%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP643+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:17 AM UTC 2025
% Result : Theorem 7.75s 7.94s
% Output : Proof 7.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP643+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:36:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.75/7.94 % SZS status Theorem
% 7.75/7.94 % SZS output start Proof
% 7.75/7.94 tff(r1_rlvect_1_type, type, (
% 7.75/7.94 r1_rlvect_1: ( $i * $i ) > $o)).
% 7.75/7.94 tff(tptp_fun_D_3_type, type, (
% 7.75/7.94 tptp_fun_D_3: $i)).
% 7.75/7.94 tff(g1_group_1_type, type, (
% 7.75/7.94 g1_group_1: ( $i * $i ) > $i)).
% 7.75/7.94 tff(u1_group_1_type, type, (
% 7.75/7.94 u1_group_1: $i > $i)).
% 7.75/7.94 tff(tptp_fun_B_1_type, type, (
% 7.75/7.94 tptp_fun_B_1: $i)).
% 7.75/7.94 tff(u1_struct_0_type, type, (
% 7.75/7.94 u1_struct_0: $i > $i)).
% 7.75/7.94 tff(l1_group_1_type, type, (
% 7.75/7.94 l1_group_1: $i > $o)).
% 7.75/7.94 tff(v3_group_1_type, type, (
% 7.75/7.94 v3_group_1: $i > $o)).
% 7.75/7.94 tff(v3_struct_0_type, type, (
% 7.75/7.94 v3_struct_0: $i > $o)).
% 7.75/7.94 tff(m1_group_2_type, type, (
% 7.75/7.94 m1_group_2: ( $i * $i ) > $o)).
% 7.75/7.94 tff(tptp_fun_A_0_type, type, (
% 7.75/7.94 tptp_fun_A_0: $i)).
% 7.75/7.94 tff(m1_subset_1_type, type, (
% 7.75/7.94 m1_subset_1: ( $i * $i ) > $o)).
% 7.75/7.94 tff(r2_hidden_type, type, (
% 7.75/7.94 r2_hidden: ( $i * $i ) > $o)).
% 7.75/7.94 tff(k1_funct_1_type, type, (
% 7.75/7.94 k1_funct_1: ( $i * $i ) > $i)).
% 7.75/7.94 tff(k1_latsubgr_type, type, (
% 7.75/7.94 k1_latsubgr: $i > $i)).
% 7.75/7.94 tff(tptp_fun_C_2_type, type, (
% 7.75/7.94 tptp_fun_C_2: $i)).
% 7.75/7.94 tff(k1_group_1_type, type, (
% 7.75/7.94 k1_group_1: ( $i * $i * $i ) > $i)).
% 7.75/7.94 tff(v1_group_1_type, type, (
% 7.75/7.94 v1_group_1: $i > $o)).
% 7.75/7.94 tff(v4_group_1_type, type, (
% 7.75/7.94 v4_group_1: $i > $o)).
% 7.75/7.94 tff(1,plain,
% 7.75/7.94 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(2,plain,
% 7.75/7.94 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[1])).
% 7.75/7.94 tff(3,plain,
% 7.75/7.94 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(4,plain,
% 7.75/7.94 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[3])).
% 7.75/7.94 tff(5,plain,
% 7.75/7.94 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 7.75/7.94 inference(transitivity,[status(thm)],[4, 2])).
% 7.75/7.94 tff(6,plain,
% 7.75/7.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(7,plain,
% 7.75/7.94 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[6])).
% 7.75/7.94 tff(8,plain,
% 7.75/7.94 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(9,plain,
% 7.75/7.94 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> (m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), rewrite((m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), (![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(10,plain,
% 7.75/7.94 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[9])).
% 7.75/7.94 tff(11,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_group_2')).
% 7.75/7.94 tff(12,plain,
% 7.75/7.94 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[11, 10])).
% 7.75/7.94 tff(13,plain,
% 7.75/7.94 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[12, 8])).
% 7.75/7.94 tff(14,plain,(
% 7.75/7.94 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 7.75/7.94 inference(skolemize,[status(sab)],[13])).
% 7.75/7.94 tff(15,plain,
% 7.75/7.94 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[14, 7])).
% 7.75/7.94 tff(16,plain,
% 7.75/7.94 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[15, 5])).
% 7.75/7.94 tff(17,plain,
% 7.75/7.94 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(18,plain,
% 7.75/7.94 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(19,plain,
% 7.75/7.94 ((~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))) <=> (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(20,plain,
% 7.75/7.94 ((m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 7.75/7.94 inference(monotonicity,[status(thm)],[19])).
% 7.75/7.94 tff(21,plain,
% 7.75/7.94 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))) <=> ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))))),
% 7.75/7.94 inference(monotonicity,[status(thm)],[20])).
% 7.75/7.94 tff(22,plain,
% 7.75/7.94 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 7.75/7.94 inference(transitivity,[status(thm)],[21, 18])).
% 7.75/7.94 tff(23,plain,
% 7.75/7.94 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))))),
% 7.75/7.94 inference(monotonicity,[status(thm)],[22])).
% 7.75/7.94 tff(24,plain,
% 7.75/7.94 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))))),
% 7.75/7.94 inference(transitivity,[status(thm)],[23, 17])).
% 7.75/7.94 tff(25,plain,
% 7.75/7.94 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(26,plain,
% 7.75/7.94 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B))) => r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(27,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B))) => r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_latsubgr')).
% 7.75/7.94 tff(28,plain,
% 7.75/7.94 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[27, 26])).
% 7.75/7.94 tff(29,plain,
% 7.75/7.94 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[28, 25])).
% 7.75/7.94 tff(30,plain,
% 7.75/7.94 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[29, 25])).
% 7.75/7.94 tff(31,plain,
% 7.75/7.94 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r2_hidden(k1_group_1(A, C, D), k1_funct_1(k1_latsubgr(A), B)) | (~(r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) & r2_hidden(D, k1_funct_1(k1_latsubgr(A), B)))) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[30, 25])).
% 7.75/7.94 tff(32,plain,
% 7.75/7.94 ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[31, 24])).
% 7.75/7.94 tff(33,plain,
% 7.75/7.94 (l1_group_1(A!0)),
% 7.75/7.94 inference(and_elim,[status(thm)],[32])).
% 7.75/7.94 tff(34,plain,
% 7.75/7.94 (v3_group_1(A!0)),
% 7.75/7.94 inference(and_elim,[status(thm)],[32])).
% 7.75/7.94 tff(35,plain,
% 7.75/7.94 (~v3_struct_0(A!0)),
% 7.75/7.94 inference(and_elim,[status(thm)],[32])).
% 7.75/7.94 tff(36,plain,
% 7.75/7.94 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(37,plain,
% 7.75/7.94 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 7.75/7.94 inference(quant_inst,[status(thm)],[])).
% 7.75/7.94 tff(38,plain,
% 7.75/7.94 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[37, 36])).
% 7.75/7.94 tff(39,plain,
% 7.75/7.94 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 7.75/7.94 inference(unit_resolution,[status(thm)],[38, 35, 34, 33, 16])).
% 7.75/7.94 tff(40,plain,
% 7.75/7.94 (m1_group_2(B!1, A!0)),
% 7.75/7.94 inference(and_elim,[status(thm)],[32])).
% 7.75/7.94 tff(41,plain,
% 7.75/7.94 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(42,plain,
% 7.75/7.94 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))),
% 7.75/7.94 inference(quant_inst,[status(thm)],[])).
% 7.75/7.94 tff(43,plain,
% 7.75/7.94 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[42, 41])).
% 7.75/7.94 tff(44,plain,
% 7.75/7.94 (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))),
% 7.75/7.94 inference(unit_resolution,[status(thm)],[43, 40, 39])).
% 7.75/7.94 tff(45,plain,
% 7.75/7.94 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | l1_group_1(B!1)),
% 7.75/7.94 inference(tautology,[status(thm)],[])).
% 7.75/7.94 tff(46,plain,
% 7.75/7.94 (l1_group_1(B!1)),
% 7.75/7.94 inference(unit_resolution,[status(thm)],[45, 44])).
% 7.75/7.94 tff(47,plain,
% 7.75/7.94 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(48,plain,
% 7.75/7.94 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[47])).
% 7.75/7.94 tff(49,plain,
% 7.75/7.94 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(50,plain,
% 7.75/7.94 (^[A: $i] : trans(monotonicity(rewrite((v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))) <=> ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> (l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))))), rewrite((l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(51,plain,
% 7.75/7.94 (![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[50])).
% 7.75/7.94 tff(52,axiom,(![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 7.75/7.94 tff(53,plain,
% 7.75/7.94 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[52, 51])).
% 7.75/7.94 tff(54,plain,
% 7.75/7.94 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[53, 49])).
% 7.75/7.94 tff(55,plain,(
% 7.75/7.94 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 7.75/7.94 inference(skolemize,[status(sab)],[54])).
% 7.75/7.94 tff(56,plain,
% 7.75/7.94 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[55, 48])).
% 7.75/7.94 tff(57,plain,
% 7.75/7.94 (v1_group_1(B!1)),
% 7.75/7.94 inference(and_elim,[status(thm)],[32])).
% 7.75/7.94 tff(58,plain,
% 7.75/7.94 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(59,plain,
% 7.75/7.94 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))),
% 7.75/7.94 inference(quant_inst,[status(thm)],[])).
% 7.75/7.94 tff(60,plain,
% 7.75/7.94 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1))),
% 7.75/7.94 inference(modus_ponens,[status(thm)],[59, 58])).
% 7.75/7.94 tff(61,plain,
% 7.75/7.94 ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(B!1))),
% 7.75/7.94 inference(unit_resolution,[status(thm)],[60, 57, 56])).
% 7.75/7.94 tff(62,plain,
% 7.75/7.94 (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))),
% 7.75/7.94 inference(unit_resolution,[status(thm)],[61, 46])).
% 7.75/7.94 tff(63,plain,
% 7.75/7.94 (g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)) = B!1),
% 7.75/7.94 inference(symmetry,[status(thm)],[62])).
% 7.75/7.94 tff(64,plain,
% 7.75/7.94 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3) <=> r1_rlvect_1(B!1, D!3)),
% 7.75/7.94 inference(monotonicity,[status(thm)],[63])).
% 7.75/7.94 tff(65,plain,
% 7.75/7.94 (r1_rlvect_1(B!1, D!3) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)),
% 7.75/7.94 inference(symmetry,[status(thm)],[64])).
% 7.75/7.94 tff(66,plain,
% 7.75/7.94 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(67,plain,
% 7.75/7.94 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[66])).
% 7.75/7.94 tff(68,plain,
% 7.75/7.94 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(69,plain,
% 7.75/7.94 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[68])).
% 7.75/7.94 tff(70,plain,
% 7.75/7.94 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.94 inference(transitivity,[status(thm)],[69, 67])).
% 7.75/7.94 tff(71,plain,
% 7.75/7.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_group_1(B) & m1_group_2(B, A)) <=> (~((~v1_group_1(B)) | (~m1_group_2(B, A))))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> (~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))))), rewrite((~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> (((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), rewrite((((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), (![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(72,plain,
% 7.75/7.94 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[71])).
% 7.75/7.94 tff(73,plain,
% 7.75/7.94 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.94 inference(rewrite,[status(thm)],[])).
% 7.75/7.94 tff(74,plain,
% 7.75/7.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), rewrite(((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), (![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))))),
% 7.75/7.94 inference(bind,[status(th)],[])).
% 7.75/7.94 tff(75,plain,
% 7.75/7.94 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.94 inference(quant_intro,[status(thm)],[74])).
% 7.75/7.94 tff(76,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_latsubgr')).
% 7.75/7.94 tff(77,plain,
% 7.75/7.94 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[76, 75])).
% 7.75/7.95 tff(78,plain,
% 7.75/7.95 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[77, 73])).
% 7.75/7.95 tff(79,plain,(
% 7.75/7.95 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.95 inference(skolemize,[status(sab)],[78])).
% 7.75/7.95 tff(80,plain,
% 7.75/7.95 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[79, 72])).
% 7.75/7.95 tff(81,plain,
% 7.75/7.95 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[80, 70])).
% 7.75/7.95 tff(82,plain,
% 7.75/7.95 (v4_group_1(A!0)),
% 7.75/7.95 inference(and_elim,[status(thm)],[32])).
% 7.75/7.95 tff(83,plain,
% 7.75/7.95 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(84,plain,
% 7.75/7.95 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))),
% 7.75/7.95 inference(quant_inst,[status(thm)],[])).
% 7.75/7.95 tff(85,plain,
% 7.75/7.95 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[84, 83])).
% 7.75/7.95 tff(86,plain,
% 7.75/7.95 (![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[85, 35, 34, 82, 33, 81])).
% 7.75/7.95 tff(87,plain,
% 7.75/7.95 (((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | ((~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))) <=> ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | (~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(88,plain,
% 7.75/7.95 ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | ((~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))),
% 7.75/7.95 inference(quant_inst,[status(thm)],[])).
% 7.75/7.95 tff(89,plain,
% 7.75/7.95 ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | (~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[88, 87])).
% 7.75/7.95 tff(90,plain,
% 7.75/7.95 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[89, 57, 40, 86])).
% 7.75/7.95 tff(91,plain,
% 7.75/7.95 (~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))),
% 7.75/7.95 inference(and_elim,[status(thm)],[32])).
% 7.75/7.95 tff(92,plain,
% 7.75/7.95 (m1_subset_1(D!3, u1_struct_0(A!0))),
% 7.75/7.95 inference(or_elim,[status(thm)],[91])).
% 7.75/7.95 tff(93,plain,
% 7.75/7.95 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3)))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(94,plain,
% 7.75/7.95 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3)))),
% 7.75/7.95 inference(quant_inst,[status(thm)],[])).
% 7.75/7.95 tff(95,plain,
% 7.75/7.95 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[94, 93])).
% 7.75/7.95 tff(96,plain,
% 7.75/7.95 (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3)),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[95, 92, 90])).
% 7.75/7.95 tff(97,plain,
% 7.75/7.95 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) & r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1))),
% 7.75/7.95 inference(or_elim,[status(thm)],[91])).
% 7.75/7.95 tff(98,plain,
% 7.75/7.95 (r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1))),
% 7.75/7.95 inference(and_elim,[status(thm)],[97])).
% 7.75/7.95 tff(99,plain,
% 7.75/7.95 ((~(r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3))) | (~r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1))) | r1_rlvect_1(B!1, D!3)),
% 7.75/7.95 inference(tautology,[status(thm)],[])).
% 7.75/7.95 tff(100,plain,
% 7.75/7.95 ((~(r2_hidden(D!3, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, D!3))) | r1_rlvect_1(B!1, D!3)),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[99, 98])).
% 7.75/7.95 tff(101,plain,
% 7.75/7.95 (r1_rlvect_1(B!1, D!3)),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[100, 96])).
% 7.75/7.95 tff(102,plain,
% 7.75/7.95 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[101, 65])).
% 7.75/7.95 tff(103,plain,
% 7.75/7.95 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2) <=> r1_rlvect_1(B!1, C!2)),
% 7.75/7.95 inference(monotonicity,[status(thm)],[63])).
% 7.75/7.95 tff(104,plain,
% 7.75/7.95 (r1_rlvect_1(B!1, C!2) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)),
% 7.75/7.95 inference(symmetry,[status(thm)],[103])).
% 7.75/7.95 tff(105,plain,
% 7.75/7.95 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 7.75/7.95 inference(and_elim,[status(thm)],[32])).
% 7.75/7.95 tff(106,plain,
% 7.75/7.95 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(107,plain,
% 7.75/7.95 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))),
% 7.75/7.95 inference(quant_inst,[status(thm)],[])).
% 7.75/7.95 tff(108,plain,
% 7.75/7.95 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[107, 106])).
% 7.75/7.95 tff(109,plain,
% 7.75/7.95 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[108, 105, 90])).
% 7.75/7.95 tff(110,plain,
% 7.75/7.95 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))),
% 7.75/7.95 inference(and_elim,[status(thm)],[97])).
% 7.75/7.95 tff(111,plain,
% 7.75/7.95 ((~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | r1_rlvect_1(B!1, C!2)),
% 7.75/7.95 inference(tautology,[status(thm)],[])).
% 7.75/7.95 tff(112,plain,
% 7.75/7.95 ((~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))) | r1_rlvect_1(B!1, C!2)),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[111, 110])).
% 7.75/7.95 tff(113,plain,
% 7.75/7.95 (r1_rlvect_1(B!1, C!2)),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[112, 109])).
% 7.75/7.95 tff(114,plain,
% 7.75/7.95 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[113, 104])).
% 7.75/7.95 tff(115,plain,
% 7.75/7.95 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))),
% 7.75/7.95 inference(monotonicity,[status(thm)],[63])).
% 7.75/7.95 tff(116,plain,
% 7.75/7.95 (r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3))),
% 7.75/7.95 inference(symmetry,[status(thm)],[115])).
% 7.75/7.95 tff(117,plain,
% 7.75/7.95 ((~r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))) <=> (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)))),
% 7.75/7.95 inference(monotonicity,[status(thm)],[116])).
% 7.75/7.95 tff(118,plain,
% 7.75/7.95 (^[A: $i, B: $i, C: $i] : refl((m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 7.75/7.95 inference(bind,[status(th)],[])).
% 7.75/7.95 tff(119,plain,
% 7.75/7.95 (![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 7.75/7.95 inference(quant_intro,[status(thm)],[118])).
% 7.75/7.95 tff(120,plain,
% 7.75/7.95 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 7.75/7.95 inference(bind,[status(th)],[])).
% 7.75/7.95 tff(121,plain,
% 7.75/7.95 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 7.75/7.95 inference(quant_intro,[status(thm)],[120])).
% 7.75/7.95 tff(122,plain,
% 7.75/7.95 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(123,plain,
% 7.75/7.95 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))), ((((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))))),
% 7.75/7.95 inference(bind,[status(th)],[])).
% 7.75/7.95 tff(124,plain,
% 7.75/7.95 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 7.75/7.95 inference(quant_intro,[status(thm)],[123])).
% 7.75/7.95 tff(125,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_group_1')).
% 7.75/7.95 tff(126,plain,
% 7.75/7.95 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[125, 124])).
% 7.75/7.95 tff(127,plain,
% 7.75/7.95 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[126, 122])).
% 7.75/7.95 tff(128,plain,(
% 7.75/7.95 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)))),
% 7.75/7.95 inference(skolemize,[status(sab)],[127])).
% 7.75/7.95 tff(129,plain,
% 7.75/7.95 (![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[128, 121])).
% 7.75/7.95 tff(130,plain,
% 7.75/7.95 (![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[129, 119])).
% 7.75/7.95 tff(131,plain,
% 7.75/7.95 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(132,plain,
% 7.75/7.95 ((m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(133,plain,
% 7.75/7.95 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))))),
% 7.75/7.95 inference(monotonicity,[status(thm)],[132])).
% 7.75/7.95 tff(134,plain,
% 7.75/7.95 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)))),
% 7.75/7.95 inference(transitivity,[status(thm)],[133, 131])).
% 7.75/7.95 tff(135,plain,
% 7.75/7.95 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 7.75/7.95 inference(quant_inst,[status(thm)],[])).
% 7.75/7.95 tff(136,plain,
% 7.75/7.95 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k1_group_1(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~l1_group_1(A!0)) | m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[135, 134])).
% 7.75/7.95 tff(137,plain,
% 7.75/7.95 (m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[136, 35, 33, 105, 92, 130])).
% 7.75/7.95 tff(138,plain,
% 7.75/7.95 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))) | (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))) | (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(139,plain,
% 7.75/7.95 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))) | (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))))),
% 7.75/7.95 inference(quant_inst,[status(thm)],[])).
% 7.75/7.95 tff(140,plain,
% 7.75/7.95 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(k1_group_1(A!0, C!2, D!3), u1_struct_0(A!0))) | (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[139, 138])).
% 7.75/7.95 tff(141,plain,
% 7.75/7.95 (r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[140, 137, 90])).
% 7.75/7.95 tff(142,plain,
% 7.75/7.95 (~r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1))),
% 7.75/7.95 inference(or_elim,[status(thm)],[91])).
% 7.75/7.95 tff(143,plain,
% 7.75/7.95 ((~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))) | r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))),
% 7.75/7.95 inference(tautology,[status(thm)],[])).
% 7.75/7.95 tff(144,plain,
% 7.75/7.95 ((~(r2_hidden(k1_group_1(A!0, C!2, D!3), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))) | (~r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3)))),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[143, 142])).
% 7.75/7.95 tff(145,plain,
% 7.75/7.95 (~r1_rlvect_1(B!1, k1_group_1(A!0, C!2, D!3))),
% 7.75/7.95 inference(unit_resolution,[status(thm)],[144, 141])).
% 7.75/7.95 tff(146,plain,
% 7.75/7.95 (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3))),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[145, 117])).
% 7.75/7.95 tff(147,plain,
% 7.75/7.95 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0) <=> m1_group_2(B!1, A!0)),
% 7.75/7.95 inference(monotonicity,[status(thm)],[63])).
% 7.75/7.95 tff(148,plain,
% 7.75/7.95 (m1_group_2(B!1, A!0) <=> m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 7.75/7.95 inference(symmetry,[status(thm)],[147])).
% 7.75/7.95 tff(149,plain,
% 7.75/7.95 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 7.75/7.95 inference(modus_ponens,[status(thm)],[40, 148])).
% 7.75/7.95 tff(150,plain,
% 7.75/7.95 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))))),
% 7.75/7.95 inference(bind,[status(th)],[])).
% 7.75/7.95 tff(151,plain,
% 7.75/7.95 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 7.75/7.95 inference(quant_intro,[status(thm)],[150])).
% 7.75/7.95 tff(152,plain,
% 7.75/7.95 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))))),
% 7.75/7.95 inference(bind,[status(th)],[])).
% 7.75/7.95 tff(153,plain,
% 7.75/7.95 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 7.75/7.95 inference(quant_intro,[status(thm)],[152])).
% 7.75/7.95 tff(154,plain,
% 7.75/7.95 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 7.75/7.95 inference(transitivity,[status(thm)],[153, 151])).
% 7.75/7.95 tff(155,plain,
% 7.75/7.95 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))))),
% 7.75/7.95 inference(bind,[status(th)],[])).
% 7.75/7.95 tff(156,plain,
% 7.75/7.95 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 7.75/7.95 inference(quant_intro,[status(thm)],[155])).
% 7.75/7.95 tff(157,plain,
% 7.75/7.95 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 7.75/7.95 inference(rewrite,[status(thm)],[])).
% 7.75/7.95 tff(158,plain,
% 7.75/7.95 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))) <=> ((~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | r1_rlvect_1(D, k1_group_1(A, B, C)))), ((m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))) <=> (m1_group_2(D, A) => ((~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | r1_rlvect_1(D, k1_group_1(A, B, C)))))), rewrite((m1_group_2(D, A) => ((~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | r1_rlvect_1(D, k1_group_1(A, B, C)))) <=> (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))), ((m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))) <=> (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))), (![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))) <=> ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))))),
% 7.75/7.96 inference(bind,[status(th)],[])).
% 7.75/7.96 tff(159,plain,
% 7.75/7.96 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 7.75/7.96 inference(quant_intro,[status(thm)],[158])).
% 7.75/7.96 tff(160,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_group_2(D, A) => ((r1_rlvect_1(D, B) & r1_rlvect_1(D, C)) => r1_rlvect_1(D, k1_group_1(A, B, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t59_group_2')).
% 7.75/7.96 tff(161,plain,
% 7.75/7.96 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 7.75/7.96 inference(modus_ponens,[status(thm)],[160, 159])).
% 7.75/7.96 tff(162,plain,
% 7.75/7.96 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 7.75/7.96 inference(modus_ponens,[status(thm)],[161, 157])).
% 7.75/7.96 tff(163,plain,(
% 7.75/7.96 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~(r1_rlvect_1(D, B) & r1_rlvect_1(D, C))) | (~m1_group_2(D, A))))))),
% 7.75/7.96 inference(skolemize,[status(sab)],[162])).
% 7.75/7.96 tff(164,plain,
% 7.75/7.96 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 7.75/7.96 inference(modus_ponens,[status(thm)],[163, 156])).
% 7.75/7.96 tff(165,plain,
% 7.75/7.96 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 7.75/7.96 inference(modus_ponens,[status(thm)],[164, 154])).
% 7.75/7.96 tff(166,plain,
% 7.75/7.96 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0))))))),
% 7.75/7.96 inference(rewrite,[status(thm)],[])).
% 7.75/7.96 tff(167,plain,
% 7.75/7.96 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0))))))),
% 7.75/7.96 inference(rewrite,[status(thm)],[])).
% 7.75/7.96 tff(168,plain,
% 7.75/7.96 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))))),
% 7.75/7.96 inference(monotonicity,[status(thm)],[167])).
% 7.75/7.96 tff(169,plain,
% 7.75/7.96 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0))))))),
% 7.75/7.96 inference(transitivity,[status(thm)],[168, 166])).
% 7.75/7.96 tff(170,plain,
% 7.75/7.96 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))),
% 7.75/7.96 inference(quant_inst,[status(thm)],[])).
% 7.75/7.96 tff(171,plain,
% 7.75/7.96 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : (r1_rlvect_1(D, k1_group_1(A, B, C)) | (~m1_group_2(D, A)) | (~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))),
% 7.75/7.96 inference(modus_ponens,[status(thm)],[170, 169])).
% 7.75/7.96 tff(172,plain,
% 7.75/7.96 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))),
% 7.75/7.96 inference(unit_resolution,[status(thm)],[171, 35, 34, 82, 33, 165])).
% 7.75/7.96 tff(173,plain,
% 7.75/7.96 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2)))))),
% 7.75/7.96 inference(rewrite,[status(thm)],[])).
% 7.75/7.96 tff(174,plain,
% 7.75/7.96 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~m1_group_2(D, A!0))))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2)))))),
% 7.75/7.96 inference(rewrite,[status(thm)],[])).
% 7.75/7.96 tff(175,plain,
% 7.75/7.96 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~m1_group_2(D, A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))))),
% 7.75/7.96 inference(monotonicity,[status(thm)],[174])).
% 7.75/7.96 tff(176,plain,
% 7.75/7.96 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~m1_group_2(D, A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2)))))),
% 7.75/7.96 inference(transitivity,[status(thm)],[175, 173])).
% 7.75/7.96 tff(177,plain,
% 7.75/7.96 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~m1_group_2(D, A!0)))))),
% 7.75/7.96 inference(quant_inst,[status(thm)],[])).
% 7.75/7.96 tff(178,plain,
% 7.75/7.96 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, B)) | (~r1_rlvect_1(D, C)) | r1_rlvect_1(D, k1_group_1(A!0, B, C)) | (~m1_group_2(D, A!0)))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))),
% 7.75/7.96 inference(modus_ponens,[status(thm)],[177, 176])).
% 7.75/7.96 tff(179,plain,
% 7.75/7.96 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))),
% 7.75/7.96 inference(unit_resolution,[status(thm)],[178, 105, 172])).
% 7.75/7.96 tff(180,plain,
% 7.75/7.96 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3))))),
% 7.75/7.96 inference(rewrite,[status(thm)],[])).
% 7.75/7.96 tff(181,plain,
% 7.75/7.96 (((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, D!3)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)))) <=> ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3))))),
% 7.75/7.96 inference(rewrite,[status(thm)],[])).
% 7.75/7.96 tff(182,plain,
% 7.75/7.96 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, D!3)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))))),
% 7.75/7.96 inference(monotonicity,[status(thm)],[181])).
% 7.75/7.96 tff(183,plain,
% 7.75/7.96 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, D!3)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3))))),
% 7.80/7.96 inference(transitivity,[status(thm)],[182, 180])).
% 7.80/7.96 tff(184,plain,
% 7.80/7.96 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, D!3)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2))))),
% 7.80/7.96 inference(quant_inst,[status(thm)],[])).
% 7.80/7.96 tff(185,plain,
% 7.80/7.96 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r1_rlvect_1(D, C)) | (~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, C)) | (~r1_rlvect_1(D, C!2))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))),
% 7.80/7.96 inference(modus_ponens,[status(thm)],[184, 183])).
% 7.80/7.96 tff(186,plain,
% 7.80/7.96 (![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))),
% 7.80/7.96 inference(unit_resolution,[status(thm)],[185, 92, 179])).
% 7.80/7.96 tff(187,plain,
% 7.80/7.96 (((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))) <=> ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))),
% 7.80/7.96 inference(rewrite,[status(thm)],[])).
% 7.80/7.96 tff(188,plain,
% 7.80/7.96 (((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3))) <=> (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))),
% 7.80/7.96 inference(rewrite,[status(thm)],[])).
% 7.80/7.96 tff(189,plain,
% 7.80/7.96 (((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))) <=> ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3))))),
% 7.80/8.01 inference(monotonicity,[status(thm)],[188])).
% 7.80/8.01 tff(190,plain,
% 7.80/8.01 (((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))) <=> ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))),
% 7.80/8.01 inference(transitivity,[status(thm)],[189, 187])).
% 7.80/8.01 tff(191,plain,
% 7.80/8.01 ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3)))),
% 7.80/8.01 inference(quant_inst,[status(thm)],[])).
% 7.80/8.01 tff(192,plain,
% 7.80/8.01 ((~![D: $i] : ((~m1_group_2(D, A!0)) | r1_rlvect_1(D, k1_group_1(A!0, C!2, D!3)) | (~r1_rlvect_1(D, C!2)) | (~r1_rlvect_1(D, D!3)))) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3))),
% 7.80/8.01 inference(modus_ponens,[status(thm)],[191, 190])).
% 7.80/8.01 tff(193,plain,
% 7.80/8.01 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k1_group_1(A!0, C!2, D!3)) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), D!3))),
% 7.80/8.01 inference(unit_resolution,[status(thm)],[192, 186])).
% 7.80/8.01 tff(194,plain,
% 7.80/8.01 ($false),
% 7.80/8.01 inference(unit_resolution,[status(thm)],[193, 149, 146, 114, 102])).
% 7.80/8.01 % SZS output end Proof
% 7.80/8.01 % E exiting
%------------------------------------------------------------------------------