%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP644+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 1.10s 1.27s
% Output : Proof 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP644+1 : TPTP v9.0.0. Released v3.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:38:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.10/1.27 % SZS status Theorem
% 1.10/1.27 % SZS output start Proof
% 1.10/1.27 tff(r1_rlvect_1_type, type, (
% 1.10/1.27 r1_rlvect_1: ( $i * $i ) > $o)).
% 1.10/1.27 tff(tptp_fun_C_2_type, type, (
% 1.10/1.27 tptp_fun_C_2: $i)).
% 1.10/1.27 tff(g1_group_1_type, type, (
% 1.10/1.27 g1_group_1: ( $i * $i ) > $i)).
% 1.10/1.27 tff(u1_group_1_type, type, (
% 1.10/1.27 u1_group_1: $i > $i)).
% 1.10/1.27 tff(tptp_fun_B_1_type, type, (
% 1.10/1.27 tptp_fun_B_1: $i)).
% 1.10/1.27 tff(u1_struct_0_type, type, (
% 1.10/1.27 u1_struct_0: $i > $i)).
% 1.10/1.27 tff(l1_group_1_type, type, (
% 1.10/1.27 l1_group_1: $i > $o)).
% 1.10/1.27 tff(v3_group_1_type, type, (
% 1.10/1.27 v3_group_1: $i > $o)).
% 1.10/1.27 tff(v3_struct_0_type, type, (
% 1.10/1.27 v3_struct_0: $i > $o)).
% 1.10/1.27 tff(m1_group_2_type, type, (
% 1.10/1.27 m1_group_2: ( $i * $i ) > $o)).
% 1.10/1.27 tff(tptp_fun_A_0_type, type, (
% 1.10/1.27 tptp_fun_A_0: $i)).
% 1.10/1.27 tff(m1_subset_1_type, type, (
% 1.10/1.27 m1_subset_1: ( $i * $i ) > $o)).
% 1.10/1.27 tff(r2_hidden_type, type, (
% 1.10/1.27 r2_hidden: ( $i * $i ) > $o)).
% 1.10/1.27 tff(k1_funct_1_type, type, (
% 1.10/1.27 k1_funct_1: ( $i * $i ) > $i)).
% 1.10/1.27 tff(k1_latsubgr_type, type, (
% 1.10/1.27 k1_latsubgr: $i > $i)).
% 1.10/1.27 tff(k3_group_1_type, type, (
% 1.10/1.27 k3_group_1: ( $i * $i ) > $i)).
% 1.10/1.27 tff(v1_group_1_type, type, (
% 1.10/1.27 v1_group_1: $i > $o)).
% 1.10/1.27 tff(v4_group_1_type, type, (
% 1.10/1.27 v4_group_1: $i > $o)).
% 1.10/1.27 tff(1,plain,
% 1.10/1.27 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(2,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[1])).
% 1.10/1.27 tff(3,plain,
% 1.10/1.27 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(4,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[3])).
% 1.10/1.27 tff(5,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.10/1.27 inference(transitivity,[status(thm)],[4, 2])).
% 1.10/1.27 tff(6,plain,
% 1.10/1.27 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(7,plain,
% 1.10/1.27 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[6])).
% 1.10/1.27 tff(8,plain,
% 1.10/1.27 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(9,plain,
% 1.10/1.27 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> (m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), rewrite((m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), (![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(10,plain,
% 1.10/1.27 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[9])).
% 1.10/1.27 tff(11,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_group_2')).
% 1.10/1.27 tff(12,plain,
% 1.10/1.27 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.10/1.27 tff(13,plain,
% 1.10/1.27 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.10/1.27 tff(14,plain,(
% 1.10/1.27 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 1.10/1.27 inference(skolemize,[status(sab)],[13])).
% 1.10/1.27 tff(15,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.10/1.27 tff(16,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.10/1.27 tff(17,plain,
% 1.10/1.27 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(18,plain,
% 1.10/1.27 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(19,plain,
% 1.10/1.27 ((~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(20,plain,
% 1.10/1.27 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))) <=> ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[19])).
% 1.10/1.27 tff(21,plain,
% 1.10/1.27 (((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))) <=> (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.10/1.27 inference(transitivity,[status(thm)],[20, 18])).
% 1.10/1.27 tff(22,plain,
% 1.10/1.27 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[21])).
% 1.10/1.27 tff(23,plain,
% 1.10/1.27 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((v1_group_1(B!1) & m1_group_2(B!1, A!0)) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 1.10/1.27 inference(transitivity,[status(thm)],[22, 17])).
% 1.10/1.27 tff(24,plain,
% 1.10/1.27 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(25,plain,
% 1.10/1.27 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) => r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(26,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) => r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_latsubgr')).
% 1.10/1.27 tff(27,plain,
% 1.10/1.27 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.10/1.27 tff(28,plain,
% 1.10/1.27 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[27, 24])).
% 1.10/1.27 tff(29,plain,
% 1.10/1.27 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.10/1.27 tff(30,plain,
% 1.10/1.27 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : (r2_hidden(k3_group_1(A, C), k1_funct_1(k1_latsubgr(A), B)) | (~r2_hidden(C, k1_funct_1(k1_latsubgr(A), B))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[29, 24])).
% 1.10/1.27 tff(31,plain,
% 1.10/1.27 ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & v1_group_1(B!1) & m1_group_2(B!1, A!0) & (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.10/1.27 tff(32,plain,
% 1.10/1.27 (l1_group_1(A!0)),
% 1.10/1.27 inference(and_elim,[status(thm)],[31])).
% 1.10/1.27 tff(33,plain,
% 1.10/1.27 (v3_group_1(A!0)),
% 1.10/1.27 inference(and_elim,[status(thm)],[31])).
% 1.10/1.27 tff(34,plain,
% 1.10/1.27 (~v3_struct_0(A!0)),
% 1.10/1.27 inference(and_elim,[status(thm)],[31])).
% 1.10/1.27 tff(35,plain,
% 1.10/1.27 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(36,plain,
% 1.10/1.27 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(37,plain,
% 1.10/1.27 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.10/1.27 tff(38,plain,
% 1.10/1.27 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[37, 34, 33, 32, 16])).
% 1.10/1.27 tff(39,plain,
% 1.10/1.27 (m1_group_2(B!1, A!0)),
% 1.10/1.27 inference(and_elim,[status(thm)],[31])).
% 1.10/1.27 tff(40,plain,
% 1.10/1.27 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(41,plain,
% 1.10/1.27 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(42,plain,
% 1.10/1.27 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(B!1, A!0)) | (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.10/1.27 tff(43,plain,
% 1.10/1.27 (~(v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[42, 39, 38])).
% 1.10/1.27 tff(44,plain,
% 1.10/1.27 ((v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1))) | l1_group_1(B!1)),
% 1.10/1.27 inference(tautology,[status(thm)],[])).
% 1.10/1.27 tff(45,plain,
% 1.10/1.27 (l1_group_1(B!1)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[44, 43])).
% 1.10/1.27 tff(46,plain,
% 1.10/1.27 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(47,plain,
% 1.10/1.27 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[46])).
% 1.10/1.27 tff(48,plain,
% 1.10/1.27 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(49,plain,
% 1.10/1.27 (^[A: $i] : trans(monotonicity(rewrite((v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))) <=> ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> (l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))))), rewrite((l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(50,plain,
% 1.10/1.27 (![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[49])).
% 1.10/1.27 tff(51,axiom,(![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 1.10/1.27 tff(52,plain,
% 1.10/1.27 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.10/1.27 tff(53,plain,
% 1.10/1.27 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.10/1.27 tff(54,plain,(
% 1.10/1.27 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.27 inference(skolemize,[status(sab)],[53])).
% 1.10/1.27 tff(55,plain,
% 1.10/1.27 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.10/1.27 tff(56,plain,
% 1.10/1.27 (v1_group_1(B!1)),
% 1.10/1.27 inference(and_elim,[status(thm)],[31])).
% 1.10/1.27 tff(57,plain,
% 1.10/1.27 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(58,plain,
% 1.10/1.27 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(59,plain,
% 1.10/1.27 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~v1_group_1(B!1)) | (~l1_group_1(B!1))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.10/1.27 tff(60,plain,
% 1.10/1.27 ((B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))) | (~l1_group_1(B!1))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[59, 56, 55])).
% 1.10/1.27 tff(61,plain,
% 1.10/1.27 (B!1 = g1_group_1(u1_struct_0(B!1), u1_group_1(B!1))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[60, 45])).
% 1.10/1.27 tff(62,plain,
% 1.10/1.27 (r1_rlvect_1(B!1, C!2) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)),
% 1.10/1.27 inference(monotonicity,[status(thm)],[61])).
% 1.10/1.27 tff(63,plain,
% 1.10/1.27 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(64,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[63])).
% 1.10/1.27 tff(65,plain,
% 1.10/1.27 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(66,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[65])).
% 1.10/1.27 tff(67,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(transitivity,[status(thm)],[66, 64])).
% 1.10/1.27 tff(68,plain,
% 1.10/1.27 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_group_1(B) & m1_group_2(B, A)) <=> (~((~v1_group_1(B)) | (~m1_group_2(B, A))))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> (~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))))), rewrite((~(~((~v1_group_1(B)) | (~m1_group_2(B, A))))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)))), ((~(v1_group_1(B) & m1_group_2(B, A))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> (((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), rewrite((((~v1_group_1(B)) | (~m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), (![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(69,plain,
% 1.10/1.27 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[68])).
% 1.10/1.27 tff(70,plain,
% 1.10/1.27 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(71,plain,
% 1.10/1.27 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), rewrite(((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))), (((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), (![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))) <=> ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(72,plain,
% 1.10/1.27 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[71])).
% 1.10/1.27 tff(73,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((v1_group_1(B) & m1_group_2(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_latsubgr')).
% 1.10/1.27 tff(74,plain,
% 1.10/1.27 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.10/1.27 tff(75,plain,
% 1.10/1.27 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.10/1.27 tff(76,plain,(
% 1.10/1.27 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_group_1(B) & m1_group_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(skolemize,[status(sab)],[75])).
% 1.10/1.27 tff(77,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.10/1.27 tff(78,plain,
% 1.10/1.27 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[77, 67])).
% 1.10/1.27 tff(79,plain,
% 1.10/1.27 (v4_group_1(A!0)),
% 1.10/1.27 inference(and_elim,[status(thm)],[31])).
% 1.10/1.27 tff(80,plain,
% 1.10/1.27 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(81,plain,
% 1.10/1.27 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C)))))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(82,plain,
% 1.10/1.28 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A), B)) <=> r1_rlvect_1(B, C)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.10/1.28 tff(83,plain,
% 1.10/1.28 (![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[82, 34, 33, 79, 32, 78])).
% 1.10/1.28 tff(84,plain,
% 1.10/1.28 (((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | ((~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))) <=> ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | (~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(85,plain,
% 1.10/1.28 ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | ((~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C))))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(86,plain,
% 1.10/1.28 ((~![B: $i] : ((~v1_group_1(B)) | (~m1_group_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B)) <=> r1_rlvect_1(B, C))))) | (~v1_group_1(B!1)) | (~m1_group_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.10/1.28 tff(87,plain,
% 1.10/1.28 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[86, 56, 39, 83])).
% 1.10/1.28 tff(88,plain,
% 1.10/1.28 (~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 1.10/1.28 inference(and_elim,[status(thm)],[31])).
% 1.10/1.28 tff(89,plain,
% 1.10/1.28 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 1.10/1.28 inference(or_elim,[status(thm)],[88])).
% 1.10/1.28 tff(90,plain,
% 1.10/1.28 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(91,plain,
% 1.10/1.28 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(92,plain,
% 1.10/1.28 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.10/1.28 tff(93,plain,
% 1.10/1.28 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[92, 89, 87])).
% 1.10/1.28 tff(94,plain,
% 1.10/1.28 (r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))),
% 1.10/1.28 inference(or_elim,[status(thm)],[88])).
% 1.10/1.28 tff(95,plain,
% 1.10/1.28 ((~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))) | (~r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1))) | r1_rlvect_1(B!1, C!2)),
% 1.10/1.28 inference(tautology,[status(thm)],[])).
% 1.10/1.28 tff(96,plain,
% 1.10/1.28 ((~(r2_hidden(C!2, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C!2))) | r1_rlvect_1(B!1, C!2)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[95, 94])).
% 1.10/1.28 tff(97,plain,
% 1.10/1.28 (r1_rlvect_1(B!1, C!2)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[96, 93])).
% 1.10/1.28 tff(98,plain,
% 1.10/1.28 (r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[97, 62])).
% 1.10/1.28 tff(99,plain,
% 1.10/1.28 (r1_rlvect_1(B!1, k3_group_1(A!0, C!2)) <=> r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[61])).
% 1.10/1.28 tff(100,plain,
% 1.10/1.28 ((~r1_rlvect_1(B!1, k3_group_1(A!0, C!2))) <=> (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2)))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[99])).
% 1.10/1.28 tff(101,plain,
% 1.10/1.28 (^[A: $i, B: $i] : refl((m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(102,plain,
% 1.10/1.28 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[101])).
% 1.10/1.28 tff(103,plain,
% 1.10/1.28 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(104,plain,
% 1.10/1.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[103])).
% 1.10/1.28 tff(105,plain,
% 1.10/1.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(106,plain,
% 1.10/1.28 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(107,plain,
% 1.10/1.28 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[106])).
% 1.10/1.28 tff(108,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_group_1')).
% 1.10/1.28 tff(109,plain,
% 1.10/1.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.10/1.28 tff(110,plain,
% 1.10/1.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[109, 105])).
% 1.10/1.28 tff(111,plain,(
% 1.10/1.28 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 1.10/1.28 inference(skolemize,[status(sab)],[110])).
% 1.10/1.28 tff(112,plain,
% 1.10/1.28 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[111, 104])).
% 1.10/1.28 tff(113,plain,
% 1.10/1.28 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[112, 102])).
% 1.10/1.28 tff(114,plain,
% 1.10/1.28 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(115,plain,
% 1.10/1.28 ((m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(116,plain,
% 1.10/1.28 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[115])).
% 1.10/1.28 tff(117,plain,
% 1.10/1.28 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[116, 114])).
% 1.10/1.28 tff(118,plain,
% 1.10/1.28 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(119,plain,
% 1.10/1.28 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.10/1.28 tff(120,plain,
% 1.10/1.28 (m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[119, 34, 33, 79, 32, 89, 113])).
% 1.10/1.28 tff(121,plain,
% 1.10/1.28 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))) | (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))) | (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2))))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(122,plain,
% 1.10/1.28 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | ((~m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))) | (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2))))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(123,plain,
% 1.10/1.28 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(C, k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, C)))) | (~m1_subset_1(k3_group_1(A!0, C!2), u1_struct_0(A!0))) | (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.10/1.28 tff(124,plain,
% 1.10/1.28 (r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[123, 120, 87])).
% 1.10/1.28 tff(125,plain,
% 1.10/1.28 (~r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1))),
% 1.10/1.28 inference(or_elim,[status(thm)],[88])).
% 1.10/1.28 tff(126,plain,
% 1.10/1.28 ((~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))) | r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) | (~r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))),
% 1.10/1.28 inference(tautology,[status(thm)],[])).
% 1.10/1.28 tff(127,plain,
% 1.10/1.28 ((~(r2_hidden(k3_group_1(A!0, C!2), k1_funct_1(k1_latsubgr(A!0), B!1)) <=> r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))) | (~r1_rlvect_1(B!1, k3_group_1(A!0, C!2)))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[126, 125])).
% 1.10/1.28 tff(128,plain,
% 1.10/1.28 (~r1_rlvect_1(B!1, k3_group_1(A!0, C!2))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[127, 124])).
% 1.10/1.28 tff(129,plain,
% 1.10/1.28 (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[128, 100])).
% 1.10/1.28 tff(130,plain,
% 1.10/1.28 (g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)) = B!1),
% 1.10/1.28 inference(symmetry,[status(thm)],[61])).
% 1.10/1.28 tff(131,plain,
% 1.10/1.28 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0) <=> m1_group_2(B!1, A!0)),
% 1.10/1.28 inference(monotonicity,[status(thm)],[130])).
% 1.10/1.28 tff(132,plain,
% 1.10/1.28 (m1_group_2(B!1, A!0) <=> m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 1.10/1.28 inference(symmetry,[status(thm)],[131])).
% 1.10/1.28 tff(133,plain,
% 1.10/1.28 (m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[39, 132])).
% 1.10/1.28 tff(134,plain,
% 1.10/1.28 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(135,plain,
% 1.10/1.28 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[134])).
% 1.10/1.28 tff(136,plain,
% 1.10/1.28 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(137,plain,
% 1.10/1.28 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[136])).
% 1.10/1.28 tff(138,plain,
% 1.10/1.28 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(139,plain,
% 1.10/1.28 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[138])).
% 1.10/1.28 tff(140,plain,
% 1.10/1.28 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[139, 137])).
% 1.10/1.28 tff(141,plain,
% 1.10/1.28 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(142,plain,
% 1.10/1.28 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[141])).
% 1.10/1.28 tff(143,plain,
% 1.10/1.28 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(144,plain,
% 1.10/1.28 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))) <=> ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A, B)))), ((m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))) <=> (m1_group_2(C, A) => ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A, B)))))), rewrite((m1_group_2(C, A) => ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A, B)))) <=> (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))), ((m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))) <=> (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))), (![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))) <=> ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(145,plain,
% 1.10/1.28 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[144])).
% 1.10/1.28 tff(146,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_group_2(C, A) => (r1_rlvect_1(C, B) => r1_rlvect_1(C, k3_group_1(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t60_group_2')).
% 1.10/1.28 tff(147,plain,
% 1.10/1.28 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[146, 145])).
% 1.10/1.28 tff(148,plain,
% 1.10/1.28 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[147, 143])).
% 1.10/1.28 tff(149,plain,(
% 1.10/1.28 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.10/1.28 inference(skolemize,[status(sab)],[148])).
% 1.10/1.28 tff(150,plain,
% 1.10/1.28 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[149, 142])).
% 1.10/1.28 tff(151,plain,
% 1.10/1.28 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[150, 140])).
% 1.10/1.28 tff(152,plain,
% 1.10/1.28 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[151, 135])).
% 1.10/1.28 tff(153,plain,
% 1.10/1.28 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0)))))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(154,plain,
% 1.10/1.28 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A!0, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A!0))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0)))))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(155,plain,
% 1.10/1.28 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A!0, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[154])).
% 1.10/1.28 tff(156,plain,
% 1.10/1.28 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A!0, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0)))))),
% 1.10/1.28 inference(transitivity,[status(thm)],[155, 153])).
% 1.10/1.28 tff(157,plain,
% 1.10/1.28 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A!0, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A!0)))))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(158,plain,
% 1.10/1.28 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_rlvect_1(C, k3_group_1(A, B)) | (~r1_rlvect_1(C, B)) | (~m1_group_2(C, A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.10/1.28 tff(159,plain,
% 1.10/1.28 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[158, 34, 33, 79, 32, 152])).
% 1.10/1.28 tff(160,plain,
% 1.10/1.28 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2))))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(161,plain,
% 1.10/1.28 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, C!2)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~m1_group_2(C, A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2))))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(162,plain,
% 1.10/1.28 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, C!2)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~m1_group_2(C, A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[161])).
% 1.10/1.28 tff(163,plain,
% 1.10/1.28 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, C!2)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~m1_group_2(C, A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2))))),
% 1.10/1.29 inference(transitivity,[status(thm)],[162, 160])).
% 1.10/1.29 tff(164,plain,
% 1.10/1.29 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, C!2)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~m1_group_2(C, A!0))))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(165,plain,
% 1.10/1.29 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~r1_rlvect_1(C, B)) | r1_rlvect_1(C, k3_group_1(A!0, B)) | (~m1_group_2(C, A!0))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[164, 163])).
% 1.10/1.29 tff(166,plain,
% 1.10/1.29 (![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[165, 89, 159])).
% 1.10/1.29 tff(167,plain,
% 1.10/1.29 (((~![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))) | ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)))) <=> ((~![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(168,plain,
% 1.10/1.29 ((~![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))) | ((~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(169,plain,
% 1.10/1.29 ((~![C: $i] : ((~m1_group_2(C, A!0)) | r1_rlvect_1(C, k3_group_1(A!0, C!2)) | (~r1_rlvect_1(C, C!2)))) | (~m1_group_2(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), A!0)) | r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), k3_group_1(A!0, C!2)) | (~r1_rlvect_1(g1_group_1(u1_struct_0(B!1), u1_group_1(B!1)), C!2))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.10/1.29 tff(170,plain,
% 1.10/1.29 ($false),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[169, 166, 133, 129, 98])).
% 1.10/1.29 % SZS output end Proof
% 1.10/1.30 % E exiting
%------------------------------------------------------------------------------