm)],[45])).
% 1.32/1.10  tff(54,plain,
% 1.32/1.10      (((~![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)))))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(55,plain,
% 1.32/1.10      ((~![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)))))),
% 1.32/1.10      inference(quant_inst,[status(thm)],[])).
% 1.32/1.10  tff(56,plain,
% 1.32/1.10      ((~![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))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[55, 54])).
% 1.32/1.10  tff(57,plain,
% 1.32/1.10      (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[56, 53, 52])).
% 1.32/1.10  tff(58,plain,
% 1.32/1.10      ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | l1_group_1(B!1)),
% 1.32/1.10      inference(tautology,[status(thm)],[])).
% 1.32/1.10  tff(59,plain,
% 1.32/1.10      (l1_group_1(B!1)),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[58, 57])).
% 1.32/1.10  tff(60,plain,
% 1.32/1.10      (^[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))))),
% 1.32/1.10      inference(bind,[status(th)],[])).
% 1.32/1.10  tff(61,plain,
% 1.32/1.10      (![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)))),
% 1.32/1.10      inference(quant_intro,[status(thm)],[60])).
% 1.32/1.10  tff(62,plain,
% 1.32/1.10      (![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)))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(63,plain,
% 1.32/1.10      (^[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)))))),
% 1.32/1.10      inference(bind,[status(th)],[])).
% 1.32/1.10  tff(64,plain,
% 1.32/1.10      (![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)))),
% 1.32/1.10      inference(quant_intro,[status(thm)],[63])).
% 1.32/1.10  tff(65,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')).
% 1.32/1.10  tff(66,plain,
% 1.32/1.10      (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[65, 64])).
% 1.32/1.10  tff(67,plain,
% 1.32/1.10      (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[66, 62])).
% 1.32/1.10  tff(68,plain,(
% 1.32/1.10      ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.32/1.10      inference(skolemize,[status(sab)],[67])).
% 1.32/1.10  tff(69,plain,
% 1.32/1.10      (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[68, 61])).
% 1.32/1.10  tff(70,plain,
% 1.32/1.10      (v1_group_1(B!1)),
% 1.32/1.10      inference(and_elim,[status(thm)],[45])).
% 1.32/1.10  tff(71,plain,
% 1.32/1.10      (((~![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)))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(72,plain,
% 1.32/1.10      ((~![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)))),
% 1.32/1.10      inference(quant_inst,[status(thm)],[])).
% 1.32/1.10  tff(73,plain,
% 1.32/1.10      ((~![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))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[72, 71])).
% 1.32/1.10  tff(74,plain,
% 1.32/1.10      ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(B!1))),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[73, 70, 69])).
% 1.32/1.10  tff(75,plain,
% 1.32/1.10      (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[74, 59])).
% 1.32/1.10  tff(76,plain,
% 1.32/1.10      (g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)) = B!1),
% 1.32/1.10      inference(symmetry,[status(thm)],[75])).
% 1.32/1.10  tff(77,plain,
% 1.32/1.10      (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)),
% 1.32/1.10      inference(monotonicity,[status(thm)],[76])).
% 1.32/1.10  tff(78,plain,
% 1.32/1.10      (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), B!1))),
% 1.32/1.10      inference(monotonicity,[status(thm)],[77])).
% 1.32/1.10  tff(79,plain,
% 1.32/1.10      (k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))),
% 1.32/1.10      inference(transitivity,[status(thm)],[78, 10])).
% 1.32/1.10  tff(80,plain,
% 1.32/1.10      (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) <=> (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))),
% 1.32/1.10      inference(bind,[status(th)],[])).
% 1.32/1.10  tff(81,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 1.32/1.10      inference(quant_intro,[status(thm)],[80])).
% 1.32/1.10  tff(82,plain,
% 1.32/1.10      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) <=> (~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))))), rewrite((~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))))), rewrite(((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))))),
% 1.32/1.10      inference(bind,[status(th)],[])).
% 1.32/1.10  tff(83,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 1.32/1.10      inference(quant_intro,[status(thm)],[82])).
% 1.32/1.10  tff(84,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(85,plain,
% 1.32/1.10      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))))),
% 1.32/1.10      inference(bind,[status(th)],[])).
% 1.32/1.10  tff(86,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 1.32/1.10      inference(quant_intro,[status(thm)],[85])).
% 1.32/1.10  tff(87,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k8_group_2(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k9_group_2')).
% 1.32/1.10  tff(88,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[87, 86])).
% 1.32/1.10  tff(89,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[88, 84])).
% 1.32/1.10  tff(90,plain,(
% 1.32/1.10      ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)))),
% 1.32/1.10      inference(skolemize,[status(sab)],[89])).
% 1.32/1.10  tff(91,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[90, 83])).
% 1.32/1.10  tff(92,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[91, 81])).
% 1.32/1.10  tff(93,plain,
% 1.32/1.10      (~((~(v1_group_1(C!2) & m1_group_2(C!2, A!0))) | (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))))),
% 1.32/1.10      inference(and_elim,[status(thm)],[45])).
% 1.32/1.10  tff(94,plain,
% 1.32/1.10      (v1_group_1(C!2) & m1_group_2(C!2, A!0)),
% 1.32/1.10      inference(or_elim,[status(thm)],[93])).
% 1.32/1.10  tff(95,plain,
% 1.32/1.10      (m1_group_2(C!2, A!0)),
% 1.32/1.10      inference(and_elim,[status(thm)],[94])).
% 1.32/1.10  tff(96,plain,
% 1.32/1.10      (v4_group_1(A!0)),
% 1.32/1.10      inference(and_elim,[status(thm)],[45])).
% 1.32/1.10  tff(97,plain,
% 1.32/1.10      (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(98,plain,
% 1.32/1.10      ((v3_struct_0(A!0) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(99,plain,
% 1.32/1.10      (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0))))),
% 1.32/1.10      inference(monotonicity,[status(thm)],[98])).
% 1.32/1.10  tff(100,plain,
% 1.32/1.10      (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 1.32/1.10      inference(transitivity,[status(thm)],[99, 97])).
% 1.32/1.10  tff(101,plain,
% 1.32/1.10      ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 1.32/1.10      inference(quant_inst,[status(thm)],[])).
% 1.32/1.10  tff(102,plain,
% 1.32/1.10      ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k9_group_2(A, B, C) = k8_group_2(A, B, C)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[101, 100])).
% 1.32/1.10  tff(103,plain,
% 1.32/1.10      (k9_group_2(A!0, B!1, C!2) = k8_group_2(A!0, B!1, C!2)),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[102, 48, 47, 96, 46, 53, 95, 92])).
% 1.32/1.10  tff(104,plain,
% 1.32/1.10      (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2))),
% 1.32/1.10      inference(monotonicity,[status(thm)],[103])).
% 1.32/1.10  tff(105,plain,
% 1.32/1.10      (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2))),
% 1.32/1.10      inference(symmetry,[status(thm)],[104])).
% 1.32/1.10  tff(106,plain,
% 1.32/1.10      (k8_group_2(A!0, B!1, C!2) = k9_group_2(A!0, B!1, C!2)),
% 1.32/1.10      inference(symmetry,[status(thm)],[103])).
% 1.32/1.10  tff(107,plain,
% 1.32/1.10      (m1_group_2(k8_group_2(A!0, B!1, C!2), A!0) <=> m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)),
% 1.32/1.10      inference(monotonicity,[status(thm)],[106])).
% 1.32/1.10  tff(108,plain,
% 1.32/1.10      (m1_group_2(k9_group_2(A!0, B!1, C!2), A!0) <=> m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)),
% 1.32/1.10      inference(symmetry,[status(thm)],[107])).
% 1.32/1.10  tff(109,plain,
% 1.32/1.10      (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))))),
% 1.32/1.10      inference(bind,[status(th)],[])).
% 1.32/1.10  tff(110,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))),
% 1.32/1.10      inference(quant_intro,[status(thm)],[109])).
% 1.32/1.10  tff(111,plain,
% 1.32/1.10      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) <=> (~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))))), rewrite((~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), rewrite((v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)) <=> (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))))), rewrite(((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))))),
% 1.32/1.10      inference(bind,[status(th)],[])).
% 1.32/1.10  tff(112,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))),
% 1.32/1.10      inference(quant_intro,[status(thm)],[111])).
% 1.32/1.10  tff(113,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(114,plain,
% 1.32/1.10      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))))),
% 1.32/1.10      inference(bind,[status(th)],[])).
% 1.32/1.10  tff(115,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 1.32/1.10      inference(quant_intro,[status(thm)],[114])).
% 1.32/1.10  tff(116,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k9_group_2')).
% 1.32/1.10  tff(117,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[116, 115])).
% 1.32/1.10  tff(118,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[117, 113])).
% 1.32/1.10  tff(119,plain,(
% 1.32/1.10      ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (v1_group_1(k9_group_2(A, B, C)) & m1_group_2(k9_group_2(A, B, C), A)))),
% 1.32/1.10      inference(skolemize,[status(sab)],[118])).
% 1.32/1.10  tff(120,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[119, 112])).
% 1.32/1.10  tff(121,plain,
% 1.32/1.10      (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[120, 110])).
% 1.32/1.10  tff(122,plain,
% 1.32/1.10      (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(123,plain,
% 1.32/1.10      ((v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))),
% 1.32/1.10      inference(rewrite,[status(thm)],[])).
% 1.32/1.10  tff(124,plain,
% 1.32/1.10      (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))))))),
% 1.32/1.10      inference(monotonicity,[status(thm)],[123])).
% 1.32/1.10  tff(125,plain,
% 1.32/1.10      (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))),
% 1.32/1.10      inference(transitivity,[status(thm)],[124, 122])).
% 1.32/1.10  tff(126,plain,
% 1.32/1.10      ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))))),
% 1.32/1.10      inference(quant_inst,[status(thm)],[])).
% 1.32/1.10  tff(127,plain,
% 1.32/1.10      ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)) | (~((~v1_group_1(k9_group_2(A, B, C))) | (~m1_group_2(k9_group_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[126, 125])).
% 1.32/1.10  tff(128,plain,
% 1.32/1.10      (~((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)))),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[127, 48, 47, 96, 46, 53, 95, 121])).
% 1.32/1.10  tff(129,plain,
% 1.32/1.10      (((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))) | m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)),
% 1.32/1.10      inference(tautology,[status(thm)],[])).
% 1.32/1.10  tff(130,plain,
% 1.32/1.10      (m1_group_2(k9_group_2(A!0, B!1, C!2), A!0)),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[129, 128])).
% 1.32/1.10  tff(131,plain,
% 1.32/1.10      (m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[130, 108])).
% 1.32/1.10  tff(132,plain,
% 1.32/1.10      (v1_group_1(k8_group_2(A!0, B!1, C!2)) <=> v1_group_1(k9_group_2(A!0, B!1, C!2))),
% 1.32/1.10      inference(monotonicity,[status(thm)],[106])).
% 1.32/1.10  tff(133,plain,
% 1.32/1.10      (v1_group_1(k9_group_2(A!0, B!1, C!2)) <=> v1_group_1(k8_group_2(A!0, B!1, C!2))),
% 1.32/1.10      inference(symmetry,[status(thm)],[132])).
% 1.32/1.10  tff(134,plain,
% 1.32/1.10      (((~v1_group_1(k9_group_2(A!0, B!1, C!2))) | (~m1_group_2(k9_group_2(A!0, B!1, C!2), A!0))) | v1_group_1(k9_group_2(A!0, B!1, C!2))),
% 1.32/1.10      inference(tautology,[status(thm)],[])).
% 1.32/1.10  tff(135,plain,
% 1.32/1.10      (v1_group_1(k9_group_2(A!0, B!1, C!2))),
% 1.32/1.10      inference(unit_resolution,[status(thm)],[134, 128])).
% 1.32/1.10  tff(136,plain,
% 1.32/1.10      (v1_group_1(k8_group_2(A!0, B!1, C!2))),
% 1.32/1.10      inference(modus_ponens,[status(thm)],[135, 133])).
% 1.32/1.10  tff(137,plain,
% 1.32/1.10      (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))))),
% 1.32/1.11      inference(bind,[status(th)],[])).
% 1.32/1.11  tff(138,plain,
% 1.32/1.11      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 1.32/1.11      inference(quant_intro,[status(thm)],[137])).
% 1.32/1.11  tff(139,plain,
% 1.32/1.11      (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))))),
% 1.32/1.11      inference(bind,[status(th)],[])).
% 1.32/1.11  tff(140,plain,
% 1.32/1.11      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 1.32/1.11      inference(quant_intro,[status(thm)],[139])).
% 1.32/1.11  tff(141,plain,
% 1.32/1.11      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 1.32/1.11      inference(transitivity,[status(thm)],[140, 138])).
% 1.32/1.11  tff(142,plain,
% 1.32/1.11      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))), ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))), ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))), trans(monotonicity(rewrite(((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) <=> ((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))), trans(monotonicity(rewrite((~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))) <=> (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))), (((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))), rewrite(((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))), (((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))), ((((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))) <=> (((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A)))) & ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))), rewrite((((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A)))) & ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))) <=> (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))), ((((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))) <=> (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))))), (![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))))) <=> ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))))),
% 1.32/1.11      inference(bind,[status(th)],[])).
% 1.32/1.11  tff(143,plain,
% 1.32/1.11      (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 1.32/1.11      inference(quant_intro,[status(thm)],[142])).
% 1.32/1.11  tff(144,plain,
% 1.32/1.11      (![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))))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(145,plain,
% 1.32/1.11      (^[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))))))))),
% 1.32/1.11      inference(bind,[status(th)],[])).
% 1.32/1.11  tff(146,plain,
% 1.32/1.11      (![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))))))),
% 1.32/1.11      inference(quant_intro,[status(thm)],[145])).
% 1.32/1.11  tff(147,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')).
% 1.32/1.11  tff(148,plain,
% 1.32/1.11      (![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))))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[147, 146])).
% 1.32/1.11  tff(149,plain,
% 1.32/1.11      (![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))))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[148, 144])).
% 1.32/1.11  tff(150,plain,(
% 1.32/1.11      ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_3(B, A)) & m1_group_2(tptp_fun_C_3(B, A), A))) | (k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A)))))))))),
% 1.32/1.11      inference(skolemize,[status(sab)],[149])).
% 1.32/1.11  tff(151,plain,
% 1.32/1.11      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[150, 143])).
% 1.32/1.11  tff(152,plain,
% 1.32/1.11      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[151, 141])).
% 1.32/1.11  tff(153,plain,
% 1.32/1.11      (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0))))))))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(154,plain,
% 1.32/1.11      ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0))))))))))),
% 1.32/1.11      inference(quant_inst,[status(thm)],[])).
% 1.32/1.11  tff(155,plain,
% 1.32/1.11      ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A)) = u1_struct_0(tptp_fun_C_3(B, A))) | (~v1_group_1(tptp_fun_C_3(B, A))) | (~m1_group_2(tptp_fun_C_3(B, A), A))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[154, 153])).
% 1.32/1.11  tff(156,plain,
% 1.32/1.11      (![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))),
% 1.32/1.11      inference(unit_resolution,[status(thm)],[155, 48, 47, 96, 46, 152])).
% 1.32/1.11  tff(157,plain,
% 1.32/1.11      (^[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))))))))),
% 1.32/1.11      inference(bind,[status(th)],[])).
% 1.32/1.11  tff(158,plain,
% 1.32/1.11      (![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)))))))),
% 1.32/1.11      inference(quant_intro,[status(thm)],[157])).
% 1.32/1.11  tff(159,plain,
% 1.32/1.11      (^[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)))))))))),
% 1.32/1.11      inference(bind,[status(th)],[])).
% 1.32/1.11  tff(160,plain,
% 1.32/1.11      (![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)))))))),
% 1.32/1.11      inference(quant_intro,[status(thm)],[159])).
% 1.32/1.11  tff(161,plain,
% 1.32/1.11      (![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)))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(162,plain,
% 1.32/1.11      (^[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)))))))),
% 1.32/1.11      inference(bind,[status(th)],[])).
% 1.32/1.11  tff(163,plain,
% 1.32/1.11      (![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)))))),
% 1.32/1.11      inference(quant_intro,[status(thm)],[162])).
% 1.32/1.11  tff(164,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')).
% 1.32/1.11  tff(165,plain,
% 1.32/1.11      (![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)))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[164, 163])).
% 1.32/1.11  tff(166,plain,
% 1.32/1.11      (![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)))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[165, 161])).
% 1.32/1.11  tff(167,plain,(
% 1.32/1.11      ![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)))))),
% 1.32/1.11      inference(skolemize,[status(sab)],[166])).
% 1.32/1.11  tff(168,plain,
% 1.32/1.11      (![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)))))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[167, 160])).
% 1.32/1.11  tff(169,plain,
% 1.32/1.11      (![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)))))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[168, 158])).
% 1.32/1.11  tff(170,plain,
% 1.32/1.11      (((~![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)))))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(171,plain,
% 1.32/1.11      ((~![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)))))))),
% 1.32/1.11      inference(quant_inst,[status(thm)],[])).
% 1.32/1.11  tff(172,plain,
% 1.32/1.11      ((~![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))))))),
% 1.32/1.11      inference(modus_ponens,[status(thm)],[171, 170])).
% 1.32/1.11  tff(173,plain,
% 1.32/1.11      (~((~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)))))),
% 1.32/1.11      inference(unit_resolution,[status(thm)],[172, 48, 47, 96, 46, 169])).
% 1.32/1.11  tff(174,plain,
% 1.32/1.11      (((~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)))),
% 1.32/1.11      inference(tautology,[status(thm)],[])).
% 1.32/1.11  tff(175,plain,
% 1.32/1.11      (m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.32/1.11      inference(unit_resolution,[status(thm)],[174, 173])).
% 1.32/1.11  tff(176,plain,
% 1.32/1.11      (((~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)))),
% 1.32/1.11      inference(tautology,[status(thm)],[])).
% 1.32/1.11  tff(177,plain,
% 1.32/1.11      (v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.32/1.11      inference(unit_resolution,[status(thm)],[176, 173])).
% 1.32/1.11  tff(178,plain,
% 1.32/1.11      (((~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))),
% 1.32/1.11      inference(tautology,[status(thm)],[])).
% 1.32/1.11  tff(179,plain,
% 1.32/1.11      (v1_funct_1(k1_latsubgr(A!0))),
% 1.32/1.11      inference(unit_resolution,[status(thm)],[178, 173])).
% 1.32/1.11  tff(180,plain,
% 1.32/1.11      (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) | ((~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)))) | ![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)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) | (~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)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(181,plain,
% 1.32/1.11      (((~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)))) | ![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_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)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(182,plain,
% 1.32/1.11      ((~(~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))) <=> ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(183,plain,
% 1.32/1.11      (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | $false) <=> (~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(184,plain,
% 1.32/1.11      ((~$true) <=> $false),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(185,plain,
% 1.32/1.11      (($true | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0))))) <=> $true),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(186,plain,
% 1.32/1.11      ((~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)))) <=> (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(187,plain,
% 1.32/1.11      ((k1_latsubgr(A!0) = k1_latsubgr(A!0)) <=> $true),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(188,plain,
% 1.32/1.11      (((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0))))) <=> ($true | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)))))),
% 1.32/1.11      inference(monotonicity,[status(thm)],[187, 186])).
% 1.32/1.11  tff(189,plain,
% 1.32/1.11      (((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0))))) <=> $true),
% 1.32/1.11      inference(transitivity,[status(thm)],[188, 185])).
% 1.32/1.11  tff(190,plain,
% 1.32/1.11      ((~((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)))))) <=> (~$true)),
% 1.32/1.11      inference(monotonicity,[status(thm)],[189])).
% 1.32/1.11  tff(191,plain,
% 1.32/1.11      ((~((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)))))) <=> $false),
% 1.32/1.11      inference(transitivity,[status(thm)],[190, 184])).
% 1.32/1.11  tff(192,plain,
% 1.32/1.11      ((~((~(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))))) <=> (~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 1.32/1.11      inference(rewrite,[status(thm)],[])).
% 1.32/1.11  tff(193,plain,
% 1.32/1.11      (((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!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)))) | $false)),
% 1.32/1.11      inference(monotonicity,[status(thm)],[192, 191])).
% 1.32/1.11  tff(194,plain,
% 1.32/1.11      (((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!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))))),
% 1.32/1.11      inference(transitivity,[status(thm)],[193, 183])).
% 1.32/1.11  tff(195,plain,
% 1.32/1.11      ((~((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!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)))))),
% 1.32/1.11      inference(monotonicity,[status(thm)],[194])).
% 1.32/1.11  tff(196,plain,
% 1.32/1.11      ((~((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!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)))),
% 1.32/1.11      inference(transitivity,[status(thm)],[195, 182])).
% 1.32/1.11  tff(197,plain,
% 1.32/1.11      (((~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)))) | (~((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), 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)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 1.32/1.11      inference(monotonicity,[status(thm)],[196])).
% 1.32/1.11  tff(198,plain,
% 1.32/1.11      (((~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)))) | (~((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), 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)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 1.32/1.12      inference(transitivity,[status(thm)],[197, 181])).
% 1.32/1.12  tff(199,plain,
% 1.32/1.12      (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) | ((~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)))) | (~((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)))))))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) | ((~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)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))))),
% 1.32/1.12      inference(monotonicity,[status(thm)],[198])).
% 1.32/1.12  tff(200,plain,
% 1.32/1.12      (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) | ((~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)))) | (~((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)))))))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) | (~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)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 1.38/1.12      inference(transitivity,[status(thm)],[199, 180])).
% 1.38/1.12  tff(201,plain,
% 1.38/1.12      ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) | ((~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)))) | (~((~((~(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)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_3(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_3(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_3(k1_latsubgr(A!0), A!0), A!0)))))))))),
% 1.38/1.12      inference(quant_inst,[status(thm)],[])).
% 1.38/1.12  tff(202,plain,
% 1.38/1.12      ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_3(B, A!0)) = u1_struct_0(tptp_fun_C_3(B, A!0))) | (~v1_group_1(tptp_fun_C_3(B, A!0))) | (~m1_group_2(tptp_fun_C_3(B, A!0), A!0)))))))))) | (~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)))) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[201, 200])).
% 1.38/1.12  tff(203,plain,
% 1.38/1.12      (![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))),
% 1.38/1.12      inference(unit_resolution,[status(thm)],[202, 179, 177, 175, 156])).
% 1.38/1.12  tff(204,plain,
% 1.38/1.12      (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | ((~v1_group_1(k8_group_2(A!0, B!1, C!2))) | (~m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)) | (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2))))) <=> ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | (~v1_group_1(k8_group_2(A!0, B!1, C!2))) | (~m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)) | (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2))))),
% 1.38/1.12      inference(rewrite,[status(thm)],[])).
% 1.38/1.12  tff(205,plain,
% 1.38/1.12      ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | ((~v1_group_1(k8_group_2(A!0, B!1, C!2))) | (~m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)) | (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2))))),
% 1.38/1.12      inference(quant_inst,[status(thm)],[])).
% 1.38/1.12  tff(206,plain,
% 1.38/1.12      ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | (~v1_group_1(k8_group_2(A!0, B!1, C!2))) | (~m1_group_2(k8_group_2(A!0, B!1, C!2), A!0)) | (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2)))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[205, 204])).
% 1.38/1.12  tff(207,plain,
% 1.38/1.12      (k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2)) = u1_struct_0(k8_group_2(A!0, B!1, C!2))),
% 1.38/1.12      inference(unit_resolution,[status(thm)],[206, 203, 136, 131])).
% 1.38/1.12  tff(208,plain,
% 1.38/1.12      (u1_struct_0(k8_group_2(A!0, B!1, C!2)) = k1_funct_1(k1_latsubgr(A!0), k8_group_2(A!0, B!1, C!2))),
% 1.38/1.12      inference(symmetry,[status(thm)],[207])).
% 1.38/1.12  tff(209,plain,
% 1.38/1.12      (^[A: $i, B: $i, C: $i] : refl(((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) <=> ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))),
% 1.38/1.12      inference(bind,[status(th)],[])).
% 1.38/1.12  tff(210,plain,
% 1.38/1.12      (![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) <=> ![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 1.38/1.12      inference(quant_intro,[status(thm)],[209])).
% 1.38/1.12  tff(211,plain,
% 1.38/1.12      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) <=> (~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))))), rewrite((~(~(v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) <=> (v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))))), rewrite(((v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))))),
% 1.38/1.12      inference(bind,[status(th)],[])).
% 1.38/1.12  tff(212,plain,
% 1.38/1.12      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 1.38/1.12      inference(quant_intro,[status(thm)],[211])).
% 1.38/1.12  tff(213,plain,
% 1.38/1.12      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 1.38/1.12      inference(rewrite,[status(thm)],[])).
% 1.38/1.12  tff(214,plain,
% 1.38/1.12      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))))),
% 1.38/1.12      inference(bind,[status(th)],[])).
% 1.38/1.12  tff(215,plain,
% 1.38/1.12      (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 1.38/1.12      inference(quant_intro,[status(thm)],[214])).
% 1.38/1.12  tff(216,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) & m1_group_2(C, A)) => (k9_group_2(A, B, C) = k9_group_2(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k9_group_2')).
% 1.38/1.12  tff(217,plain,
% 1.38/1.12      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[216, 215])).
% 1.38/1.12  tff(218,plain,
% 1.38/1.12      (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[217, 213])).
% 1.38/1.12  tff(219,plain,(
% 1.38/1.12      ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A) & m1_group_2(C, A))) | (k9_group_2(A, B, C) = k9_group_2(A, C, B)))),
% 1.38/1.12      inference(skolemize,[status(sab)],[218])).
% 1.38/1.12  tff(220,plain,
% 1.38/1.12      (![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[219, 212])).
% 1.38/1.12  tff(221,plain,
% 1.38/1.12      (![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[220, 210])).
% 1.38/1.12  tff(222,plain,
% 1.38/1.12      (((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)))),
% 1.38/1.12      inference(rewrite,[status(thm)],[])).
% 1.38/1.12  tff(223,plain,
% 1.38/1.12      (((k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)) | v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)))),
% 1.38/1.12      inference(rewrite,[status(thm)],[])).
% 1.38/1.12  tff(224,plain,
% 1.38/1.12      (((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | ((k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)) | v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1))))),
% 1.38/1.12      inference(monotonicity,[status(thm)],[223])).
% 1.38/1.12  tff(225,plain,
% 1.38/1.12      (((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | ((k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)) | v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)))),
% 1.38/1.12      inference(transitivity,[status(thm)],[224, 222])).
% 1.38/1.12  tff(226,plain,
% 1.38/1.12      ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | ((k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)) | v3_struct_0(A!0) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)))),
% 1.38/1.12      inference(quant_inst,[status(thm)],[])).
% 1.38/1.12  tff(227,plain,
% 1.38/1.12      ((~![A: $i, B: $i, C: $i] : ((k9_group_2(A, B, C) = k9_group_2(A, C, B)) | v3_struct_0(A) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_group_2(B, A)) | (~m1_group_2(C, A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~m1_group_2(B!1, A!0)) | (~m1_group_2(C!2, A!0)) | (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[226, 225])).
% 1.38/1.12  tff(228,plain,
% 1.38/1.12      (k9_group_2(A!0, B!1, C!2) = k9_group_2(A!0, C!2, B!1)),
% 1.38/1.12      inference(unit_resolution,[status(thm)],[227, 48, 47, 96, 46, 53, 95, 221])).
% 1.38/1.12  tff(229,plain,
% 1.38/1.12      (k9_group_2(A!0, C!2, B!1) = k9_group_2(A!0, B!1, C!2)),
% 1.38/1.12      inference(symmetry,[status(thm)],[228])).
% 1.38/1.12  tff(230,plain,
% 1.38/1.12      (k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k9_group_2(A!0, C!2, B!1)),
% 1.38/1.12      inference(monotonicity,[status(thm)],[76])).
% 1.38/1.12  tff(231,plain,
% 1.38/1.12      (k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k8_group_2(A!0, B!1, C!2)),
% 1.38/1.12      inference(transitivity,[status(thm)],[230, 229, 103])).
% 1.38/1.12  tff(232,plain,
% 1.38/1.12      (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = u1_struct_0(k8_group_2(A!0, B!1, C!2))),
% 1.38/1.12      inference(monotonicity,[status(thm)],[231])).
% 1.38/1.12  tff(233,plain,
% 1.38/1.12      (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2))),
% 1.38/1.12      inference(transitivity,[status(thm)],[232, 208, 105])).
% 1.38/1.12  tff(234,plain,
% 1.38/1.12      ((u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) <=> (k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))),
% 1.38/1.12      inference(monotonicity,[status(thm)],[233, 79])).
% 1.38/1.12  tff(235,plain,
% 1.38/1.12      ((k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2))) <=> (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.38/1.12      inference(symmetry,[status(thm)],[234])).
% 1.38/1.12  tff(236,plain,
% 1.38/1.12      ((~(k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))) <=> (~(u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 1.38/1.12      inference(monotonicity,[status(thm)],[235])).
% 1.38/1.12  tff(237,plain,
% 1.38/1.12      (~(k1_funct_1(k1_latsubgr(A!0), k9_group_2(A!0, B!1, C!2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B!1), k1_funct_1(k1_latsubgr(A!0), C!2)))),
% 1.38/1.12      inference(or_elim,[status(thm)],[93])).
% 1.38/1.12  tff(238,plain,
% 1.38/1.12      (~(u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[237, 236])).
% 1.38/1.12  tff(239,plain,
% 1.38/1.12      (v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) <=> v1_group_1(B!1)),
% 1.38/1.12      inference(monotonicity,[status(thm)],[76])).
% 1.38/1.12  tff(240,plain,
% 1.38/1.12      (v1_group_1(B!1) <=> v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.38/1.12      inference(symmetry,[status(thm)],[239])).
% 1.38/1.12  tff(241,plain,
% 1.38/1.12      (v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[70, 240])).
% 1.38/1.12  tff(242,plain,
% 1.38/1.12      (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)),
% 1.38/1.12      inference(monotonicity,[status(thm)],[76])).
% 1.38/1.12  tff(243,plain,
% 1.38/1.12      (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)),
% 1.38/1.12      inference(symmetry,[status(thm)],[242])).
% 1.38/1.12  tff(244,plain,
% 1.38/1.12      (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[53, 243])).
% 1.38/1.12  tff(245,plain,
% 1.38/1.12      (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))))),
% 1.38/1.12      inference(bind,[status(th)],[])).
% 1.38/1.12  tff(246,plain,
% 1.38/1.12      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 1.38/1.12      inference(quant_intro,[status(thm)],[245])).
% 1.38/1.12  tff(247,plain,
% 1.38/1.12      (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))))),
% 1.38/1.12      inference(bind,[status(th)],[])).
% 1.38/1.12  tff(248,plain,
% 1.38/1.12      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 1.38/1.12      inference(quant_intro,[status(thm)],[247])).
% 1.38/1.12  tff(249,plain,
% 1.38/1.12      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 1.38/1.12      inference(transitivity,[status(thm)],[248, 246])).
% 1.38/1.12  tff(250,plain,
% 1.38/1.12      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_group_1(B) & m1_group_2(B, A)) <=> (~((~v1_group_1(B)) | (~m1_group_2(B, A))))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> (~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))))), rewrite((~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_group_1(C) & m1_group_2(C, A)) <=> (~((~v1_group_1(C)) | (~m1_group_2(C, A))))), ((~(v1_group_1(C) & m1_group_2(C, A))) <=> (~(~((~v1_group_1(C)) | (~m1_group_2(C, A))))))), rewrite((~(~((~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> ((~v1_group_1(C)) | (~m1_group_2(C, A)))), ((~(v1_group_1(C) & m1_group_2(C, A))) <=> ((~v1_group_1(C)) | (~m1_group_2(C, A))))), (((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> (((~v1_group_1(C)) | (~m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))), rewrite((((~v1_group_1(C)) | (~m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))), (((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))), (![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> (((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))), rewrite((((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))))), (![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))))),
% 1.38/1.12      inference(bind,[status(th)],[])).
% 1.38/1.12  tff(251,plain,
% 1.38/1.12      (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 1.38/1.12      inference(quant_intro,[status(thm)],[250])).
% 1.38/1.12  tff(252,plain,
% 1.38/1.12      (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.38/1.12      inference(rewrite,[status(thm)],[])).
% 1.38/1.12  tff(253,plain,
% 1.38/1.12      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))), (![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))) <=> ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), rewrite(((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))))), (![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))) <=> ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))))),
% 1.38/1.12      inference(bind,[status(th)],[])).
% 1.38/1.12  tff(254,plain,
% 1.38/1.12      (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.38/1.12      inference(quant_intro,[status(thm)],[253])).
% 1.38/1.12  tff(255,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((v1_group_1(C) & m1_group_2(C, A)) => (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_latsubgr')).
% 1.38/1.12  tff(256,plain,
% 1.38/1.12      (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[255, 254])).
% 1.38/1.12  tff(257,plain,
% 1.38/1.12      (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[256, 252])).
% 1.38/1.12  tff(258,plain,(
% 1.38/1.12      ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))))))),
% 1.38/1.12      inference(skolemize,[status(sab)],[257])).
% 1.38/1.12  tff(259,plain,
% 1.38/1.12      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[258, 251])).
% 1.38/1.12  tff(260,plain,
% 1.38/1.12      (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))),
% 1.38/1.12      inference(modus_ponens,[status(thm)],[259, 249])).
% 1.38/1.12  tff(261,plain,
% 1.38/1.12      (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))))))),
% 1.38/1.13      inference(rewrite,[status(thm)],[])).
% 1.38/1.13  tff(262,plain,
% 1.38/1.13      ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))))))),
% 1.38/1.13      inference(rewrite,[status(thm)],[])).
% 1.38/1.13  tff(263,plain,
% 1.38/1.13      (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C)))))))),
% 1.38/1.13      inference(monotonicity,[status(thm)],[262])).
% 1.38/1.13  tff(264,plain,
% 1.38/1.13      (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))))))),
% 1.38/1.13      inference(transitivity,[status(thm)],[263, 261])).
% 1.38/1.13  tff(265,plain,
% 1.38/1.13      ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A!0)))))),
% 1.38/1.13      inference(quant_inst,[status(thm)],[])).
% 1.38/1.13  tff(266,plain,
% 1.38/1.13      ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((u1_struct_0(k9_group_2(A, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A), B), k1_funct_1(k1_latsubgr(A), C))) | (~v1_group_1(C)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C)))))),
% 1.38/1.13      inference(modus_ponens,[status(thm)],[265, 264])).
% 1.38/1.13  tff(267,plain,
% 1.38/1.13      (![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C)))))),
% 1.38/1.13      inference(unit_resolution,[status(thm)],[266, 48, 47, 96, 46, 260])).
% 1.38/1.13  tff(268,plain,
% 1.38/1.13      (v1_group_1(C!2)),
% 1.38/1.13      inference(and_elim,[status(thm)],[94])).
% 1.38/1.13  tff(269,plain,
% 1.38/1.13      (((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C)))))) | ((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C)))))) <=> ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C)))))) | (~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C)))))),
% 1.38/1.13      inference(rewrite,[status(thm)],[])).
% 1.38/1.13  tff(270,plain,
% 1.38/1.13      ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C)))))) | ((~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C)))))),
% 1.38/1.13      inference(quant_inst,[status(thm)],[])).
% 1.38/1.13  tff(271,plain,
% 1.38/1.13      ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, B, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), B), k1_funct_1(k1_latsubgr(A!0), C)))))) | (~v1_group_1(C!2)) | (~m1_group_2(C!2, A!0)) | ![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))),
% 1.38/1.13      inference(modus_ponens,[status(thm)],[270, 269])).
% 1.38/1.13  tff(272,plain,
% 1.38/1.13      (![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))),
% 1.38/1.13      inference(unit_resolution,[status(thm)],[271, 268, 95, 267])).
% 1.38/1.13  tff(273,plain,
% 1.38/1.13      (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))) | ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))) <=> ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))) | (~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 1.38/1.13      inference(rewrite,[status(thm)],[])).
% 1.38/1.13  tff(274,plain,
% 1.38/1.13      ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))) | ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 1.38/1.13      inference(quant_inst,[status(thm)],[])).
% 1.38/1.13  tff(275,plain,
% 1.38/1.13      ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), C))))) | (~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.38/1.13      inference(modus_ponens,[status(thm)],[274, 273])).
% 1.38/1.13  tff(276,plain,
% 1.38/1.13      ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (u1_struct_0(k9_group_2(A!0, C!2, g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) = k3_xboole_0(k1_funct_1(k1_latsubgr(A!0), C!2), k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 1.38/1.13      inference(unit_resolution,[status(thm)],[275, 272])).
% 1.38/1.13  tff(277,plain,
% 1.38/1.13      ($false),
% 1.38/1.13      inference(unit_resolution,[status(thm)],[276, 244, 241, 238])).
% 1.38/1.13  % SZS output end Proof
%------------------------------------------------------------------------------