TSTP Solution File: ALG216+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG216+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 : Tue Sep 6 16:09:15 EDT 2022
% Result : Theorem 0.82s 0.81s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG216+1 : TPTP v8.1.0. Released v3.4.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 13:53:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.82/0.81 % SZS status Theorem
% 0.82/0.81 % SZS output start Proof
% 0.82/0.81 tff(m1_subset_1_type, type, (
% 0.82/0.81 m1_subset_1: ( $i * $i ) > $o)).
% 0.82/0.81 tff(u1_struct_0_type, type, (
% 0.82/0.81 u1_struct_0: $i > $i)).
% 0.82/0.81 tff(tptp_fun_B_1_type, type, (
% 0.82/0.81 tptp_fun_B_1: $i)).
% 0.82/0.81 tff(v1_rmod_5_type, type, (
% 0.82/0.81 v1_rmod_5: ( $i * $i * $i ) > $o)).
% 0.82/0.81 tff(tptp_fun_A_0_type, type, (
% 0.82/0.81 tptp_fun_A_0: $i)).
% 0.82/0.81 tff(k8_rlvect_2_type, type, (
% 0.82/0.81 k8_rlvect_2: ( $i * $i * $i ) > $i)).
% 0.82/0.81 tff(k1_rlvect_1_type, type, (
% 0.82/0.81 k1_rlvect_1: $i > $i)).
% 0.82/0.81 tff(k2_group_1_type, type, (
% 0.82/0.81 k2_group_1: $i > $i)).
% 0.82/0.81 tff(v5_vectsp_2_type, type, (
% 0.82/0.81 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.82/0.81 tff(l1_vectsp_2_type, type, (
% 0.82/0.81 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.82/0.81 tff(v6_rlvect_1_type, type, (
% 0.82/0.81 v6_rlvect_1: $i > $o)).
% 0.82/0.81 tff(v5_rlvect_1_type, type, (
% 0.82/0.81 v5_rlvect_1: $i > $o)).
% 0.82/0.81 tff(v4_rlvect_1_type, type, (
% 0.82/0.81 v4_rlvect_1: $i > $o)).
% 0.82/0.81 tff(v3_rlvect_1_type, type, (
% 0.82/0.81 v3_rlvect_1: $i > $o)).
% 0.82/0.81 tff(v3_struct_0_type, type, (
% 0.82/0.81 v3_struct_0: $i > $o)).
% 0.82/0.81 tff(v8_vectsp_1_type, type, (
% 0.82/0.81 v8_vectsp_1: $i > $o)).
% 0.82/0.81 tff(v7_vectsp_1_type, type, (
% 0.82/0.81 v7_vectsp_1: $i > $o)).
% 0.82/0.81 tff(v6_vectsp_1_type, type, (
% 0.82/0.81 v6_vectsp_1: $i > $o)).
% 0.82/0.81 tff(v4_group_1_type, type, (
% 0.82/0.81 v4_group_1: $i > $o)).
% 0.82/0.81 tff(l3_vectsp_1_type, type, (
% 0.82/0.81 l3_vectsp_1: $i > $o)).
% 0.82/0.81 tff(tptp_fun_C_2_type, type, (
% 0.82/0.81 tptp_fun_C_2: $i)).
% 0.82/0.81 tff(l2_struct_0_type, type, (
% 0.82/0.81 l2_struct_0: $i > $o)).
% 0.82/0.81 tff(l1_rlvect_1_type, type, (
% 0.82/0.81 l1_rlvect_1: $i > $o)).
% 0.82/0.81 tff(l1_struct_0_type, type, (
% 0.82/0.81 l1_struct_0: $i > $o)).
% 0.82/0.81 tff(l2_vectsp_1_type, type, (
% 0.82/0.81 l2_vectsp_1: $i > $o)).
% 0.82/0.81 tff(1,plain,
% 0.82/0.81 (^[A: $i] : refl((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(2,plain,
% 0.82/0.81 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[1])).
% 0.82/0.81 tff(3,plain,
% 0.82/0.81 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(4,plain,
% 0.82/0.81 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[3])).
% 0.82/0.81 tff(5,plain,
% 0.82/0.81 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.82/0.81 inference(transitivity,[status(thm)],[4, 2])).
% 0.82/0.81 tff(6,plain,
% 0.82/0.81 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) <=> (~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))), (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))))), rewrite(((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(7,plain,
% 0.82/0.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[6])).
% 0.82/0.81 tff(8,plain,
% 0.82/0.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.82/0.81 inference(rewrite,[status(thm)],[])).
% 0.82/0.81 tff(9,plain,
% 0.82/0.81 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))) <=> ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)))), ((m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))) <=> (m1_subset_1(D, u1_struct_0(B)) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)))))), rewrite((m1_subset_1(D, u1_struct_0(B)) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)))) <=> ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))), ((m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))) <=> ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))) <=> ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))), ((m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))) <=> (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))), rewrite((m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))), ((m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(10,plain,
% 0.82/0.81 (![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[9])).
% 0.82/0.81 tff(11,axiom,(![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => (v1_rmod_5(k8_rlvect_2(B, C, D), A, B) => ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_rmod_5')).
% 0.82/0.81 tff(12,plain,
% 0.82/0.81 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.82/0.82 tff(13,plain,
% 0.82/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.82/0.82 tff(14,plain,(
% 0.82/0.82 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | ((~(C = k1_rlvect_1(B))) & (~(D = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B)))))))),
% 0.82/0.82 inference(skolemize,[status(sab)],[13])).
% 0.82/0.82 tff(15,plain,
% 0.82/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.82/0.82 tff(16,plain,
% 0.82/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.82/0.82 tff(17,plain,
% 0.82/0.82 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)) & ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(18,plain,
% 0.82/0.82 ((((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(19,plain,
% 0.82/0.82 ((~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))) <=> (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(20,plain,
% 0.82/0.82 ((~(~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(21,plain,
% 0.82/0.82 (((~(~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & (~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))) <=> (((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.82/0.82 inference(monotonicity,[status(thm)],[20, 19])).
% 0.82/0.82 tff(22,plain,
% 0.82/0.82 (((~(~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & (~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))) <=> ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.82/0.82 inference(transitivity,[status(thm)],[21, 18])).
% 0.82/0.82 tff(23,plain,
% 0.82/0.82 ((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(24,plain,
% 0.82/0.82 (((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & (~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))) <=> (((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)) & ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))))),
% 0.82/0.82 inference(monotonicity,[status(thm)],[23, 22])).
% 0.82/0.82 tff(25,plain,
% 0.82/0.82 (((~(~((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))) & (~(((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))))),
% 0.82/0.82 inference(transitivity,[status(thm)],[24, 17])).
% 0.82/0.82 tff(26,plain,
% 0.82/0.82 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B)))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(27,plain,
% 0.82/0.82 ((~![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ((~(k1_rlvect_1(A) = k2_group_1(A))) => ((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B)))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(28,axiom,(~![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => ((~(k1_rlvect_1(A) = k2_group_1(A))) => ((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_rmod_5')).
% 0.82/0.82 tff(29,plain,
% 0.82/0.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.82/0.82 tff(30,plain,
% 0.82/0.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.82/0.82 tff(31,plain,
% 0.82/0.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.82/0.82 tff(32,plain,
% 0.82/0.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.82/0.82 tff(33,plain,
% 0.82/0.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.82/0.82 tff(34,plain,
% 0.82/0.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.82/0.82 tff(35,plain,
% 0.82/0.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : (((~v1_rmod_5(k8_rlvect_2(B, C, k1_rlvect_1(B)), A, B)) & (~v1_rmod_5(k8_rlvect_2(B, k1_rlvect_1(B), C), A, B))) | (k1_rlvect_1(A) = k2_group_1(A)) | (~m1_subset_1(C, u1_struct_0(B))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.82/0.82 tff(36,plain,
% 0.82/0.82 ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & l3_vectsp_1(A!0) & (~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1)))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.82/0.82 tff(37,plain,
% 0.82/0.82 (l3_vectsp_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(38,plain,
% 0.82/0.82 (v8_vectsp_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(39,plain,
% 0.82/0.82 (v7_vectsp_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(40,plain,
% 0.82/0.82 (v6_vectsp_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(41,plain,
% 0.82/0.82 (v4_group_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(42,plain,
% 0.82/0.82 (v6_rlvect_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(43,plain,
% 0.82/0.82 (v5_rlvect_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(44,plain,
% 0.82/0.82 (v4_rlvect_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(45,plain,
% 0.82/0.82 (v3_rlvect_1(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(46,plain,
% 0.82/0.82 (~v3_struct_0(A!0)),
% 0.82/0.82 inference(and_elim,[status(thm)],[36])).
% 0.82/0.82 tff(47,plain,
% 0.82/0.82 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(48,plain,
% 0.82/0.82 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(49,plain,
% 0.82/0.82 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))), (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))), rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(50,plain,
% 0.82/0.82 (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[49])).
% 0.82/0.82 tff(51,plain,
% 0.82/0.82 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.82/0.82 inference(monotonicity,[status(thm)],[50])).
% 0.82/0.82 tff(52,plain,
% 0.82/0.82 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))))))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.82/0.82 inference(transitivity,[status(thm)],[51, 48])).
% 0.82/0.82 tff(53,plain,
% 0.82/0.82 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))))),
% 0.82/0.82 inference(monotonicity,[status(thm)],[52])).
% 0.82/0.82 tff(54,plain,
% 0.82/0.82 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B))))))),
% 0.82/0.83 inference(transitivity,[status(thm)],[53, 47])).
% 0.82/0.83 tff(55,plain,
% 0.82/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))),
% 0.82/0.83 inference(quant_inst,[status(thm)],[])).
% 0.82/0.83 tff(56,plain,
% 0.82/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((k1_rlvect_1(A) = k2_group_1(A)) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A, B)) | (~m1_subset_1(D, u1_struct_0(B))) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B))))))))) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))),
% 0.82/0.83 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.82/0.83 tff(57,plain,
% 0.82/0.83 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))),
% 0.82/0.83 inference(unit_resolution,[status(thm)],[56, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 16])).
% 0.82/0.83 tff(58,plain,
% 0.82/0.83 (l1_vectsp_2(B!1, A!0)),
% 0.82/0.83 inference(and_elim,[status(thm)],[36])).
% 0.82/0.83 tff(59,plain,
% 0.82/0.83 (v5_vectsp_2(B!1, A!0)),
% 0.82/0.83 inference(and_elim,[status(thm)],[36])).
% 0.82/0.83 tff(60,plain,
% 0.82/0.83 (v6_rlvect_1(B!1)),
% 0.82/0.83 inference(and_elim,[status(thm)],[36])).
% 0.82/0.83 tff(61,plain,
% 0.82/0.83 (v5_rlvect_1(B!1)),
% 0.82/0.83 inference(and_elim,[status(thm)],[36])).
% 0.82/0.83 tff(62,plain,
% 0.82/0.83 (v4_rlvect_1(B!1)),
% 0.82/0.83 inference(and_elim,[status(thm)],[36])).
% 0.82/0.83 tff(63,plain,
% 0.82/0.83 (v3_rlvect_1(B!1)),
% 0.82/0.83 inference(and_elim,[status(thm)],[36])).
% 0.82/0.83 tff(64,plain,
% 0.82/0.83 (~v3_struct_0(B!1)),
% 0.82/0.83 inference(and_elim,[status(thm)],[36])).
% 0.82/0.83 tff(65,plain,
% 0.82/0.83 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.82/0.83 inference(rewrite,[status(thm)],[])).
% 0.82/0.83 tff(66,plain,
% 0.82/0.83 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) <=> (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.82/0.83 inference(rewrite,[status(thm)],[])).
% 0.82/0.83 tff(67,plain,
% 0.82/0.83 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))))),
% 0.92/0.83 inference(monotonicity,[status(thm)],[66])).
% 0.92/0.83 tff(68,plain,
% 0.92/0.83 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.92/0.83 inference(transitivity,[status(thm)],[67, 65])).
% 0.92/0.83 tff(69,plain,
% 0.92/0.83 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1)))))),
% 0.92/0.83 inference(quant_inst,[status(thm)],[])).
% 0.92/0.83 tff(70,plain,
% 0.92/0.83 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~l1_vectsp_2(B, A!0)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((D = k1_rlvect_1(B)) | (C = k1_rlvect_1(B)))) | (~v1_rmod_5(k8_rlvect_2(B, C, D), A!0, B)))))) | v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~l1_vectsp_2(B!1, A!0)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.92/0.83 tff(71,plain,
% 0.92/0.83 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[70, 64, 63, 62, 61, 60, 59, 58, 57])).
% 0.92/0.83 tff(72,plain,
% 0.92/0.83 (^[A: $i] : refl(((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))) <=> ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(73,plain,
% 0.92/0.83 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[72])).
% 0.92/0.83 tff(74,plain,
% 0.92/0.83 (^[A: $i] : rewrite(((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(75,plain,
% 0.92/0.83 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[74])).
% 0.92/0.83 tff(76,plain,
% 0.92/0.83 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(77,plain,
% 0.92/0.83 (^[A: $i] : rewrite((l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(78,plain,
% 0.92/0.83 (![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[77])).
% 0.92/0.83 tff(79,axiom,(![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_vectsp_1')).
% 0.92/0.83 tff(80,plain,
% 0.92/0.83 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.92/0.83 tff(81,plain,
% 0.92/0.83 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.92/0.83 tff(82,plain,(
% 0.92/0.83 ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.92/0.83 inference(skolemize,[status(sab)],[81])).
% 0.92/0.83 tff(83,plain,
% 0.92/0.83 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.92/0.83 tff(84,plain,
% 0.92/0.83 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.92/0.83 tff(85,plain,
% 0.92/0.83 (((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | ((~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))) <=> ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | (~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(86,plain,
% 0.92/0.83 ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | ((~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))),
% 0.92/0.83 inference(quant_inst,[status(thm)],[])).
% 0.92/0.83 tff(87,plain,
% 0.92/0.83 ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | (~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.92/0.83 tff(88,plain,
% 0.92/0.83 (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[87, 37, 84])).
% 0.92/0.83 tff(89,plain,
% 0.92/0.83 (((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))) | l1_rlvect_1(A!0)),
% 0.92/0.83 inference(tautology,[status(thm)],[])).
% 0.92/0.83 tff(90,plain,
% 0.92/0.83 (l1_rlvect_1(A!0)),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.92/0.83 tff(91,plain,
% 0.92/0.83 (^[A: $i] : refl((l2_struct_0(A) | (~l1_rlvect_1(A))) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(92,plain,
% 0.92/0.83 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[91])).
% 0.92/0.83 tff(93,plain,
% 0.92/0.83 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(94,plain,
% 0.92/0.83 (^[A: $i] : rewrite((l1_rlvect_1(A) => l2_struct_0(A)) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(95,plain,
% 0.92/0.83 (![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A)) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[94])).
% 0.92/0.83 tff(96,axiom,(![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_rlvect_1')).
% 0.92/0.83 tff(97,plain,
% 0.92/0.83 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.92/0.83 tff(98,plain,
% 0.92/0.83 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.92/0.83 tff(99,plain,(
% 0.92/0.83 ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.92/0.83 inference(skolemize,[status(sab)],[98])).
% 0.92/0.83 tff(100,plain,
% 0.92/0.83 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.92/0.83 tff(101,plain,
% 0.92/0.83 (((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))) <=> ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(102,plain,
% 0.92/0.83 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.92/0.83 inference(quant_inst,[status(thm)],[])).
% 0.92/0.83 tff(103,plain,
% 0.92/0.83 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.92/0.83 tff(104,plain,
% 0.92/0.83 (l2_struct_0(A!0)),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[103, 100, 90])).
% 0.92/0.83 tff(105,plain,
% 0.92/0.83 (^[A: $i] : refl((l1_struct_0(A) | (~l2_struct_0(A))) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(106,plain,
% 0.92/0.83 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[105])).
% 0.92/0.83 tff(107,plain,
% 0.92/0.83 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(108,plain,
% 0.92/0.83 (^[A: $i] : rewrite((l2_struct_0(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(109,plain,
% 0.92/0.83 (![A: $i] : (l2_struct_0(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[108])).
% 0.92/0.83 tff(110,axiom,(![A: $i] : (l2_struct_0(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_struct_0')).
% 0.92/0.83 tff(111,plain,
% 0.92/0.83 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.92/0.83 tff(112,plain,
% 0.92/0.83 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.92/0.83 tff(113,plain,(
% 0.92/0.83 ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.92/0.83 inference(skolemize,[status(sab)],[112])).
% 0.92/0.83 tff(114,plain,
% 0.92/0.83 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.92/0.83 tff(115,plain,
% 0.92/0.83 (((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(116,plain,
% 0.92/0.83 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.92/0.83 inference(quant_inst,[status(thm)],[])).
% 0.92/0.83 tff(117,plain,
% 0.92/0.83 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.92/0.83 tff(118,plain,
% 0.92/0.83 (l1_struct_0(A!0)),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[117, 114, 104])).
% 0.92/0.83 tff(119,plain,
% 0.92/0.83 (^[A: $i] : refl(((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(120,plain,
% 0.92/0.83 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[119])).
% 0.92/0.83 tff(121,plain,
% 0.92/0.83 (^[A: $i] : rewrite(((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(122,plain,
% 0.92/0.83 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[121])).
% 0.92/0.83 tff(123,plain,
% 0.92/0.83 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(transitivity,[status(thm)],[122, 120])).
% 0.92/0.83 tff(124,plain,
% 0.92/0.83 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(125,plain,
% 0.92/0.83 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((l1_vectsp_2(B, A) => l1_rlvect_1(B)) <=> (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))), (![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B)) <=> ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))), ((l1_struct_0(A) => ![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B))) <=> (l1_struct_0(A) => ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))))), rewrite((l1_struct_0(A) => ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A)))) <=> ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))), ((l1_struct_0(A) => ![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B))) <=> ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(126,plain,
% 0.92/0.83 (![A: $i] : (l1_struct_0(A) => ![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B))) <=> ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[125])).
% 0.92/0.83 tff(127,axiom,(![A: $i] : (l1_struct_0(A) => ![B: $i] : (l1_vectsp_2(B, A) => l1_rlvect_1(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_vectsp_2')).
% 0.92/0.83 tff(128,plain,
% 0.92/0.83 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.92/0.83 tff(129,plain,
% 0.92/0.83 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.92/0.83 tff(130,plain,(
% 0.92/0.83 ![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(skolemize,[status(sab)],[129])).
% 0.92/0.83 tff(131,plain,
% 0.92/0.83 (![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.92/0.83 tff(132,plain,
% 0.92/0.83 (((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))) | ((~l1_struct_0(A!0)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0))))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))) | (~l1_struct_0(A!0)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0))))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(133,plain,
% 0.92/0.83 ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))) | ((~l1_struct_0(A!0)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0))))),
% 0.92/0.83 inference(quant_inst,[status(thm)],[])).
% 0.92/0.83 tff(134,plain,
% 0.92/0.83 ((~![A: $i] : ((~l1_struct_0(A)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A))))) | (~l1_struct_0(A!0)) | ![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.92/0.83 tff(135,plain,
% 0.92/0.83 (![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[134, 131, 118])).
% 0.92/0.83 tff(136,plain,
% 0.92/0.83 (((~![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))) | (l1_rlvect_1(B!1) | (~l1_vectsp_2(B!1, A!0)))) <=> ((~![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))) | l1_rlvect_1(B!1) | (~l1_vectsp_2(B!1, A!0)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(137,plain,
% 0.92/0.83 ((~![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))) | (l1_rlvect_1(B!1) | (~l1_vectsp_2(B!1, A!0)))),
% 0.92/0.83 inference(quant_inst,[status(thm)],[])).
% 0.92/0.83 tff(138,plain,
% 0.92/0.83 ((~![B: $i] : (l1_rlvect_1(B) | (~l1_vectsp_2(B, A!0)))) | l1_rlvect_1(B!1) | (~l1_vectsp_2(B!1, A!0))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.92/0.83 tff(139,plain,
% 0.92/0.83 (l1_rlvect_1(B!1)),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[138, 58, 135])).
% 0.92/0.83 tff(140,plain,
% 0.92/0.83 (((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(B!1) | (~l1_rlvect_1(B!1)))) <=> ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(B!1) | (~l1_rlvect_1(B!1)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(141,plain,
% 0.92/0.83 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(B!1) | (~l1_rlvect_1(B!1)))),
% 0.92/0.83 inference(quant_inst,[status(thm)],[])).
% 0.92/0.83 tff(142,plain,
% 0.92/0.83 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(B!1) | (~l1_rlvect_1(B!1))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.92/0.83 tff(143,plain,
% 0.92/0.83 (l2_struct_0(B!1)),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[142, 100, 139])).
% 0.92/0.83 tff(144,plain,
% 0.92/0.83 (^[A: $i] : refl(((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(145,plain,
% 0.92/0.83 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[144])).
% 0.92/0.83 tff(146,plain,
% 0.92/0.83 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(147,plain,
% 0.92/0.83 (^[A: $i] : rewrite((l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))))),
% 0.92/0.83 inference(bind,[status(th)],[])).
% 0.92/0.83 tff(148,plain,
% 0.92/0.83 (![A: $i] : (l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.92/0.83 inference(quant_intro,[status(thm)],[147])).
% 0.92/0.83 tff(149,axiom,(![A: $i] : (l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_rlvect_1')).
% 0.92/0.83 tff(150,plain,
% 0.92/0.83 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.92/0.83 tff(151,plain,
% 0.92/0.83 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.92/0.83 tff(152,plain,(
% 0.92/0.83 ![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.92/0.83 inference(skolemize,[status(sab)],[151])).
% 0.92/0.83 tff(153,plain,
% 0.92/0.83 (![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.92/0.83 tff(154,plain,
% 0.92/0.83 (((~![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))) | ((~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))) <=> ((~![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))) | (~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(155,plain,
% 0.92/0.83 ((~![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))) | ((~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))),
% 0.92/0.83 inference(quant_inst,[status(thm)],[])).
% 0.92/0.83 tff(156,plain,
% 0.92/0.83 ((~![A: $i] : ((~l2_struct_0(A)) | m1_subset_1(k1_rlvect_1(A), u1_struct_0(A)))) | (~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))),
% 0.92/0.83 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.92/0.83 tff(157,plain,
% 0.92/0.83 ((~l2_struct_0(B!1)) | m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[156, 153])).
% 0.92/0.83 tff(158,plain,
% 0.92/0.83 (m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))),
% 0.92/0.83 inference(unit_resolution,[status(thm)],[157, 143])).
% 0.92/0.83 tff(159,plain,
% 0.92/0.83 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1)))))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(160,plain,
% 0.92/0.83 (((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (k1_rlvect_1(B!1) = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)))) <=> ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1)))))),
% 0.92/0.83 inference(rewrite,[status(thm)],[])).
% 0.92/0.83 tff(161,plain,
% 0.92/0.83 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (k1_rlvect_1(B!1) = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))))),
% 0.92/0.83 inference(monotonicity,[status(thm)],[160])).
% 0.92/0.83 tff(162,plain,
% 0.92/0.83 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (k1_rlvect_1(B!1) = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1)))))),
% 0.92/0.84 inference(transitivity,[status(thm)],[161, 159])).
% 0.92/0.84 tff(163,plain,
% 0.92/0.84 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (k1_rlvect_1(B!1) = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1))))),
% 0.92/0.84 inference(quant_inst,[status(thm)],[])).
% 0.92/0.84 tff(164,plain,
% 0.92/0.84 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))),
% 0.92/0.84 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.92/0.84 tff(165,plain,
% 0.92/0.84 (![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))),
% 0.92/0.84 inference(unit_resolution,[status(thm)],[164, 158, 71])).
% 0.92/0.84 tff(166,plain,
% 0.92/0.84 (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | ((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) | (~m1_subset_1(C!2, u1_struct_0(B!1))))),
% 0.92/0.84 inference(and_elim,[status(thm)],[36])).
% 0.92/0.84 tff(167,plain,
% 0.92/0.84 (m1_subset_1(C!2, u1_struct_0(B!1))),
% 0.92/0.84 inference(or_elim,[status(thm)],[166])).
% 0.92/0.84 tff(168,plain,
% 0.92/0.84 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(C!2, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1))))),
% 0.92/0.84 inference(rewrite,[status(thm)],[])).
% 0.92/0.84 tff(169,plain,
% 0.92/0.84 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | ((~m1_subset_1(C!2, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1))))),
% 0.92/0.84 inference(quant_inst,[status(thm)],[])).
% 0.92/0.84 tff(170,plain,
% 0.92/0.84 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C, D), A!0, B!1))))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))),
% 0.92/0.84 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.92/0.84 tff(171,plain,
% 0.92/0.84 (![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))),
% 0.92/0.84 inference(unit_resolution,[status(thm)],[170, 167, 71])).
% 0.92/0.84 tff(172,plain,
% 0.92/0.84 (~(k1_rlvect_1(A!0) = k2_group_1(A!0))),
% 0.92/0.84 inference(or_elim,[status(thm)],[166])).
% 0.92/0.84 tff(173,plain,
% 0.92/0.84 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))),
% 0.92/0.84 inference(rewrite,[status(thm)],[])).
% 0.92/0.84 tff(174,plain,
% 0.92/0.84 (((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | $false | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1))) <=> ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))),
% 0.92/0.84 inference(rewrite,[status(thm)],[])).
% 0.92/0.84 tff(175,plain,
% 0.92/0.84 ((~$true) <=> $false),
% 0.92/0.84 inference(rewrite,[status(thm)],[])).
% 0.92/0.84 tff(176,plain,
% 0.92/0.84 (($true | (C!2 = k1_rlvect_1(B!1))) <=> $true),
% 0.92/0.84 inference(rewrite,[status(thm)],[])).
% 0.92/0.84 tff(177,plain,
% 0.92/0.84 ((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) <=> $true),
% 0.92/0.84 inference(rewrite,[status(thm)],[])).
% 0.92/0.84 tff(178,plain,
% 0.92/0.84 (((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1))) <=> ($true | (C!2 = k1_rlvect_1(B!1)))),
% 0.92/0.84 inference(monotonicity,[status(thm)],[177])).
% 0.92/0.84 tff(179,plain,
% 0.92/0.84 (((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1))) <=> $true),
% 0.92/0.84 inference(transitivity,[status(thm)],[178, 176])).
% 0.92/0.84 tff(180,plain,
% 0.92/0.84 ((~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) <=> (~$true)),
% 0.92/0.84 inference(monotonicity,[status(thm)],[179])).
% 0.92/0.84 tff(181,plain,
% 0.92/0.84 ((~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) <=> $false),
% 0.92/0.84 inference(transitivity,[status(thm)],[180, 175])).
% 0.92/0.84 tff(182,plain,
% 0.92/0.84 (((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1))) <=> ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | $false | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)))),
% 0.92/0.84 inference(monotonicity,[status(thm)],[181])).
% 0.92/0.84 tff(183,plain,
% 0.92/0.84 (((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1))) <=> ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))),
% 0.92/0.84 inference(transitivity,[status(thm)],[182, 174])).
% 0.92/0.84 tff(184,plain,
% 0.92/0.84 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))))),
% 0.92/0.84 inference(monotonicity,[status(thm)],[183])).
% 0.92/0.84 tff(185,plain,
% 0.92/0.84 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))))),
% 0.92/0.84 inference(transitivity,[status(thm)],[184, 173])).
% 0.92/0.84 tff(186,plain,
% 0.92/0.84 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1))) | (~((k1_rlvect_1(B!1) = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)))),
% 0.92/0.84 inference(quant_inst,[status(thm)],[])).
% 0.92/0.84 tff(187,plain,
% 0.92/0.84 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~((D = k1_rlvect_1(B!1)) | (C!2 = k1_rlvect_1(B!1)))) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, D), A!0, B!1)))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) | (~m1_subset_1(k1_rlvect_1(B!1), u1_struct_0(B!1)))),
% 0.92/0.84 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.92/0.84 tff(188,plain,
% 0.92/0.84 (~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)),
% 0.92/0.84 inference(unit_resolution,[status(thm)],[187, 172, 158, 171])).
% 0.92/0.84 tff(189,plain,
% 0.92/0.84 ((~(~(v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))) <=> (v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))),
% 0.92/0.84 inference(rewrite,[status(thm)],[])).
% 0.92/0.84 tff(190,plain,
% 0.92/0.84 (((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))) <=> (~(v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))),
% 0.92/0.84 inference(rewrite,[status(thm)],[])).
% 0.92/0.84 tff(191,plain,
% 0.92/0.84 ((~((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))) <=> (~(~(v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))))),
% 0.92/0.84 inference(monotonicity,[status(thm)],[190])).
% 0.92/0.84 tff(192,plain,
% 0.92/0.84 ((~((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))) <=> (v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1))),
% 0.92/0.85 inference(transitivity,[status(thm)],[191, 189])).
% 0.92/0.85 tff(193,plain,
% 0.92/0.85 (~((~v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1)) & (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)))),
% 0.92/0.85 inference(or_elim,[status(thm)],[166])).
% 0.92/0.85 tff(194,plain,
% 0.92/0.85 (v1_rmod_5(k8_rlvect_2(B!1, C!2, k1_rlvect_1(B!1)), A!0, B!1) | v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)),
% 0.92/0.85 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.92/0.85 tff(195,plain,
% 0.92/0.85 (v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)),
% 0.92/0.85 inference(unit_resolution,[status(thm)],[194, 188])).
% 0.92/0.85 tff(196,plain,
% 0.92/0.85 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))),
% 0.92/0.85 inference(rewrite,[status(thm)],[])).
% 0.92/0.85 tff(197,plain,
% 0.92/0.85 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)) | (~m1_subset_1(C!2, u1_struct_0(B!1))))),
% 0.92/0.85 inference(quant_inst,[status(thm)],[])).
% 0.92/0.85 tff(198,plain,
% 0.92/0.85 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), D), A!0, B!1)) | (~m1_subset_1(D, u1_struct_0(B!1))))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~v1_rmod_5(k8_rlvect_2(B!1, k1_rlvect_1(B!1), C!2), A!0, B!1)) | (~m1_subset_1(C!2, u1_struct_0(B!1)))),
% 0.92/0.85 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.92/0.85 tff(199,plain,
% 0.92/0.85 ($false),
% 0.92/0.85 inference(unit_resolution,[status(thm)],[198, 172, 195, 167, 165])).
% 0.92/0.85 % SZS output end Proof
%------------------------------------------------------------------------------