TSTP Solution File: GRP643+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP643+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 22:29:06 EDT 2022
% Result : Theorem 13.22s 8.74s
% Output : Proof 13.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP643+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 19:07:13 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 13.22/8.74 % SZS status Theorem
% 13.22/8.74 % SZS output start Proof
% 13.22/8.74 tff(r1_rlvect_1_type, type, (
% 13.22/8.74 r1_rlvect_1: ( $i * $i ) > $o)).
% 13.22/8.74 tff(tptp_fun_D_3_type, type, (
% 13.22/8.74 tptp_fun_D_3: $i)).
% 13.22/8.74 tff(g1_group_1_type, type, (
% 13.22/8.74 g1_group_1: ( $i * $i ) > $i)).
% 13.22/8.74 tff(u1_group_1_type, type, (
% 13.22/8.74 u1_group_1: $i > $i)).
% 13.22/8.74 tff(tptp_fun_B_1_type, type, (
% 13.22/8.74 tptp_fun_B_1: $i)).
% 13.22/8.74 tff(u1_struct_0_type, type, (
% 13.22/8.74 u1_struct_0: $i > $i)).
% 13.22/8.74 tff(l1_group_1_type, type, (
% 13.22/8.74 l1_group_1: $i > $o)).
% 13.22/8.74 tff(v3_group_1_type, type, (
% 13.22/8.74 v3_group_1: $i > $o)).
% 13.22/8.74 tff(v3_struct_0_type, type, (
% 13.22/8.74 v3_struct_0: $i > $o)).
% 13.22/8.74 tff(m1_group_2_type, type, (
% 13.22/8.74 m1_group_2: ( $i * $i ) > $o)).
% 13.22/8.74 tff(tptp_fun_A_0_type, type, (
% 13.22/8.74 tptp_fun_A_0: $i)).
% 13.22/8.74 tff(m1_subset_1_type, type, (
% 13.22/8.74 m1_subset_1: ( $i * $i ) > $o)).
% 13.22/8.74 tff(r2_hidden_type, type, (
% 13.22/8.74 r2_hidden: ( $i * $i ) > $o)).
% 13.22/8.74 tff(k1_funct_1_type, type, (
% 13.22/8.74 k1_funct_1: ( $i * $i ) > $i)).
% 13.22/8.74 tff(k1_latsubgr_type, type, (
% 13.22/8.74 k1_latsubgr: $i > $i)).
% 13.22/8.74 tff(tptp_fun_C_2_type, type, (
% 13.22/8.74 tptp_fun_C_2: $i)).
% 13.22/8.74 tff(k1_group_1_type, type, (
% 13.22/8.74 k1_group_1: ( $i * $i * $i ) > $i)).
% 13.22/8.74 tff(v1_group_1_type, type, (
% 13.22/8.74 v1_group_1: $i > $o)).
% 13.22/8.74 tff(v4_group_1_type, type, (
% 13.22/8.74 v4_group_1: $i > $o)).
% 13.22/8.74 tff(1,plain,
% 13.22/8.74 (^[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)))))))),
% 13.22/8.74 inference(bind,[status(th)],[])).
% 13.22/8.74 tff(2,plain,
% 13.22/8.74 (![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))))))),
% 13.22/8.74 inference(quant_intro,[status(thm)],[1])).
% 13.22/8.74 tff(3,plain,
% 13.22/8.74 (^[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)))))))),
% 13.22/8.74 inference(bind,[status(th)],[])).
% 13.22/8.74 tff(4,plain,
% 13.22/8.74 (![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))))))),
% 13.22/8.74 inference(quant_intro,[status(thm)],[3])).
% 13.22/8.74 tff(5,plain,
% 13.22/8.74 (![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))))))),
% 13.22/8.74 inference(transitivity,[status(thm)],[4, 2])).
% 13.22/8.74 tff(6,plain,
% 13.22/8.74 (^[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))))))))),
% 13.22/8.74 inference(bind,[status(th)],[])).
% 13.22/8.74 tff(7,plain,
% 13.22/8.74 (![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))))))),
% 13.22/8.74 inference(quant_intro,[status(thm)],[6])).
% 13.22/8.74 tff(8,plain,
% 13.22/8.74 (![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))))),
% 13.22/8.74 inference(rewrite,[status(thm)],[])).
% 13.22/8.74 tff(9,plain,
% 13.22/8.74 (^[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))))))),
% 13.22/8.74 inference(bind,[status(th)],[])).
% 13.22/8.74 tff(10,plain,
% 13.22/8.74 (![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))))),
% 13.22/8.74 inference(quant_intro,[status(thm)],[9])).
% 13.22/8.74 tff(11,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')).
% 13.22/8.75 tff(12,plain,
% 13.22/8.75 (![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))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[11, 10])).
% 13.22/8.75 tff(13,plain,
% 13.22/8.75 (![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))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[12, 8])).
% 13.22/8.75 tff(14,plain,(
% 13.22/8.75 ![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))))),
% 13.22/8.75 inference(skolemize,[status(sab)],[13])).
% 13.22/8.75 tff(15,plain,
% 13.22/8.75 (![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))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[14, 7])).
% 13.22/8.75 tff(16,plain,
% 13.22/8.75 (![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))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[15, 5])).
% 13.22/8.75 tff(17,plain,
% 13.22/8.75 ((((~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) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!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) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(18,plain,
% 13.22/8.75 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(19,plain,
% 13.22/8.75 (((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(20,plain,
% 13.22/8.75 ((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(21,plain,
% 13.22/8.75 (((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))) <=> ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))))),
% 13.22/8.75 inference(monotonicity,[status(thm)],[20, 19])).
% 13.22/8.75 tff(22,plain,
% 13.22/8.75 (((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 13.22/8.75 inference(transitivity,[status(thm)],[21, 18])).
% 13.22/8.75 tff(23,plain,
% 13.22/8.75 ((~(~((~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))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(24,plain,
% 13.22/8.75 (((~(~((~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)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!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) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))))),
% 13.22/8.75 inference(monotonicity,[status(thm)],[23, 22])).
% 13.22/8.75 tff(25,plain,
% 13.22/8.75 (((~(~((~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)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!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) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 13.22/8.75 inference(transitivity,[status(thm)],[24, 17])).
% 13.22/8.75 tff(26,plain,
% 13.22/8.75 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(27,plain,
% 13.22/8.75 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B))) => r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(28,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B))) => r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_latsubgr')).
% 13.22/8.75 tff(29,plain,
% 13.22/8.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[28, 27])).
% 13.22/8.75 tff(30,plain,
% 13.22/8.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[29, 26])).
% 13.22/8.75 tff(31,plain,
% 13.22/8.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[30, 26])).
% 13.22/8.75 tff(32,plain,
% 13.22/8.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[31, 26])).
% 13.22/8.75 tff(33,plain,
% 13.22/8.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[32, 26])).
% 13.22/8.75 tff(34,plain,
% 13.22/8.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[33, 26])).
% 13.22/8.75 tff(35,plain,
% 13.22/8.75 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[34, 26])).
% 13.22/8.75 tff(36,plain,
% 13.22/8.75 ((~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) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[35, 25])).
% 13.22/8.75 tff(37,plain,
% 13.22/8.75 (l1_group_1(A!0)),
% 13.22/8.75 inference(and_elim,[status(thm)],[36])).
% 13.22/8.75 tff(38,plain,
% 13.22/8.75 (v3_group_1(A!0)),
% 13.22/8.75 inference(and_elim,[status(thm)],[36])).
% 13.22/8.75 tff(39,plain,
% 13.22/8.75 (~v3_struct_0(A!0)),
% 13.22/8.75 inference(and_elim,[status(thm)],[36])).
% 13.22/8.75 tff(40,plain,
% 13.22/8.75 (((~![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))))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(41,plain,
% 13.22/8.75 ((~![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))))))),
% 13.22/8.75 inference(quant_inst,[status(thm)],[])).
% 13.22/8.75 tff(42,plain,
% 13.22/8.75 ((~![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)))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[41, 40])).
% 13.22/8.75 tff(43,plain,
% 13.22/8.75 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 13.22/8.75 inference(unit_resolution,[status(thm)],[42, 39, 38, 37, 16])).
% 13.22/8.75 tff(44,plain,
% 13.22/8.75 (m1_group_2(B!1, A!0)),
% 13.22/8.75 inference(and_elim,[status(thm)],[36])).
% 13.22/8.75 tff(45,plain,
% 13.22/8.75 (((~![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)))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(46,plain,
% 13.22/8.75 ((~![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)))))),
% 13.22/8.75 inference(quant_inst,[status(thm)],[])).
% 13.22/8.75 tff(47,plain,
% 13.22/8.75 ((~![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))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[46, 45])).
% 13.22/8.75 tff(48,plain,
% 13.22/8.75 (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))),
% 13.22/8.75 inference(unit_resolution,[status(thm)],[47, 44, 43])).
% 13.22/8.75 tff(49,plain,
% 13.22/8.75 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | l1_group_1(B!1)),
% 13.22/8.75 inference(tautology,[status(thm)],[])).
% 13.22/8.75 tff(50,plain,
% 13.22/8.75 (l1_group_1(B!1)),
% 13.22/8.75 inference(unit_resolution,[status(thm)],[49, 48])).
% 13.22/8.75 tff(51,plain,
% 13.22/8.75 (^[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))))),
% 13.22/8.75 inference(bind,[status(th)],[])).
% 13.22/8.75 tff(52,plain,
% 13.22/8.75 (![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)))),
% 13.22/8.75 inference(quant_intro,[status(thm)],[51])).
% 13.22/8.75 tff(53,plain,
% 13.22/8.75 (![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)))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(54,plain,
% 13.22/8.75 (^[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)))))),
% 13.22/8.75 inference(bind,[status(th)],[])).
% 13.22/8.75 tff(55,plain,
% 13.22/8.75 (![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)))),
% 13.22/8.75 inference(quant_intro,[status(thm)],[54])).
% 13.22/8.75 tff(56,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')).
% 13.22/8.75 tff(57,plain,
% 13.22/8.75 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[56, 55])).
% 13.22/8.75 tff(58,plain,
% 13.22/8.75 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[57, 53])).
% 13.22/8.75 tff(59,plain,(
% 13.22/8.75 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 13.22/8.75 inference(skolemize,[status(sab)],[58])).
% 13.22/8.75 tff(60,plain,
% 13.22/8.75 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[59, 52])).
% 13.22/8.75 tff(61,plain,
% 13.22/8.75 (v1_group_1(B!1)),
% 13.22/8.75 inference(and_elim,[status(thm)],[36])).
% 13.22/8.75 tff(62,plain,
% 13.22/8.75 (((~![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)))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(63,plain,
% 13.22/8.75 ((~![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)))),
% 13.22/8.75 inference(quant_inst,[status(thm)],[])).
% 13.22/8.75 tff(64,plain,
% 13.22/8.75 ((~![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))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[63, 62])).
% 13.22/8.75 tff(65,plain,
% 13.22/8.75 ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(B!1))),
% 13.22/8.75 inference(unit_resolution,[status(thm)],[64, 61, 60])).
% 13.22/8.75 tff(66,plain,
% 13.22/8.75 (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))),
% 13.22/8.75 inference(unit_resolution,[status(thm)],[65, 50])).
% 13.22/8.75 tff(67,plain,
% 13.22/8.75 (g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)) = B!1),
% 13.22/8.75 inference(symmetry,[status(thm)],[66])).
% 13.22/8.75 tff(68,plain,
% 13.22/8.75 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3) <=> r1_rlvect_1(B!1, D!3)),
% 13.22/8.75 inference(monotonicity,[status(thm)],[67])).
% 13.22/8.75 tff(69,plain,
% 13.22/8.75 (r1_rlvect_1(B!1, D!3) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)),
% 13.22/8.75 inference(symmetry,[status(thm)],[68])).
% 13.22/8.75 tff(70,plain,
% 13.22/8.75 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))),
% 13.22/8.75 inference(bind,[status(th)],[])).
% 13.22/8.75 tff(71,plain,
% 13.22/8.75 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(quant_intro,[status(thm)],[70])).
% 13.22/8.75 tff(72,plain,
% 13.22/8.75 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))),
% 13.22/8.75 inference(bind,[status(th)],[])).
% 13.22/8.75 tff(73,plain,
% 13.22/8.75 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(quant_intro,[status(thm)],[72])).
% 13.22/8.75 tff(74,plain,
% 13.22/8.75 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(transitivity,[status(thm)],[73, 71])).
% 13.22/8.75 tff(75,plain,
% 13.22/8.75 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_group_1(B) & m1_group_2(B, A)) <=> (~((~v1_group_1(B)) | (~m1_group_2(B, A))))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> (~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))))), rewrite((~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> (((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), rewrite((((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), (![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))))),
% 13.22/8.75 inference(bind,[status(th)],[])).
% 13.22/8.75 tff(76,plain,
% 13.22/8.75 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(quant_intro,[status(thm)],[75])).
% 13.22/8.75 tff(77,plain,
% 13.22/8.75 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(78,plain,
% 13.22/8.75 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), rewrite(((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), (![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))))),
% 13.22/8.75 inference(bind,[status(th)],[])).
% 13.22/8.75 tff(79,plain,
% 13.22/8.75 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(quant_intro,[status(thm)],[78])).
% 13.22/8.75 tff(80,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_latsubgr')).
% 13.22/8.75 tff(81,plain,
% 13.22/8.75 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[80, 79])).
% 13.22/8.75 tff(82,plain,
% 13.22/8.75 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[81, 77])).
% 13.22/8.75 tff(83,plain,(
% 13.22/8.75 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(skolemize,[status(sab)],[82])).
% 13.22/8.75 tff(84,plain,
% 13.22/8.75 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[83, 76])).
% 13.22/8.75 tff(85,plain,
% 13.22/8.75 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(modus_ponens,[status(thm)],[84, 74])).
% 13.22/8.75 tff(86,plain,
% 13.22/8.75 (v4_group_1(A!0)),
% 13.22/8.75 inference(and_elim,[status(thm)],[36])).
% 13.22/8.75 tff(87,plain,
% 13.22/8.75 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.75 inference(rewrite,[status(thm)],[])).
% 13.22/8.75 tff(88,plain,
% 13.22/8.75 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))),
% 13.22/8.76 inference(quant_inst,[status(thm)],[])).
% 13.22/8.76 tff(89,plain,
% 13.22/8.76 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[88, 87])).
% 13.22/8.76 tff(90,plain,
% 13.22/8.76 (![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[89, 39, 38, 86, 37, 85])).
% 13.22/8.76 tff(91,plain,
% 13.22/8.76 (((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | ((~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))) <=> ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | (~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))),
% 13.22/8.76 inference(rewrite,[status(thm)],[])).
% 13.22/8.76 tff(92,plain,
% 13.22/8.76 ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | ((~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))),
% 13.22/8.76 inference(quant_inst,[status(thm)],[])).
% 13.22/8.76 tff(93,plain,
% 13.22/8.76 ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | (~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[92, 91])).
% 13.22/8.76 tff(94,plain,
% 13.22/8.76 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[93, 61, 44, 90])).
% 13.22/8.76 tff(95,plain,
% 13.22/8.76 (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))),
% 13.22/8.76 inference(and_elim,[status(thm)],[36])).
% 13.22/8.76 tff(96,plain,
% 13.22/8.76 (m1_subset_1(D!3, u1_struct_0(A!0))),
% 13.22/8.76 inference(or_elim,[status(thm)],[95])).
% 13.22/8.76 tff(97,plain,
% 13.22/8.76 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3)))),
% 13.22/8.76 inference(rewrite,[status(thm)],[])).
% 13.22/8.76 tff(98,plain,
% 13.22/8.76 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3)))),
% 13.22/8.76 inference(quant_inst,[status(thm)],[])).
% 13.22/8.76 tff(99,plain,
% 13.22/8.76 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[98, 97])).
% 13.22/8.76 tff(100,plain,
% 13.22/8.76 (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3)),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[99, 96, 94])).
% 13.22/8.76 tff(101,plain,
% 13.22/8.76 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1))),
% 13.22/8.76 inference(or_elim,[status(thm)],[95])).
% 13.22/8.76 tff(102,plain,
% 13.22/8.76 (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1))),
% 13.22/8.76 inference(and_elim,[status(thm)],[101])).
% 13.22/8.76 tff(103,plain,
% 13.22/8.76 ((~(r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3))) | (~r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1))) | r1_rlvect_1(B!1, D!3)),
% 13.22/8.76 inference(tautology,[status(thm)],[])).
% 13.22/8.76 tff(104,plain,
% 13.22/8.76 ((~(r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3))) | r1_rlvect_1(B!1, D!3)),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[103, 102])).
% 13.22/8.76 tff(105,plain,
% 13.22/8.76 (r1_rlvect_1(B!1, D!3)),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[104, 100])).
% 13.22/8.76 tff(106,plain,
% 13.22/8.76 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[105, 69])).
% 13.22/8.76 tff(107,plain,
% 13.22/8.76 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2) <=> r1_rlvect_1(B!1, C!2)),
% 13.22/8.76 inference(monotonicity,[status(thm)],[67])).
% 13.22/8.76 tff(108,plain,
% 13.22/8.76 (r1_rlvect_1(B!1, C!2) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)),
% 13.22/8.76 inference(symmetry,[status(thm)],[107])).
% 13.22/8.76 tff(109,plain,
% 13.22/8.76 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 13.22/8.76 inference(and_elim,[status(thm)],[36])).
% 13.22/8.76 tff(110,plain,
% 13.22/8.76 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))),
% 13.22/8.76 inference(rewrite,[status(thm)],[])).
% 13.22/8.76 tff(111,plain,
% 13.22/8.76 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))),
% 13.22/8.76 inference(quant_inst,[status(thm)],[])).
% 13.22/8.76 tff(112,plain,
% 13.22/8.76 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[111, 110])).
% 13.22/8.76 tff(113,plain,
% 13.22/8.76 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[112, 109, 94])).
% 13.22/8.76 tff(114,plain,
% 13.22/8.76 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))),
% 13.22/8.76 inference(and_elim,[status(thm)],[101])).
% 13.22/8.76 tff(115,plain,
% 13.22/8.76 ((~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | r1_rlvect_1(B!1, C!2)),
% 13.22/8.76 inference(tautology,[status(thm)],[])).
% 13.22/8.76 tff(116,plain,
% 13.22/8.76 ((~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))) | r1_rlvect_1(B!1, C!2)),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[115, 114])).
% 13.22/8.76 tff(117,plain,
% 13.22/8.76 (r1_rlvect_1(B!1, C!2)),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[116, 113])).
% 13.22/8.76 tff(118,plain,
% 13.22/8.76 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[117, 108])).
% 13.22/8.76 tff(119,plain,
% 13.22/8.76 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))),
% 13.22/8.76 inference(monotonicity,[status(thm)],[67])).
% 13.22/8.76 tff(120,plain,
% 13.22/8.76 (r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3))),
% 13.22/8.76 inference(symmetry,[status(thm)],[119])).
% 13.22/8.76 tff(121,plain,
% 13.22/8.76 ((~r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))) <=> (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)))),
% 13.22/8.76 inference(monotonicity,[status(thm)],[120])).
% 13.22/8.76 tff(122,plain,
% 13.22/8.76 (^[A: $i, B: $i, C: $i] : refl((m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 13.22/8.76 inference(bind,[status(th)],[])).
% 13.22/8.76 tff(123,plain,
% 13.22/8.76 (![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 13.22/8.76 inference(quant_intro,[status(thm)],[122])).
% 13.22/8.76 tff(124,plain,
% 13.22/8.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 13.22/8.76 inference(bind,[status(th)],[])).
% 13.22/8.76 tff(125,plain,
% 13.22/8.76 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 13.22/8.76 inference(quant_intro,[status(thm)],[124])).
% 13.22/8.76 tff(126,plain,
% 13.22/8.76 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 13.22/8.76 inference(rewrite,[status(thm)],[])).
% 13.22/8.76 tff(127,plain,
% 13.22/8.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))), ((((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))))),
% 13.22/8.76 inference(bind,[status(th)],[])).
% 13.22/8.76 tff(128,plain,
% 13.22/8.76 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 13.22/8.76 inference(quant_intro,[status(thm)],[127])).
% 13.22/8.76 tff(129,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_group_1')).
% 13.22/8.76 tff(130,plain,
% 13.22/8.76 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[129, 128])).
% 13.22/8.76 tff(131,plain,
% 13.22/8.76 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[130, 126])).
% 13.22/8.76 tff(132,plain,(
% 13.22/8.76 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 13.22/8.76 inference(skolemize,[status(sab)],[131])).
% 13.22/8.76 tff(133,plain,
% 13.22/8.76 (![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[132, 125])).
% 13.22/8.76 tff(134,plain,
% 13.22/8.76 (![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[133, 123])).
% 13.22/8.76 tff(135,plain,
% 13.22/8.76 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)))),
% 13.22/8.76 inference(rewrite,[status(thm)],[])).
% 13.22/8.76 tff(136,plain,
% 13.22/8.76 ((m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)))),
% 13.22/8.76 inference(rewrite,[status(thm)],[])).
% 13.22/8.76 tff(137,plain,
% 13.22/8.76 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))))),
% 13.22/8.76 inference(monotonicity,[status(thm)],[136])).
% 13.22/8.76 tff(138,plain,
% 13.22/8.76 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)))),
% 13.22/8.76 inference(transitivity,[status(thm)],[137, 135])).
% 13.22/8.76 tff(139,plain,
% 13.22/8.76 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 13.22/8.76 inference(quant_inst,[status(thm)],[])).
% 13.22/8.76 tff(140,plain,
% 13.22/8.76 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[139, 138])).
% 13.22/8.76 tff(141,plain,
% 13.22/8.76 (m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[140, 39, 37, 109, 96, 134])).
% 13.22/8.76 tff(142,plain,
% 13.22/8.76 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))) | (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))) | (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))))),
% 13.22/8.76 inference(rewrite,[status(thm)],[])).
% 13.22/8.76 tff(143,plain,
% 13.22/8.76 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))) | (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))))),
% 13.22/8.76 inference(quant_inst,[status(thm)],[])).
% 13.22/8.76 tff(144,plain,
% 13.22/8.76 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))) | (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[143, 142])).
% 13.22/8.76 tff(145,plain,
% 13.22/8.76 (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[144, 141, 94])).
% 13.22/8.76 tff(146,plain,
% 13.22/8.76 (~r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1))),
% 13.22/8.76 inference(or_elim,[status(thm)],[95])).
% 13.22/8.76 tff(147,plain,
% 13.22/8.76 ((~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))) | r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))),
% 13.22/8.76 inference(tautology,[status(thm)],[])).
% 13.22/8.76 tff(148,plain,
% 13.22/8.76 ((~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))) | (~r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[147, 146])).
% 13.22/8.76 tff(149,plain,
% 13.22/8.76 (~r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))),
% 13.22/8.76 inference(unit_resolution,[status(thm)],[148, 145])).
% 13.22/8.76 tff(150,plain,
% 13.22/8.76 (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[149, 121])).
% 13.22/8.76 tff(151,plain,
% 13.22/8.76 (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)),
% 13.22/8.76 inference(monotonicity,[status(thm)],[67])).
% 13.22/8.76 tff(152,plain,
% 13.22/8.76 (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)),
% 13.22/8.76 inference(symmetry,[status(thm)],[151])).
% 13.22/8.76 tff(153,plain,
% 13.22/8.76 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[44, 152])).
% 13.22/8.76 tff(154,plain,
% 13.22/8.76 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))))),
% 13.22/8.76 inference(bind,[status(th)],[])).
% 13.22/8.76 tff(155,plain,
% 13.22/8.76 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 13.22/8.76 inference(quant_intro,[status(thm)],[154])).
% 13.22/8.76 tff(156,plain,
% 13.22/8.76 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))))),
% 13.22/8.76 inference(bind,[status(th)],[])).
% 13.22/8.76 tff(157,plain,
% 13.22/8.76 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 13.22/8.76 inference(quant_intro,[status(thm)],[156])).
% 13.22/8.76 tff(158,plain,
% 13.22/8.76 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 13.22/8.76 inference(transitivity,[status(thm)],[157, 155])).
% 13.22/8.76 tff(159,plain,
% 13.22/8.76 (^[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] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))))),
% 13.22/8.76 inference(bind,[status(th)],[])).
% 13.22/8.76 tff(160,plain,
% 13.22/8.76 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 13.22/8.76 inference(quant_intro,[status(thm)],[159])).
% 13.22/8.76 tff(161,plain,
% 13.22/8.76 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 13.22/8.76 inference(rewrite,[status(thm)],[])).
% 13.22/8.76 tff(162,plain,
% 13.22/8.76 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))) <=> ((~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | r1_rlvect_1(D, k1_group_1(A, B, C)))), ((m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))) <=> (m1_group_2(D, A) => ((~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | r1_rlvect_1(D, k1_group_1(A, B, C)))))), rewrite((m1_group_2(D, A) => ((~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | r1_rlvect_1(D, k1_group_1(A, B, C)))) <=> (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))), ((m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))) <=> (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))), (![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))) <=> ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))))),
% 13.22/8.76 inference(bind,[status(th)],[])).
% 13.22/8.76 tff(163,plain,
% 13.22/8.76 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 13.22/8.76 inference(quant_intro,[status(thm)],[162])).
% 13.22/8.76 tff(164,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t59_group_2')).
% 13.22/8.76 tff(165,plain,
% 13.22/8.76 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[164, 163])).
% 13.22/8.76 tff(166,plain,
% 13.22/8.76 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 13.22/8.76 inference(modus_ponens,[status(thm)],[165, 161])).
% 13.22/8.76 tff(167,plain,(
% 13.22/8.76 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 13.22/8.76 inference(skolemize,[status(sab)],[166])).
% 13.22/8.76 tff(168,plain,
% 13.22/8.76 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 13.22/8.77 inference(modus_ponens,[status(thm)],[167, 160])).
% 13.22/8.77 tff(169,plain,
% 13.22/8.77 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 13.22/8.77 inference(modus_ponens,[status(thm)],[168, 158])).
% 13.22/8.77 tff(170,plain,
% 13.22/8.77 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0))))))),
% 13.22/8.77 inference(rewrite,[status(thm)],[])).
% 13.22/8.77 tff(171,plain,
% 13.22/8.77 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0))))))),
% 13.22/8.77 inference(rewrite,[status(thm)],[])).
% 13.22/8.77 tff(172,plain,
% 13.22/8.77 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))))),
% 13.22/8.77 inference(monotonicity,[status(thm)],[171])).
% 13.22/8.77 tff(173,plain,
% 13.22/8.77 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0))))))),
% 13.22/8.77 inference(transitivity,[status(thm)],[172, 170])).
% 13.22/8.77 tff(174,plain,
% 13.22/8.77 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 13.22/8.77 inference(quant_inst,[status(thm)],[])).
% 13.22/8.77 tff(175,plain,
% 13.22/8.77 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))),
% 13.22/8.77 inference(modus_ponens,[status(thm)],[174, 173])).
% 13.22/8.77 tff(176,plain,
% 13.22/8.77 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))),
% 13.22/8.77 inference(unit_resolution,[status(thm)],[175, 39, 38, 86, 37, 169])).
% 13.22/8.77 tff(177,plain,
% 13.22/8.77 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)))))),
% 13.22/8.77 inference(rewrite,[status(thm)],[])).
% 13.22/8.77 tff(178,plain,
% 13.22/8.77 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~m1_group_2(D, A!0))))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)))))),
% 13.22/8.77 inference(rewrite,[status(thm)],[])).
% 13.22/8.77 tff(179,plain,
% 13.22/8.77 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~m1_group_2(D, A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))))),
% 13.22/8.77 inference(monotonicity,[status(thm)],[178])).
% 13.22/8.77 tff(180,plain,
% 13.22/8.77 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~m1_group_2(D, A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)))))),
% 13.22/8.77 inference(transitivity,[status(thm)],[179, 177])).
% 13.22/8.77 tff(181,plain,
% 13.22/8.77 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~m1_group_2(D, A!0)))))),
% 13.22/8.77 inference(quant_inst,[status(thm)],[])).
% 13.22/8.77 tff(182,plain,
% 13.22/8.77 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))),
% 13.22/8.77 inference(modus_ponens,[status(thm)],[181, 180])).
% 13.22/8.77 tff(183,plain,
% 13.22/8.77 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))),
% 13.22/8.77 inference(unit_resolution,[status(thm)],[182, 109, 176])).
% 13.22/8.77 tff(184,plain,
% 13.22/8.77 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3))))),
% 13.22/8.77 inference(rewrite,[status(thm)],[])).
% 13.22/8.77 tff(185,plain,
% 13.22/8.77 (((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, D!3)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)))) <=> ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3))))),
% 13.22/8.77 inference(rewrite,[status(thm)],[])).
% 13.22/8.77 tff(186,plain,
% 13.22/8.77 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, D!3)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))))),
% 13.22/8.77 inference(monotonicity,[status(thm)],[185])).
% 13.22/8.77 tff(187,plain,
% 13.22/8.77 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, D!3)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3))))),
% 13.22/8.77 inference(transitivity,[status(thm)],[186, 184])).
% 13.22/8.77 tff(188,plain,
% 13.22/8.77 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, D!3)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3))))),
% 13.22/8.77 inference(quant_inst,[status(thm)],[])).
% 13.22/8.77 tff(189,plain,
% 13.22/8.77 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, C!2)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))),
% 13.22/8.77 inference(modus_ponens,[status(thm)],[188, 187])).
% 13.22/8.77 tff(190,plain,
% 13.22/8.77 (![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))),
% 13.22/8.77 inference(unit_resolution,[status(thm)],[189, 96, 183])).
% 13.22/8.77 tff(191,plain,
% 13.22/8.77 (((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))) <=> ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))),
% 13.22/8.77 inference(rewrite,[status(thm)],[])).
% 13.22/8.77 tff(192,plain,
% 13.22/8.77 (((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3))) <=> (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))),
% 13.32/8.78 inference(rewrite,[status(thm)],[])).
% 13.32/8.78 tff(193,plain,
% 13.32/8.78 (((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))) <=> ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3))))),
% 13.32/8.78 inference(monotonicity,[status(thm)],[192])).
% 13.32/8.78 tff(194,plain,
% 13.32/8.78 (((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))) <=> ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))),
% 13.32/8.78 inference(transitivity,[status(thm)],[193, 191])).
% 13.32/8.78 tff(195,plain,
% 13.32/8.78 ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))),
% 13.32/8.78 inference(quant_inst,[status(thm)],[])).
% 13.32/8.78 tff(196,plain,
% 13.32/8.78 ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3))),
% 13.32/8.78 inference(modus_ponens,[status(thm)],[195, 194])).
% 13.32/8.78 tff(197,plain,
% 13.32/8.78 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3))),
% 13.32/8.78 inference(unit_resolution,[status(thm)],[196, 190])).
% 13.32/8.78 tff(198,plain,
% 13.32/8.78 ($false),
% 13.32/8.78 inference(unit_resolution,[status(thm)],[197, 153, 150, 118, 106])).
% 13.32/8.78 % SZS output end Proof
%------------------------------------------------------------------------------