TSTP Solution File: GRP642+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:29:05 EDT 2022
% Result : Theorem 2.10s 1.58s
% Output : Proof 2.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 31 18:54:50 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 2.10/1.58 % SZS status Theorem
% 2.10/1.58 % SZS output start Proof
% 2.10/1.58 tff(v1_xboole_0_type, type, (
% 2.10/1.58 v1_xboole_0: $i > $o)).
% 2.10/1.58 tff(u1_struct_0_type, type, (
% 2.10/1.58 u1_struct_0: $i > $i)).
% 2.10/1.58 tff(g1_group_1_type, type, (
% 2.10/1.58 g1_group_1: ( $i * $i ) > $i)).
% 2.10/1.58 tff(u1_group_1_type, type, (
% 2.10/1.58 u1_group_1: $i > $i)).
% 2.10/1.58 tff(tptp_fun_B_1_type, type, (
% 2.10/1.58 tptp_fun_B_1: $i)).
% 2.10/1.58 tff(k1_xboole_0_type, type, (
% 2.10/1.58 k1_xboole_0: $i)).
% 2.10/1.58 tff(k1_funct_1_type, type, (
% 2.10/1.58 k1_funct_1: ( $i * $i ) > $i)).
% 2.10/1.58 tff(k1_latsubgr_type, type, (
% 2.10/1.58 k1_latsubgr: $i > $i)).
% 2.10/1.58 tff(tptp_fun_A_0_type, type, (
% 2.10/1.58 tptp_fun_A_0: $i)).
% 2.10/1.58 tff(m1_group_2_type, type, (
% 2.10/1.58 m1_group_2: ( $i * $i ) > $o)).
% 2.10/1.58 tff(v1_group_1_type, type, (
% 2.10/1.58 v1_group_1: $i > $o)).
% 2.10/1.58 tff(l1_group_1_type, type, (
% 2.10/1.58 l1_group_1: $i > $o)).
% 2.10/1.58 tff(v4_group_1_type, type, (
% 2.10/1.58 v4_group_1: $i > $o)).
% 2.10/1.58 tff(v3_group_1_type, type, (
% 2.10/1.58 v3_group_1: $i > $o)).
% 2.10/1.58 tff(v3_struct_0_type, type, (
% 2.10/1.58 v3_struct_0: $i > $o)).
% 2.10/1.58 tff(tptp_fun_C_2_type, type, (
% 2.10/1.58 tptp_fun_C_2: ( $i * $i ) > $i)).
% 2.10/1.58 tff(m2_relset_1_type, type, (
% 2.10/1.58 m2_relset_1: ( $i * $i * $i ) > $o)).
% 2.10/1.58 tff(k1_zfmisc_1_type, type, (
% 2.10/1.58 k1_zfmisc_1: $i > $i)).
% 2.10/1.58 tff(k1_group_3_type, type, (
% 2.10/1.58 k1_group_3: $i > $i)).
% 2.10/1.58 tff(v1_funct_2_type, type, (
% 2.10/1.58 v1_funct_2: ( $i * $i * $i ) > $o)).
% 2.10/1.58 tff(v1_funct_1_type, type, (
% 2.10/1.58 v1_funct_1: $i > $o)).
% 2.10/1.58 tff(l1_struct_0_type, type, (
% 2.10/1.58 l1_struct_0: $i > $o)).
% 2.10/1.58 tff(1,plain,
% 2.10/1.58 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0)))))),
% 2.10/1.58 inference(rewrite,[status(thm)],[])).
% 2.10/1.58 tff(2,plain,
% 2.10/1.58 ((~(~((~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))),
% 2.10/1.58 inference(rewrite,[status(thm)],[])).
% 2.10/1.58 tff(3,plain,
% 2.10/1.58 (((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) & (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0)))))),
% 2.10/1.58 inference(monotonicity,[status(thm)],[2])).
% 2.10/1.58 tff(4,plain,
% 2.10/1.58 (((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) & (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0)))))),
% 2.10/1.58 inference(transitivity,[status(thm)],[3, 1])).
% 2.10/1.58 tff(5,plain,
% 2.10/1.58 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0)))))),
% 2.10/1.58 inference(rewrite,[status(thm)],[])).
% 2.10/1.58 tff(6,plain,
% 2.10/1.58 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0)))))),
% 2.10/1.58 inference(rewrite,[status(thm)],[])).
% 2.10/1.58 tff(7,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_latsubgr')).
% 2.10/1.58 tff(8,plain,
% 2.10/1.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.10/1.58 tff(9,plain,
% 2.10/1.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[8, 5])).
% 2.10/1.58 tff(10,plain,
% 2.10/1.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[9, 5])).
% 2.10/1.58 tff(11,plain,
% 2.10/1.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[10, 5])).
% 2.10/1.58 tff(12,plain,
% 2.10/1.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[11, 5])).
% 2.10/1.58 tff(13,plain,
% 2.10/1.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[12, 5])).
% 2.10/1.58 tff(14,plain,
% 2.10/1.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | (~(k1_funct_1(k1_latsubgr(A), B) = k1_xboole_0))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[13, 5])).
% 2.10/1.58 tff(15,plain,
% 2.10/1.58 ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[14, 4])).
% 2.10/1.58 tff(16,plain,
% 2.10/1.58 (~((~(v1_group_1(B!1) & m1_group_2(B!1, A!0))) | (~(k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0)))),
% 2.10/1.58 inference(and_elim,[status(thm)],[15])).
% 2.10/1.58 tff(17,plain,
% 2.10/1.58 (k1_funct_1(k1_latsubgr(A!0), B!1) = k1_xboole_0),
% 2.10/1.58 inference(or_elim,[status(thm)],[16])).
% 2.10/1.58 tff(18,plain,
% 2.10/1.58 (^[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)))))))),
% 2.10/1.58 inference(bind,[status(th)],[])).
% 2.10/1.58 tff(19,plain,
% 2.10/1.58 (![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))))))),
% 2.10/1.58 inference(quant_intro,[status(thm)],[18])).
% 2.10/1.58 tff(20,plain,
% 2.10/1.58 (^[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)))))))),
% 2.10/1.58 inference(bind,[status(th)],[])).
% 2.10/1.58 tff(21,plain,
% 2.10/1.58 (![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))))))),
% 2.10/1.58 inference(quant_intro,[status(thm)],[20])).
% 2.10/1.58 tff(22,plain,
% 2.10/1.58 (![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))))))),
% 2.10/1.58 inference(transitivity,[status(thm)],[21, 19])).
% 2.10/1.58 tff(23,plain,
% 2.10/1.58 (^[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))))))))),
% 2.10/1.58 inference(bind,[status(th)],[])).
% 2.10/1.58 tff(24,plain,
% 2.10/1.58 (![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))))))),
% 2.10/1.58 inference(quant_intro,[status(thm)],[23])).
% 2.10/1.58 tff(25,plain,
% 2.10/1.58 (![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))))),
% 2.10/1.58 inference(rewrite,[status(thm)],[])).
% 2.10/1.58 tff(26,plain,
% 2.10/1.58 (^[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))))))),
% 2.10/1.58 inference(bind,[status(th)],[])).
% 2.10/1.58 tff(27,plain,
% 2.10/1.58 (![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))))),
% 2.10/1.58 inference(quant_intro,[status(thm)],[26])).
% 2.10/1.58 tff(28,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')).
% 2.10/1.58 tff(29,plain,
% 2.10/1.58 (![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))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[28, 27])).
% 2.10/1.58 tff(30,plain,
% 2.10/1.58 (![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))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[29, 25])).
% 2.10/1.58 tff(31,plain,(
% 2.10/1.58 ![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))))),
% 2.10/1.58 inference(skolemize,[status(sab)],[30])).
% 2.10/1.58 tff(32,plain,
% 2.10/1.58 (![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))))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[31, 24])).
% 2.10/1.58 tff(33,plain,
% 2.10/1.58 (![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))))))),
% 2.10/1.58 inference(modus_ponens,[status(thm)],[32, 22])).
% 2.10/1.58 tff(34,plain,
% 2.10/1.58 (l1_group_1(A!0)),
% 2.10/1.58 inference(and_elim,[status(thm)],[15])).
% 2.10/1.58 tff(35,plain,
% 2.10/1.58 (v3_group_1(A!0)),
% 2.10/1.58 inference(and_elim,[status(thm)],[15])).
% 2.10/1.58 tff(36,plain,
% 2.10/1.58 (~v3_struct_0(A!0)),
% 2.10/1.58 inference(and_elim,[status(thm)],[15])).
% 2.10/1.58 tff(37,plain,
% 2.10/1.58 (((~![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))))))),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(38,plain,
% 2.10/1.59 ((~![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))))))),
% 2.10/1.59 inference(quant_inst,[status(thm)],[])).
% 2.10/1.59 tff(39,plain,
% 2.10/1.59 ((~![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)))))),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[38, 37])).
% 2.10/1.59 tff(40,plain,
% 2.10/1.59 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 2.10/1.59 inference(unit_resolution,[status(thm)],[39, 36, 35, 34, 33])).
% 2.10/1.59 tff(41,plain,
% 2.10/1.59 (v1_group_1(B!1) & m1_group_2(B!1, A!0)),
% 2.10/1.59 inference(or_elim,[status(thm)],[16])).
% 2.10/1.59 tff(42,plain,
% 2.10/1.59 (m1_group_2(B!1, A!0)),
% 2.10/1.59 inference(and_elim,[status(thm)],[41])).
% 2.10/1.59 tff(43,plain,
% 2.10/1.59 (((~![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)))))),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(44,plain,
% 2.10/1.59 ((~![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)))))),
% 2.10/1.59 inference(quant_inst,[status(thm)],[])).
% 2.10/1.59 tff(45,plain,
% 2.10/1.59 ((~![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))))),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.10/1.59 tff(46,plain,
% 2.10/1.59 (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))),
% 2.10/1.59 inference(unit_resolution,[status(thm)],[45, 42, 40])).
% 2.10/1.59 tff(47,plain,
% 2.10/1.59 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | l1_group_1(B!1)),
% 2.10/1.59 inference(tautology,[status(thm)],[])).
% 2.10/1.59 tff(48,plain,
% 2.10/1.59 (l1_group_1(B!1)),
% 2.10/1.59 inference(unit_resolution,[status(thm)],[47, 46])).
% 2.10/1.59 tff(49,plain,
% 2.10/1.59 (^[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))))),
% 2.10/1.59 inference(bind,[status(th)],[])).
% 2.10/1.59 tff(50,plain,
% 2.10/1.59 (![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)))),
% 2.10/1.59 inference(quant_intro,[status(thm)],[49])).
% 2.10/1.59 tff(51,plain,
% 2.10/1.59 (![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)))),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(52,plain,
% 2.10/1.59 (^[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)))))),
% 2.10/1.59 inference(bind,[status(th)],[])).
% 2.10/1.59 tff(53,plain,
% 2.10/1.59 (![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)))),
% 2.10/1.59 inference(quant_intro,[status(thm)],[52])).
% 2.10/1.59 tff(54,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')).
% 2.10/1.59 tff(55,plain,
% 2.10/1.59 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[54, 53])).
% 2.10/1.59 tff(56,plain,
% 2.10/1.59 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[55, 51])).
% 2.10/1.59 tff(57,plain,(
% 2.10/1.59 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.10/1.59 inference(skolemize,[status(sab)],[56])).
% 2.10/1.59 tff(58,plain,
% 2.10/1.59 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[57, 50])).
% 2.10/1.59 tff(59,plain,
% 2.10/1.59 (v1_group_1(B!1)),
% 2.10/1.59 inference(and_elim,[status(thm)],[41])).
% 2.10/1.59 tff(60,plain,
% 2.10/1.59 (((~![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)))),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(61,plain,
% 2.10/1.59 ((~![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)))),
% 2.10/1.59 inference(quant_inst,[status(thm)],[])).
% 2.10/1.59 tff(62,plain,
% 2.10/1.59 ((~![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))),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[61, 60])).
% 2.10/1.59 tff(63,plain,
% 2.10/1.59 ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(B!1))),
% 2.10/1.59 inference(unit_resolution,[status(thm)],[62, 59, 58])).
% 2.10/1.59 tff(64,plain,
% 2.10/1.59 (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))),
% 2.10/1.59 inference(unit_resolution,[status(thm)],[63, 48])).
% 2.10/1.59 tff(65,plain,
% 2.10/1.59 (g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)) = B!1),
% 2.10/1.59 inference(symmetry,[status(thm)],[64])).
% 2.10/1.59 tff(66,plain,
% 2.10/1.59 (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)),
% 2.10/1.59 inference(monotonicity,[status(thm)],[65])).
% 2.10/1.59 tff(67,plain,
% 2.10/1.59 (v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) <=> v1_group_1(B!1)),
% 2.10/1.59 inference(monotonicity,[status(thm)],[65])).
% 2.10/1.59 tff(68,plain,
% 2.10/1.59 (v1_group_1(B!1) <=> v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.10/1.59 inference(symmetry,[status(thm)],[67])).
% 2.10/1.59 tff(69,plain,
% 2.10/1.59 (v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[59, 68])).
% 2.10/1.59 tff(70,plain,
% 2.10/1.59 (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)),
% 2.10/1.59 inference(monotonicity,[status(thm)],[65])).
% 2.10/1.59 tff(71,plain,
% 2.10/1.59 (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)),
% 2.10/1.59 inference(symmetry,[status(thm)],[70])).
% 2.10/1.59 tff(72,plain,
% 2.10/1.59 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[42, 71])).
% 2.10/1.59 tff(73,plain,
% 2.10/1.59 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))))),
% 2.10/1.59 inference(bind,[status(th)],[])).
% 2.10/1.59 tff(74,plain,
% 2.10/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 2.10/1.59 inference(quant_intro,[status(thm)],[73])).
% 2.10/1.59 tff(75,plain,
% 2.10/1.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))))),
% 2.10/1.59 inference(bind,[status(th)],[])).
% 2.10/1.59 tff(76,plain,
% 2.10/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 2.10/1.59 inference(quant_intro,[status(thm)],[75])).
% 2.10/1.59 tff(77,plain,
% 2.10/1.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 2.10/1.59 inference(transitivity,[status(thm)],[76, 74])).
% 2.10/1.59 tff(78,plain,
% 2.10/1.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))), ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))))), ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))))), trans(monotonicity(rewrite(((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) <=> ((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))), trans(monotonicity(rewrite((~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))))) <=> (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))), (((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))), rewrite(((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))), (((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))) <=> ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))), ((((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))))))) <=> (((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A)))) & ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))), rewrite((((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A)))) & ((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))) <=> (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))), ((((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))))))) <=> (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))))), (![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))))) <=> ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A)))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))))),
% 2.10/1.59 inference(bind,[status(th)],[])).
% 2.10/1.59 tff(79,plain,
% 2.10/1.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 2.10/1.59 inference(quant_intro,[status(thm)],[78])).
% 2.10/1.59 tff(80,plain,
% 2.10/1.59 (![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))))))),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(81,plain,
% 2.10/1.59 (^[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))))))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(82,plain,
% 2.10/1.60 (![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))))))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[81])).
% 2.10/1.60 tff(83,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')).
% 2.10/1.60 tff(84,plain,
% 2.10/1.60 (![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))))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.10/1.60 tff(85,plain,
% 2.10/1.60 (![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))))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[84, 80])).
% 2.10/1.60 tff(86,plain,(
% 2.10/1.60 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A))))) | (((~(B = k1_latsubgr(A))) | ![C: $i] : ((~(v1_group_1(C) & m1_group_2(C, A))) | (k1_funct_1(B, C) = u1_struct_0(C)))) & ((B = k1_latsubgr(A)) | (~((~(v1_group_1(tptp_fun_C_2(B, A)) & m1_group_2(tptp_fun_C_2(B, A), A))) | (k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A)))))))))),
% 2.10/1.60 inference(skolemize,[status(sab)],[85])).
% 2.10/1.60 tff(87,plain,
% 2.10/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[86, 79])).
% 2.10/1.60 tff(88,plain,
% 2.10/1.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[87, 77])).
% 2.10/1.60 tff(89,plain,
% 2.10/1.60 (v4_group_1(A!0)),
% 2.10/1.60 inference(and_elim,[status(thm)],[15])).
% 2.10/1.60 tff(90,plain,
% 2.10/1.60 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0))))))))))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(91,plain,
% 2.10/1.60 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0))))))))))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(92,plain,
% 2.10/1.60 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~m2_relset_1(B, k1_group_3(A), k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~(B = k1_latsubgr(A))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A))))) | (~((B = k1_latsubgr(A)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A)) = u1_struct_0(tptp_fun_C_2(B, A))) | (~v1_group_1(tptp_fun_C_2(B, A))) | (~m1_group_2(tptp_fun_C_2(B, A), A))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[91, 90])).
% 2.10/1.60 tff(93,plain,
% 2.10/1.60 (![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[92, 36, 35, 89, 34, 88])).
% 2.10/1.60 tff(94,plain,
% 2.10/1.60 (^[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))))))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(95,plain,
% 2.10/1.60 (![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)))))))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[94])).
% 2.10/1.60 tff(96,plain,
% 2.10/1.60 (^[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)))))))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(97,plain,
% 2.10/1.60 (![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)))))))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[96])).
% 2.10/1.60 tff(98,plain,
% 2.10/1.60 (![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)))))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(99,plain,
% 2.10/1.60 (^[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)))))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(100,plain,
% 2.10/1.60 (![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)))))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[99])).
% 2.10/1.60 tff(101,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')).
% 2.10/1.60 tff(102,plain,
% 2.10/1.60 (![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)))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[101, 100])).
% 2.10/1.60 tff(103,plain,
% 2.10/1.60 (![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)))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[102, 98])).
% 2.10/1.60 tff(104,plain,(
% 2.10/1.60 ![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)))))),
% 2.10/1.60 inference(skolemize,[status(sab)],[103])).
% 2.10/1.60 tff(105,plain,
% 2.10/1.60 (![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)))))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[104, 97])).
% 2.10/1.60 tff(106,plain,
% 2.10/1.60 (![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)))))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[105, 95])).
% 2.10/1.60 tff(107,plain,
% 2.10/1.60 (((~![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)))))))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(108,plain,
% 2.10/1.60 ((~![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)))))))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(109,plain,
% 2.10/1.60 ((~![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))))))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[108, 107])).
% 2.10/1.60 tff(110,plain,
% 2.10/1.60 (~((~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)))))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[109, 36, 35, 89, 34, 106])).
% 2.10/1.60 tff(111,plain,
% 2.10/1.60 (((~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)))),
% 2.10/1.60 inference(tautology,[status(thm)],[])).
% 2.10/1.60 tff(112,plain,
% 2.10/1.60 (m2_relset_1(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[111, 110])).
% 2.10/1.60 tff(113,plain,
% 2.10/1.60 (((~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)))),
% 2.10/1.60 inference(tautology,[status(thm)],[])).
% 2.10/1.60 tff(114,plain,
% 2.10/1.60 (v1_funct_2(k1_latsubgr(A!0), k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[113, 110])).
% 2.10/1.60 tff(115,plain,
% 2.10/1.60 (((~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))),
% 2.10/1.60 inference(tautology,[status(thm)],[])).
% 2.10/1.60 tff(116,plain,
% 2.10/1.60 (v1_funct_1(k1_latsubgr(A!0))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[115, 110])).
% 2.10/1.60 tff(117,plain,
% 2.10/1.60 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))) | ((~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_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))) | (~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))))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(118,plain,
% 2.10/1.61 (((~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))))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(119,plain,
% 2.10/1.61 ((~(~![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)))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(120,plain,
% 2.10/1.61 (((~![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: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C))))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(121,plain,
% 2.10/1.61 ((~$true) <=> $false),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(122,plain,
% 2.10/1.61 (($true | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0))))) <=> $true),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(123,plain,
% 2.10/1.61 ((~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0)))) <=> (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0))))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(124,plain,
% 2.10/1.61 ((k1_latsubgr(A!0) = k1_latsubgr(A!0)) <=> $true),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(125,plain,
% 2.10/1.61 (((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0))))) <=> ($true | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0)))))),
% 2.10/1.61 inference(monotonicity,[status(thm)],[124, 123])).
% 2.10/1.61 tff(126,plain,
% 2.10/1.61 (((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0))))) <=> $true),
% 2.10/1.61 inference(transitivity,[status(thm)],[125, 122])).
% 2.10/1.61 tff(127,plain,
% 2.10/1.61 ((~((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0)))))) <=> (~$true)),
% 2.10/1.61 inference(monotonicity,[status(thm)],[126])).
% 2.10/1.61 tff(128,plain,
% 2.10/1.61 ((~((k1_latsubgr(A!0) = k1_latsubgr(A!0)) | (~((k1_funct_1(k1_latsubgr(A!0), tptp_fun_C_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0)))))) <=> $false),
% 2.10/1.61 inference(transitivity,[status(thm)],[127, 121])).
% 2.10/1.61 tff(129,plain,
% 2.10/1.61 ((~((~(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))))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(130,plain,
% 2.10/1.61 (((~((~(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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(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)),
% 2.10/1.61 inference(monotonicity,[status(thm)],[129, 128])).
% 2.10/1.61 tff(131,plain,
% 2.10/1.61 (((~((~(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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(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))))),
% 2.10/1.61 inference(transitivity,[status(thm)],[130, 120])).
% 2.10/1.61 tff(132,plain,
% 2.10/1.61 ((~((~((~(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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(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)))))),
% 2.10/1.61 inference(monotonicity,[status(thm)],[131])).
% 2.10/1.61 tff(133,plain,
% 2.10/1.61 ((~((~((~(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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(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)))),
% 2.10/1.61 inference(transitivity,[status(thm)],[132, 119])).
% 2.10/1.61 tff(134,plain,
% 2.10/1.61 (((~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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(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))))),
% 2.10/1.61 inference(monotonicity,[status(thm)],[133])).
% 2.10/1.61 tff(135,plain,
% 2.10/1.61 (((~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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(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))))),
% 2.10/1.61 inference(transitivity,[status(thm)],[134, 118])).
% 2.10/1.61 tff(136,plain,
% 2.10/1.61 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))) | ((~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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))) | ((~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)))))),
% 2.10/1.61 inference(monotonicity,[status(thm)],[135])).
% 2.10/1.61 tff(137,plain,
% 2.10/1.61 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))) | ((~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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(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_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))) | (~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))))),
% 2.23/1.62 inference(transitivity,[status(thm)],[136, 117])).
% 2.23/1.62 tff(138,plain,
% 2.23/1.62 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))) | ((~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_2(k1_latsubgr(A!0), A!0)) = u1_struct_0(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~v1_group_1(tptp_fun_C_2(k1_latsubgr(A!0), A!0))) | (~m1_group_2(tptp_fun_C_2(k1_latsubgr(A!0), A!0), A!0)))))))))),
% 2.23/1.62 inference(quant_inst,[status(thm)],[])).
% 2.23/1.62 tff(139,plain,
% 2.23/1.62 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m2_relset_1(B, k1_group_3(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~(B = k1_latsubgr(A!0))) | ![C: $i] : ((k1_funct_1(B, C) = u1_struct_0(C)) | (~v1_group_1(C)) | (~m1_group_2(C, A!0))))) | (~((B = k1_latsubgr(A!0)) | (~((k1_funct_1(B, tptp_fun_C_2(B, A!0)) = u1_struct_0(tptp_fun_C_2(B, A!0))) | (~v1_group_1(tptp_fun_C_2(B, A!0))) | (~m1_group_2(tptp_fun_C_2(B, A!0), A!0)))))))))) | (~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)))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[138, 137])).
% 2.23/1.62 tff(140,plain,
% 2.23/1.62 (![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))),
% 2.23/1.62 inference(unit_resolution,[status(thm)],[139, 116, 114, 112, 93])).
% 2.23/1.62 tff(141,plain,
% 2.23/1.62 (((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))) <=> ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | (~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 2.23/1.62 inference(rewrite,[status(thm)],[])).
% 2.23/1.62 tff(142,plain,
% 2.23/1.62 ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 2.23/1.62 inference(quant_inst,[status(thm)],[])).
% 2.23/1.62 tff(143,plain,
% 2.23/1.62 ((~![C: $i] : ((~v1_group_1(C)) | (~m1_group_2(C, A!0)) | (k1_funct_1(k1_latsubgr(A!0), C) = u1_struct_0(C)))) | (~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[142, 141])).
% 2.23/1.62 tff(144,plain,
% 2.23/1.62 ((~v1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 2.23/1.62 inference(unit_resolution,[status(thm)],[143, 140])).
% 2.23/1.62 tff(145,plain,
% 2.23/1.62 (k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.23/1.62 inference(unit_resolution,[status(thm)],[144, 72, 69])).
% 2.23/1.62 tff(146,plain,
% 2.23/1.62 (u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k1_funct_1(k1_latsubgr(A!0), g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.23/1.62 inference(symmetry,[status(thm)],[145])).
% 2.23/1.62 tff(147,plain,
% 2.23/1.62 (u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) = k1_xboole_0),
% 2.23/1.62 inference(transitivity,[status(thm)],[146, 66, 17])).
% 2.23/1.62 tff(148,plain,
% 2.23/1.62 (v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) <=> v1_xboole_0(k1_xboole_0)),
% 2.23/1.62 inference(monotonicity,[status(thm)],[147])).
% 2.23/1.62 tff(149,plain,
% 2.23/1.62 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 2.23/1.62 inference(symmetry,[status(thm)],[148])).
% 2.23/1.62 tff(150,plain,
% 2.23/1.62 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 2.23/1.62 inference(rewrite,[status(thm)],[])).
% 2.23/1.62 tff(151,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 2.23/1.62 tff(152,plain,
% 2.23/1.62 (v1_xboole_0(k1_xboole_0)),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[151, 150])).
% 2.23/1.62 tff(153,plain,
% 2.23/1.62 (v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[152, 149])).
% 2.23/1.62 tff(154,plain,
% 2.23/1.62 (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) <=> v3_struct_0(B!1)),
% 2.23/1.62 inference(monotonicity,[status(thm)],[65])).
% 2.23/1.62 tff(155,plain,
% 2.23/1.62 (v3_struct_0(B!1) <=> v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.23/1.62 inference(symmetry,[status(thm)],[154])).
% 2.23/1.62 tff(156,plain,
% 2.23/1.62 ((~v3_struct_0(B!1)) <=> (~v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 2.23/1.62 inference(monotonicity,[status(thm)],[155])).
% 2.23/1.62 tff(157,plain,
% 2.23/1.62 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | (~v3_struct_0(B!1))),
% 2.23/1.62 inference(tautology,[status(thm)],[])).
% 2.23/1.62 tff(158,plain,
% 2.23/1.62 (~v3_struct_0(B!1)),
% 2.23/1.62 inference(unit_resolution,[status(thm)],[157, 46])).
% 2.23/1.62 tff(159,plain,
% 2.23/1.62 (~v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[158, 156])).
% 2.23/1.62 tff(160,plain,
% 2.23/1.62 (l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) <=> l1_group_1(B!1)),
% 2.23/1.62 inference(monotonicity,[status(thm)],[65])).
% 2.23/1.62 tff(161,plain,
% 2.23/1.62 (l1_group_1(B!1) <=> l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.23/1.62 inference(symmetry,[status(thm)],[160])).
% 2.23/1.62 tff(162,plain,
% 2.23/1.62 (l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[48, 161])).
% 2.23/1.62 tff(163,plain,
% 2.23/1.62 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 2.23/1.62 inference(bind,[status(th)],[])).
% 2.23/1.62 tff(164,plain,
% 2.23/1.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.23/1.62 inference(quant_intro,[status(thm)],[163])).
% 2.23/1.62 tff(165,plain,
% 2.23/1.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.23/1.62 inference(rewrite,[status(thm)],[])).
% 2.23/1.62 tff(166,plain,
% 2.23/1.62 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 2.23/1.62 inference(bind,[status(th)],[])).
% 2.23/1.62 tff(167,plain,
% 2.23/1.62 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.23/1.62 inference(quant_intro,[status(thm)],[166])).
% 2.23/1.62 tff(168,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 2.23/1.62 tff(169,plain,
% 2.23/1.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[168, 167])).
% 2.23/1.62 tff(170,plain,
% 2.23/1.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[169, 165])).
% 2.23/1.62 tff(171,plain,(
% 2.23/1.62 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.23/1.62 inference(skolemize,[status(sab)],[170])).
% 2.23/1.62 tff(172,plain,
% 2.23/1.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[171, 164])).
% 2.23/1.62 tff(173,plain,
% 2.23/1.62 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 2.23/1.62 inference(rewrite,[status(thm)],[])).
% 2.23/1.62 tff(174,plain,
% 2.23/1.62 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 2.23/1.62 inference(quant_inst,[status(thm)],[])).
% 2.23/1.62 tff(175,plain,
% 2.23/1.62 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[174, 173])).
% 2.23/1.62 tff(176,plain,
% 2.23/1.62 (l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 2.23/1.62 inference(unit_resolution,[status(thm)],[175, 172])).
% 2.23/1.62 tff(177,plain,
% 2.23/1.62 (l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))),
% 2.23/1.62 inference(unit_resolution,[status(thm)],[176, 162])).
% 2.23/1.62 tff(178,plain,
% 2.23/1.62 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 2.23/1.62 inference(bind,[status(th)],[])).
% 2.23/1.62 tff(179,plain,
% 2.23/1.62 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.23/1.62 inference(quant_intro,[status(thm)],[178])).
% 2.23/1.62 tff(180,plain,
% 2.23/1.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 2.23/1.62 inference(bind,[status(th)],[])).
% 2.23/1.62 tff(181,plain,
% 2.23/1.62 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.23/1.62 inference(quant_intro,[status(thm)],[180])).
% 2.23/1.62 tff(182,plain,
% 2.23/1.62 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.23/1.62 inference(rewrite,[status(thm)],[])).
% 2.23/1.62 tff(183,plain,
% 2.23/1.62 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 2.23/1.62 inference(bind,[status(th)],[])).
% 2.23/1.62 tff(184,plain,
% 2.23/1.62 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.23/1.62 inference(quant_intro,[status(thm)],[183])).
% 2.23/1.62 tff(185,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 2.23/1.62 tff(186,plain,
% 2.23/1.62 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[185, 184])).
% 2.23/1.62 tff(187,plain,
% 2.23/1.62 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[186, 182])).
% 2.23/1.62 tff(188,plain,(
% 2.23/1.62 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.23/1.62 inference(skolemize,[status(sab)],[187])).
% 2.23/1.62 tff(189,plain,
% 2.23/1.62 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[188, 181])).
% 2.23/1.62 tff(190,plain,
% 2.23/1.62 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.23/1.62 inference(modus_ponens,[status(thm)],[189, 179])).
% 2.23/1.62 tff(191,plain,
% 2.23/1.62 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 2.23/1.62 inference(rewrite,[status(thm)],[])).
% 2.23/1.62 tff(192,plain,
% 2.23/1.62 ((v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) <=> (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 2.23/1.62 inference(rewrite,[status(thm)],[])).
% 2.23/1.62 tff(193,plain,
% 2.23/1.62 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))))),
% 2.23/1.63 inference(monotonicity,[status(thm)],[192])).
% 2.23/1.63 tff(194,plain,
% 2.23/1.63 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))))),
% 2.23/1.63 inference(transitivity,[status(thm)],[193, 191])).
% 2.23/1.63 tff(195,plain,
% 2.23/1.63 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 2.23/1.63 inference(quant_inst,[status(thm)],[])).
% 2.23/1.63 tff(196,plain,
% 2.23/1.63 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 2.23/1.63 inference(modus_ponens,[status(thm)],[195, 194])).
% 2.23/1.63 tff(197,plain,
% 2.23/1.63 (v3_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)))))),
% 2.23/1.63 inference(unit_resolution,[status(thm)],[196, 190])).
% 2.23/1.63 tff(198,plain,
% 2.23/1.63 (~v1_xboole_0(u1_struct_0(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))))),
% 2.23/1.63 inference(unit_resolution,[status(thm)],[197, 177, 159])).
% 2.23/1.63 tff(199,plain,
% 2.23/1.63 ($false),
% 2.23/1.63 inference(unit_resolution,[status(thm)],[198, 153])).
% 2.23/1.63 % SZS output end Proof
%------------------------------------------------------------------------------