TSTP Solution File: GRP644+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP644+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:29:07 EDT 2022
% Result : Theorem 1.59s 1.23s
% Output : Proof 1.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP644+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 18:55:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.59/1.23 % SZS status Theorem
% 1.59/1.23 % SZS output start Proof
% 1.59/1.23 tff(r1_rlvect_1_type, type, (
% 1.59/1.23 r1_rlvect_1: ( $i * $i ) > $o)).
% 1.59/1.23 tff(tptp_fun_C_2_type, type, (
% 1.59/1.23 tptp_fun_C_2: $i)).
% 1.59/1.23 tff(g1_group_1_type, type, (
% 1.59/1.23 g1_group_1: ( $i * $i ) > $i)).
% 1.59/1.23 tff(u1_group_1_type, type, (
% 1.59/1.23 u1_group_1: $i > $i)).
% 1.59/1.23 tff(tptp_fun_B_1_type, type, (
% 1.59/1.23 tptp_fun_B_1: $i)).
% 1.59/1.23 tff(u1_struct_0_type, type, (
% 1.59/1.23 u1_struct_0: $i > $i)).
% 1.59/1.23 tff(l1_group_1_type, type, (
% 1.59/1.23 l1_group_1: $i > $o)).
% 1.59/1.23 tff(v3_group_1_type, type, (
% 1.59/1.23 v3_group_1: $i > $o)).
% 1.59/1.23 tff(v3_struct_0_type, type, (
% 1.59/1.23 v3_struct_0: $i > $o)).
% 1.59/1.23 tff(m1_group_2_type, type, (
% 1.59/1.23 m1_group_2: ( $i * $i ) > $o)).
% 1.59/1.23 tff(tptp_fun_A_0_type, type, (
% 1.59/1.23 tptp_fun_A_0: $i)).
% 1.59/1.23 tff(m1_subset_1_type, type, (
% 1.59/1.23 m1_subset_1: ( $i * $i ) > $o)).
% 1.59/1.23 tff(r2_hidden_type, type, (
% 1.59/1.23 r2_hidden: ( $i * $i ) > $o)).
% 1.59/1.23 tff(k1_funct_1_type, type, (
% 1.59/1.23 k1_funct_1: ( $i * $i ) > $i)).
% 1.59/1.23 tff(k1_latsubgr_type, type, (
% 1.59/1.23 k1_latsubgr: $i > $i)).
% 1.59/1.23 tff(k3_group_1_type, type, (
% 1.59/1.23 k3_group_1: ( $i * $i ) > $i)).
% 1.59/1.23 tff(v1_group_1_type, type, (
% 1.59/1.23 v1_group_1: $i > $o)).
% 1.59/1.23 tff(v4_group_1_type, type, (
% 1.59/1.23 v4_group_1: $i > $o)).
% 1.59/1.23 tff(1,plain,
% 1.59/1.23 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 1.59/1.23 inference(bind,[status(th)],[])).
% 1.59/1.23 tff(2,plain,
% 1.59/1.23 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.59/1.23 inference(quant_intro,[status(thm)],[1])).
% 1.59/1.23 tff(3,plain,
% 1.59/1.23 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 1.59/1.23 inference(bind,[status(th)],[])).
% 1.59/1.23 tff(4,plain,
% 1.59/1.23 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.59/1.23 inference(quant_intro,[status(thm)],[3])).
% 1.59/1.23 tff(5,plain,
% 1.59/1.23 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.59/1.23 inference(transitivity,[status(thm)],[4, 2])).
% 1.59/1.23 tff(6,plain,
% 1.59/1.23 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))))),
% 1.59/1.24 inference(bind,[status(th)],[])).
% 1.59/1.24 tff(7,plain,
% 1.59/1.24 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.59/1.24 inference(quant_intro,[status(thm)],[6])).
% 1.59/1.24 tff(8,plain,
% 1.59/1.24 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(9,plain,
% 1.59/1.24 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> (m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), rewrite((m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), (![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))))),
% 1.59/1.24 inference(bind,[status(th)],[])).
% 1.59/1.24 tff(10,plain,
% 1.59/1.24 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.59/1.24 inference(quant_intro,[status(thm)],[9])).
% 1.59/1.24 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')).
% 1.60/1.24 tff(12,plain,
% 1.60/1.24 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.60/1.24 tff(13,plain,
% 1.60/1.24 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.60/1.24 tff(14,plain,(
% 1.60/1.24 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.60/1.24 inference(skolemize,[status(sab)],[13])).
% 1.60/1.24 tff(15,plain,
% 1.60/1.24 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.60/1.24 tff(16,plain,
% 1.60/1.24 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.60/1.24 tff(17,plain,
% 1.60/1.24 ((((~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) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, 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) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(18,plain,
% 1.60/1.24 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(19,plain,
% 1.60/1.24 ((~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(20,plain,
% 1.60/1.24 ((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(21,plain,
% 1.60/1.24 (((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))) <=> ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.60/1.24 inference(monotonicity,[status(thm)],[20, 19])).
% 1.60/1.24 tff(22,plain,
% 1.60/1.24 (((~(~(v1_group_1(B!1) & m1_group_2(B!1, A!0)))) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.60/1.24 inference(transitivity,[status(thm)],[21, 18])).
% 1.60/1.24 tff(23,plain,
% 1.60/1.24 ((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(24,plain,
% 1.60/1.24 (((~(~((~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)))) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, 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) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))))),
% 1.60/1.24 inference(monotonicity,[status(thm)],[23, 22])).
% 1.60/1.24 tff(25,plain,
% 1.60/1.24 (((~(~((~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)))) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, 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) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.60/1.24 inference(transitivity,[status(thm)],[24, 17])).
% 1.60/1.24 tff(26,plain,
% 1.60/1.24 ((~![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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, 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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(27,plain,
% 1.60/1.24 ((~![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)) => r2_hidden(k3_group_1(A, C), 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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 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)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) => r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_latsubgr')).
% 1.60/1.24 tff(29,plain,
% 1.60/1.24 (~![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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.60/1.24 tff(30,plain,
% 1.60/1.24 (~![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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[29, 26])).
% 1.60/1.24 tff(31,plain,
% 1.60/1.24 (~![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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.60/1.24 tff(32,plain,
% 1.60/1.24 (~![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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[31, 26])).
% 1.60/1.24 tff(33,plain,
% 1.60/1.24 (~![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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[32, 26])).
% 1.60/1.24 tff(34,plain,
% 1.60/1.24 (~![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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.60/1.24 tff(35,plain,
% 1.60/1.24 (~![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] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[34, 26])).
% 1.60/1.24 tff(36,plain,
% 1.60/1.24 ((~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) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[35, 25])).
% 1.60/1.24 tff(37,plain,
% 1.60/1.24 (l1_group_1(A!0)),
% 1.60/1.24 inference(and_elim,[status(thm)],[36])).
% 1.60/1.24 tff(38,plain,
% 1.60/1.24 (v3_group_1(A!0)),
% 1.60/1.24 inference(and_elim,[status(thm)],[36])).
% 1.60/1.24 tff(39,plain,
% 1.60/1.24 (~v3_struct_0(A!0)),
% 1.60/1.24 inference(and_elim,[status(thm)],[36])).
% 1.60/1.24 tff(40,plain,
% 1.60/1.24 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(41,plain,
% 1.60/1.24 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.60/1.24 inference(quant_inst,[status(thm)],[])).
% 1.60/1.24 tff(42,plain,
% 1.60/1.24 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.60/1.24 tff(43,plain,
% 1.60/1.24 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 1.60/1.24 inference(unit_resolution,[status(thm)],[42, 39, 38, 37, 16])).
% 1.60/1.24 tff(44,plain,
% 1.60/1.24 (m1_group_2(B!1, A!0)),
% 1.60/1.24 inference(and_elim,[status(thm)],[36])).
% 1.60/1.24 tff(45,plain,
% 1.60/1.24 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(46,plain,
% 1.60/1.24 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))),
% 1.60/1.24 inference(quant_inst,[status(thm)],[])).
% 1.60/1.24 tff(47,plain,
% 1.60/1.24 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.60/1.24 tff(48,plain,
% 1.60/1.24 (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))),
% 1.60/1.24 inference(unit_resolution,[status(thm)],[47, 44, 43])).
% 1.60/1.24 tff(49,plain,
% 1.60/1.24 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | l1_group_1(B!1)),
% 1.60/1.24 inference(tautology,[status(thm)],[])).
% 1.60/1.24 tff(50,plain,
% 1.60/1.24 (l1_group_1(B!1)),
% 1.60/1.24 inference(unit_resolution,[status(thm)],[49, 48])).
% 1.60/1.24 tff(51,plain,
% 1.60/1.24 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))))),
% 1.60/1.24 inference(bind,[status(th)],[])).
% 1.60/1.24 tff(52,plain,
% 1.60/1.24 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.24 inference(quant_intro,[status(thm)],[51])).
% 1.60/1.24 tff(53,plain,
% 1.60/1.24 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(54,plain,
% 1.60/1.24 (^[A: $i] : trans(monotonicity(rewrite((v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))) <=> ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> (l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))))), rewrite((l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))))),
% 1.60/1.24 inference(bind,[status(th)],[])).
% 1.60/1.24 tff(55,plain,
% 1.60/1.24 (![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.24 inference(quant_intro,[status(thm)],[54])).
% 1.60/1.24 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')).
% 1.60/1.24 tff(57,plain,
% 1.60/1.24 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.60/1.24 tff(58,plain,
% 1.60/1.24 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[57, 53])).
% 1.60/1.24 tff(59,plain,(
% 1.60/1.24 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.24 inference(skolemize,[status(sab)],[58])).
% 1.60/1.24 tff(60,plain,
% 1.60/1.24 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[59, 52])).
% 1.60/1.24 tff(61,plain,
% 1.60/1.24 (v1_group_1(B!1)),
% 1.60/1.24 inference(and_elim,[status(thm)],[36])).
% 1.60/1.24 tff(62,plain,
% 1.60/1.24 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(63,plain,
% 1.60/1.24 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))),
% 1.60/1.24 inference(quant_inst,[status(thm)],[])).
% 1.60/1.24 tff(64,plain,
% 1.60/1.24 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.60/1.24 tff(65,plain,
% 1.60/1.24 ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(B!1))),
% 1.60/1.24 inference(unit_resolution,[status(thm)],[64, 61, 60])).
% 1.60/1.24 tff(66,plain,
% 1.60/1.24 (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))),
% 1.60/1.24 inference(unit_resolution,[status(thm)],[65, 50])).
% 1.60/1.24 tff(67,plain,
% 1.60/1.24 (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)),
% 1.60/1.24 inference(monotonicity,[status(thm)],[66])).
% 1.60/1.24 tff(68,plain,
% 1.60/1.24 (^[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))))))),
% 1.60/1.24 inference(bind,[status(th)],[])).
% 1.60/1.24 tff(69,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(quant_intro,[status(thm)],[68])).
% 1.60/1.24 tff(70,plain,
% 1.60/1.24 (^[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))))))),
% 1.60/1.24 inference(bind,[status(th)],[])).
% 1.60/1.24 tff(71,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(quant_intro,[status(thm)],[70])).
% 1.60/1.24 tff(72,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(transitivity,[status(thm)],[71, 69])).
% 1.60/1.24 tff(73,plain,
% 1.60/1.24 (^[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)))))))),
% 1.60/1.24 inference(bind,[status(th)],[])).
% 1.60/1.24 tff(74,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(quant_intro,[status(thm)],[73])).
% 1.60/1.24 tff(75,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(76,plain,
% 1.60/1.24 (^[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)))))))),
% 1.60/1.24 inference(bind,[status(th)],[])).
% 1.60/1.24 tff(77,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(quant_intro,[status(thm)],[76])).
% 1.60/1.24 tff(78,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')).
% 1.60/1.24 tff(79,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.60/1.24 tff(80,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.60/1.24 tff(81,plain,(
% 1.60/1.24 ![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)))))),
% 1.60/1.24 inference(skolemize,[status(sab)],[80])).
% 1.60/1.24 tff(82,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[81, 74])).
% 1.60/1.24 tff(83,plain,
% 1.60/1.24 (![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)))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[82, 72])).
% 1.60/1.24 tff(84,plain,
% 1.60/1.24 (v4_group_1(A!0)),
% 1.60/1.24 inference(and_elim,[status(thm)],[36])).
% 1.60/1.24 tff(85,plain,
% 1.60/1.24 (((~![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)))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(86,plain,
% 1.60/1.24 ((~![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)))))),
% 1.60/1.24 inference(quant_inst,[status(thm)],[])).
% 1.60/1.24 tff(87,plain,
% 1.60/1.24 ((~![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))))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.60/1.24 tff(88,plain,
% 1.60/1.24 (![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))))),
% 1.60/1.24 inference(unit_resolution,[status(thm)],[87, 39, 38, 84, 37, 83])).
% 1.60/1.24 tff(89,plain,
% 1.60/1.24 (((~![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))))),
% 1.60/1.24 inference(rewrite,[status(thm)],[])).
% 1.60/1.24 tff(90,plain,
% 1.60/1.24 ((~![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))))),
% 1.60/1.24 inference(quant_inst,[status(thm)],[])).
% 1.60/1.24 tff(91,plain,
% 1.60/1.24 ((~![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)))),
% 1.60/1.24 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.60/1.25 tff(92,plain,
% 1.60/1.25 (![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)))),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[91, 61, 44, 88])).
% 1.60/1.25 tff(93,plain,
% 1.60/1.25 (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 1.60/1.25 inference(and_elim,[status(thm)],[36])).
% 1.60/1.25 tff(94,plain,
% 1.60/1.25 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 1.60/1.25 inference(or_elim,[status(thm)],[93])).
% 1.60/1.25 tff(95,plain,
% 1.60/1.25 (((~![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)))),
% 1.60/1.25 inference(rewrite,[status(thm)],[])).
% 1.60/1.25 tff(96,plain,
% 1.60/1.25 ((~![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)))),
% 1.60/1.25 inference(quant_inst,[status(thm)],[])).
% 1.60/1.25 tff(97,plain,
% 1.60/1.25 ((~![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))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.60/1.25 tff(98,plain,
% 1.60/1.25 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[97, 94, 92])).
% 1.60/1.25 tff(99,plain,
% 1.60/1.25 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))),
% 1.60/1.25 inference(or_elim,[status(thm)],[93])).
% 1.60/1.25 tff(100,plain,
% 1.60/1.25 ((~(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)),
% 1.60/1.25 inference(tautology,[status(thm)],[])).
% 1.60/1.25 tff(101,plain,
% 1.60/1.25 ((~(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)),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[100, 99])).
% 1.60/1.25 tff(102,plain,
% 1.60/1.25 (r1_rlvect_1(B!1, C!2)),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[101, 98])).
% 1.60/1.25 tff(103,plain,
% 1.60/1.25 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[102, 67])).
% 1.60/1.25 tff(104,plain,
% 1.60/1.25 (g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)) = B!1),
% 1.60/1.25 inference(symmetry,[status(thm)],[66])).
% 1.60/1.25 tff(105,plain,
% 1.60/1.25 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0) <=> m1_group_2(B!1, A!0)),
% 1.60/1.25 inference(monotonicity,[status(thm)],[104])).
% 1.60/1.25 tff(106,plain,
% 1.60/1.25 (m1_group_2(B!1, A!0) <=> m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 1.60/1.25 inference(symmetry,[status(thm)],[105])).
% 1.60/1.25 tff(107,plain,
% 1.60/1.25 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[44, 106])).
% 1.60/1.25 tff(108,plain,
% 1.60/1.25 (r1_rlvect_1(B!1, k3_group_1(A!0, C!2)) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2))),
% 1.60/1.25 inference(monotonicity,[status(thm)],[66])).
% 1.60/1.25 tff(109,plain,
% 1.60/1.25 ((~r1_rlvect_1(B!1, k3_group_1(A!0, C!2))) <=> (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2)))),
% 1.60/1.25 inference(monotonicity,[status(thm)],[108])).
% 1.60/1.25 tff(110,plain,
% 1.60/1.25 (^[A: $i, B: $i] : refl((m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 1.60/1.25 inference(bind,[status(th)],[])).
% 1.60/1.25 tff(111,plain,
% 1.60/1.25 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.25 inference(quant_intro,[status(thm)],[110])).
% 1.60/1.25 tff(112,plain,
% 1.60/1.25 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))))),
% 1.60/1.25 inference(bind,[status(th)],[])).
% 1.60/1.25 tff(113,plain,
% 1.60/1.25 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.25 inference(quant_intro,[status(thm)],[112])).
% 1.60/1.25 tff(114,plain,
% 1.60/1.25 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.60/1.25 inference(rewrite,[status(thm)],[])).
% 1.60/1.25 tff(115,plain,
% 1.60/1.25 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))))),
% 1.60/1.25 inference(bind,[status(th)],[])).
% 1.60/1.25 tff(116,plain,
% 1.60/1.25 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.60/1.25 inference(quant_intro,[status(thm)],[115])).
% 1.60/1.25 tff(117,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_group_1')).
% 1.60/1.25 tff(118,plain,
% 1.60/1.25 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.60/1.25 tff(119,plain,
% 1.60/1.25 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[118, 114])).
% 1.60/1.25 tff(120,plain,(
% 1.60/1.25 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.60/1.25 inference(skolemize,[status(sab)],[119])).
% 1.60/1.25 tff(121,plain,
% 1.60/1.25 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[120, 113])).
% 1.60/1.25 tff(122,plain,
% 1.60/1.25 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[121, 111])).
% 1.60/1.25 tff(123,plain,
% 1.60/1.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)))),
% 1.60/1.25 inference(rewrite,[status(thm)],[])).
% 1.60/1.25 tff(124,plain,
% 1.60/1.25 ((m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)))),
% 1.60/1.25 inference(rewrite,[status(thm)],[])).
% 1.60/1.25 tff(125,plain,
% 1.60/1.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))))),
% 1.60/1.25 inference(monotonicity,[status(thm)],[124])).
% 1.60/1.25 tff(126,plain,
% 1.60/1.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)))),
% 1.60/1.25 inference(transitivity,[status(thm)],[125, 123])).
% 1.60/1.25 tff(127,plain,
% 1.60/1.25 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))),
% 1.60/1.25 inference(quant_inst,[status(thm)],[])).
% 1.60/1.25 tff(128,plain,
% 1.60/1.25 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.60/1.25 tff(129,plain,
% 1.60/1.25 (m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[128, 39, 38, 84, 37, 94, 122])).
% 1.60/1.25 tff(130,plain,
% 1.60/1.25 (((~![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(k3_group_1(A!0, C!2), u1_struct_0(A!0))) | (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, 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(k3_group_1(A!0, C!2), u1_struct_0(A!0))) | (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2))))),
% 1.60/1.25 inference(rewrite,[status(thm)],[])).
% 1.60/1.25 tff(131,plain,
% 1.60/1.25 ((~![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(k3_group_1(A!0, C!2), u1_struct_0(A!0))) | (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2))))),
% 1.60/1.25 inference(quant_inst,[status(thm)],[])).
% 1.60/1.25 tff(132,plain,
% 1.60/1.25 ((~![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(k3_group_1(A!0, C!2), u1_struct_0(A!0))) | (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.60/1.25 tff(133,plain,
% 1.60/1.25 (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2))),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[132, 129, 92])).
% 1.60/1.25 tff(134,plain,
% 1.60/1.25 (~r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1))),
% 1.60/1.25 inference(or_elim,[status(thm)],[93])).
% 1.60/1.25 tff(135,plain,
% 1.60/1.25 ((~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))) | r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))),
% 1.60/1.25 inference(tautology,[status(thm)],[])).
% 1.60/1.25 tff(136,plain,
% 1.60/1.25 ((~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))) | (~r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[135, 134])).
% 1.60/1.25 tff(137,plain,
% 1.60/1.25 (~r1_rlvect_1(B!1, k3_group_1(A!0, C!2))),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[136, 133])).
% 1.60/1.25 tff(138,plain,
% 1.60/1.25 (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[137, 109])).
% 1.60/1.25 tff(139,plain,
% 1.60/1.25 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, 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)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))))),
% 1.60/1.25 inference(bind,[status(th)],[])).
% 1.60/1.25 tff(140,plain,
% 1.60/1.25 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.60/1.25 inference(quant_intro,[status(thm)],[139])).
% 1.60/1.25 tff(141,plain,
% 1.60/1.25 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 1.60/1.25 inference(bind,[status(th)],[])).
% 1.60/1.25 tff(142,plain,
% 1.60/1.25 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.60/1.25 inference(quant_intro,[status(thm)],[141])).
% 1.60/1.25 tff(143,plain,
% 1.60/1.25 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 1.60/1.25 inference(bind,[status(th)],[])).
% 1.60/1.25 tff(144,plain,
% 1.60/1.25 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.60/1.25 inference(quant_intro,[status(thm)],[143])).
% 1.60/1.25 tff(145,plain,
% 1.60/1.25 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.60/1.25 inference(transitivity,[status(thm)],[144, 142])).
% 1.60/1.25 tff(146,plain,
% 1.60/1.25 (^[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))))), (((~((~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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, 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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))))), 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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, 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))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 1.60/1.25 inference(bind,[status(th)],[])).
% 1.60/1.25 tff(147,plain,
% 1.60/1.25 (![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.60/1.25 inference(quant_intro,[status(thm)],[146])).
% 1.60/1.25 tff(148,plain,
% 1.60/1.25 (![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, 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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.60/1.25 inference(rewrite,[status(thm)],[])).
% 1.60/1.25 tff(149,plain,
% 1.60/1.25 (^[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(rewrite((r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))) <=> ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A, B)))), ((m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))) <=> (m1_group_2(C, A) => ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A, B)))))), rewrite((m1_group_2(C, A) => ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A, B)))) <=> (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))), ((m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))) <=> (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))), (![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))) <=> ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, 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_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))))) <=> (((~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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, 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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, 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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, 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_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))))) <=> ((~((~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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))))),
% 1.60/1.25 inference(bind,[status(th)],[])).
% 1.60/1.25 tff(150,plain,
% 1.60/1.25 (![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_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))))) <=> ![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.60/1.25 inference(quant_intro,[status(thm)],[149])).
% 1.60/1.25 tff(151,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_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t60_group_2')).
% 1.60/1.25 tff(152,plain,
% 1.60/1.25 (![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.60/1.25 tff(153,plain,
% 1.60/1.25 (![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.60/1.25 tff(154,plain,(
% 1.60/1.25 ![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.60/1.25 inference(skolemize,[status(sab)],[153])).
% 1.60/1.25 tff(155,plain,
% 1.60/1.25 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[154, 147])).
% 1.60/1.25 tff(156,plain,
% 1.60/1.25 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[155, 145])).
% 1.60/1.25 tff(157,plain,
% 1.60/1.25 (![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[156, 140])).
% 1.60/1.25 tff(158,plain,
% 1.60/1.25 (((~![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0)))))),
% 1.60/1.25 inference(rewrite,[status(thm)],[])).
% 1.60/1.25 tff(159,plain,
% 1.60/1.25 ((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] : (r1_rlvect_1(C, k3_group_1(A!0, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A!0))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0)))))),
% 1.60/1.25 inference(rewrite,[status(thm)],[])).
% 1.60/1.25 tff(160,plain,
% 1.60/1.25 (((~![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A!0, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))))),
% 1.60/1.25 inference(monotonicity,[status(thm)],[159])).
% 1.60/1.25 tff(161,plain,
% 1.60/1.25 (((~![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A!0, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0)))))),
% 1.60/1.25 inference(transitivity,[status(thm)],[160, 158])).
% 1.60/1.25 tff(162,plain,
% 1.60/1.25 ((~![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A!0, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A!0)))))),
% 1.60/1.25 inference(quant_inst,[status(thm)],[])).
% 1.60/1.25 tff(163,plain,
% 1.60/1.25 ((~![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] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))),
% 1.60/1.25 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.60/1.25 tff(164,plain,
% 1.60/1.25 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))),
% 1.60/1.25 inference(unit_resolution,[status(thm)],[163, 39, 38, 84, 37, 157])).
% 1.60/1.25 tff(165,plain,
% 1.60/1.25 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2))))),
% 1.60/1.26 inference(rewrite,[status(thm)],[])).
% 1.60/1.26 tff(166,plain,
% 1.60/1.26 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, C!2)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~m1_group_2(C, A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2))))),
% 1.60/1.26 inference(rewrite,[status(thm)],[])).
% 1.60/1.26 tff(167,plain,
% 1.60/1.26 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, C!2)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~m1_group_2(C, A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))))),
% 1.60/1.26 inference(monotonicity,[status(thm)],[166])).
% 1.60/1.26 tff(168,plain,
% 1.60/1.26 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, C!2)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~m1_group_2(C, A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2))))),
% 1.60/1.26 inference(transitivity,[status(thm)],[167, 165])).
% 1.60/1.26 tff(169,plain,
% 1.60/1.26 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, C!2)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~m1_group_2(C, A!0))))),
% 1.60/1.26 inference(quant_inst,[status(thm)],[])).
% 1.60/1.26 tff(170,plain,
% 1.60/1.26 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))),
% 1.60/1.26 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.60/1.26 tff(171,plain,
% 1.60/1.26 (![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))),
% 1.60/1.26 inference(unit_resolution,[status(thm)],[170, 94, 164])).
% 1.60/1.26 tff(172,plain,
% 1.60/1.26 (((~![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))) | ((~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)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)))) <=> ((~![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))) | (~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)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)))),
% 1.60/1.26 inference(rewrite,[status(thm)],[])).
% 1.60/1.26 tff(173,plain,
% 1.60/1.26 ((~![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))) | ((~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)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)))),
% 1.60/1.26 inference(quant_inst,[status(thm)],[])).
% 1.60/1.26 tff(174,plain,
% 1.60/1.26 ((~![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2))),
% 1.60/1.26 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.60/1.26 tff(175,plain,
% 1.60/1.26 ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2))),
% 1.60/1.26 inference(unit_resolution,[status(thm)],[174, 171])).
% 1.60/1.26 tff(176,plain,
% 1.60/1.26 ($false),
% 1.60/1.26 inference(unit_resolution,[status(thm)],[175, 138, 107, 103])).
% 1.60/1.26 % SZS output end Proof
%------------------------------------------------------------------------------