%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:11:49 AM UTC 2026
% Result : Theorem 195.78s 196.39s
% Output : Proof 197.38s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t6_rmod_5,conjecture,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k1_rlvect_1(A) != k2_group_1(A)
=> ( ~ v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B)
& ~ v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B) ) ) ) ) ),
file('theBenchmark.p',t6_rmod_5) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(existence_l1_vectsp_1,axiom,
? [A] : l1_vectsp_1(A),
file('theBenchmark.p',existence_l1_vectsp_1) ).
fof(dt_l1_vectsp_1,axiom,
! [A] :
( l1_vectsp_1(A)
=> l1_group_1(A) ),
file('theBenchmark.p',dt_l1_vectsp_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_rlvect_2,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( v1_finset_1(B)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc2_rlvect_2) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : k2_tarski(A,B) = k2_tarski(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(existence_l1_group_1,axiom,
? [A] : l1_group_1(A),
file('theBenchmark.p',existence_l1_group_1) ).
fof(existence_l1_rlvect_1,axiom,
? [A] : l1_rlvect_1(A),
file('theBenchmark.p',existence_l1_rlvect_1) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l2_struct_0,axiom,
? [A] : l2_struct_0(A),
file('theBenchmark.p',existence_l2_struct_0) ).
fof(existence_l2_vectsp_1,axiom,
? [A] : l2_vectsp_1(A),
file('theBenchmark.p',existence_l2_vectsp_1) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_l1_rlvect_1,axiom,
! [A] :
( l1_rlvect_1(A)
=> l2_struct_0(A) ),
file('theBenchmark.p',dt_l1_rlvect_1) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l2_struct_0,axiom,
! [A] :
( l2_struct_0(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l2_struct_0) ).
fof(dt_l2_vectsp_1,axiom,
! [A] :
( l2_vectsp_1(A)
=> ( l2_struct_0(A)
& l1_vectsp_1(A) ) ),
file('theBenchmark.p',dt_l2_vectsp_1) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc4_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l2_struct_0(A) ),
file('theBenchmark.p',rc4_struct_0) ).
fof(rc9_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( ~ v3_struct_0(B)
& l1_vectsp_2(B,A) ) ),
file('theBenchmark.p',rc9_vectsp_2) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(commutativity_k8_rlvect_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_struct_0(A)
& ~ v3_struct_0(A) )
=> k8_rlvect_2(A,B,C) = k8_rlvect_2(A,C,B) ),
file('theBenchmark.p',commutativity_k8_rlvect_2) ).
fof(existence_l1_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] : l1_vectsp_2(B,A) ),
file('theBenchmark.p',existence_l1_vectsp_2) ).
fof(existence_l3_vectsp_1,axiom,
? [A] : l3_vectsp_1(A),
file('theBenchmark.p',existence_l3_vectsp_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(redefinition_k8_rlvect_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_struct_0(A)
& ~ v3_struct_0(A) )
=> k8_rlvect_2(A,B,C) = k2_tarski(B,C) ),
file('theBenchmark.p',redefinition_k8_rlvect_2) ).
fof(dt_k1_rlvect_1,axiom,
! [A] :
( l2_struct_0(A)
=> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k1_rlvect_1) ).
fof(dt_k2_group_1,axiom,
! [A] :
( ( l1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k2_group_1(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k2_group_1) ).
fof(dt_k8_rlvect_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ( m1_subset_1(k8_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(k8_rlvect_2(A,B,C)) ) ),
file('theBenchmark.p',dt_k8_rlvect_2) ).
fof(dt_l1_vectsp_2,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_vectsp_2(B,A)
=> l1_rlvect_1(B) ) ),
file('theBenchmark.p',dt_l1_vectsp_2) ).
fof(dt_l3_vectsp_1,axiom,
! [A] :
( l3_vectsp_1(A)
=> ( l2_vectsp_1(A)
& l1_rlvect_1(A) ) ),
file('theBenchmark.p',dt_l3_vectsp_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(t5_rmod_5,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( v1_rmod_5(k8_rlvect_2(B,C,D),A,B)
=> ( ( D != k1_rlvect_1(B)
& C != k1_rlvect_1(B) )
| k1_rlvect_1(A) = k2_group_1(A) ) ) ) ) ) ),
file('theBenchmark.p',t5_rmod_5) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k1_rlvect_1(A) != k2_group_1(A)
=> ( ~ v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B)
& ~ v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B) ) ) ) ) ),
inference(negate,[status(cth)],[t6_rmod_5]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ( v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B)
| v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B) )
& k1_rlvect_1(A) != k2_group_1(A)
& m1_subset_1(C,u1_struct_0(B)) )
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ( v1_rmod_5(k8_rlvect_2(U_1,k1_rlvect_1(U_1),U_0),U_2,U_1)
| v1_rmod_5(k8_rlvect_2(U_1,U_0,k1_rlvect_1(U_1)),U_2,U_1) )
& k1_rlvect_1(U_2) != k2_group_1(U_2)
& m1_subset_1(U_0,u1_struct_0(U_1)) )
& l1_vectsp_2(U_1,U_2)
& v5_vectsp_2(U_1,U_2)
& v6_rlvect_1(U_1)
& v5_rlvect_1(U_1)
& v4_rlvect_1(U_1)
& v3_rlvect_1(U_1)
& ~ v3_struct_0(U_1) )
& l3_vectsp_1(U_2)
& v8_vectsp_1(U_2)
& v7_vectsp_1(U_2)
& v6_vectsp_1(U_2)
& v4_group_1(U_2)
& v6_rlvect_1(U_2)
& v5_rlvect_1(U_2)
& v4_rlvect_1(U_2)
& v3_rlvect_1(U_2)
& ~ v3_struct_0(U_2) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( ( v1_rmod_5(k8_rlvect_2(U_1,k1_rlvect_1(U_1),U_0),sK1,U_1)
| v1_rmod_5(k8_rlvect_2(U_1,U_0,k1_rlvect_1(U_1)),sK1,U_1) )
& k1_rlvect_1(sK1) != k2_group_1(sK1)
& m1_subset_1(U_0,u1_struct_0(U_1)) )
& l1_vectsp_2(U_1,sK1)
& v5_vectsp_2(U_1,sK1)
& v6_rlvect_1(U_1)
& v5_rlvect_1(U_1)
& v4_rlvect_1(U_1)
& v3_rlvect_1(U_1)
& ~ v3_struct_0(U_1) )
& l3_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v4_group_1(sK1)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_0] :
( ( v1_rmod_5(k8_rlvect_2(sK2,k1_rlvect_1(sK2),U_0),sK1,sK2)
| v1_rmod_5(k8_rlvect_2(sK2,U_0,k1_rlvect_1(sK2)),sK1,sK2) )
& k1_rlvect_1(sK1) != k2_group_1(sK1)
& m1_subset_1(U_0,u1_struct_0(sK2)) )
& l1_vectsp_2(sK2,sK1)
& v5_vectsp_2(sK2,sK1)
& v6_rlvect_1(sK2)
& v5_rlvect_1(sK2)
& v4_rlvect_1(sK2)
& v3_rlvect_1(sK2)
& ~ v3_struct_0(sK2)
& l3_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v4_group_1(sK1)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( v1_rmod_5(k8_rlvect_2(sK2,k1_rlvect_1(sK2),sK3),sK1,sK2)
| v1_rmod_5(k8_rlvect_2(sK2,sK3,k1_rlvect_1(sK2)),sK1,sK2) )
& k1_rlvect_1(sK1) != k2_group_1(sK1)
& m1_subset_1(sK3,u1_struct_0(sK2))
& l1_vectsp_2(sK2,sK1)
& v5_vectsp_2(sK2,sK1)
& v6_rlvect_1(sK2)
& v5_rlvect_1(sK2)
& v4_rlvect_1(sK2)
& v3_rlvect_1(sK2)
& ~ v3_struct_0(sK2)
& l3_vectsp_1(sK1)
& v8_vectsp_1(sK1)
& v7_vectsp_1(sK1)
& v6_vectsp_1(sK1)
& v4_group_1(sK1)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3)],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
v3_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
v4_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,negated_conjecture,
v5_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_11,negated_conjecture,
v6_rlvect_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_12,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_13,negated_conjecture,
v6_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_14,negated_conjecture,
v7_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_15,negated_conjecture,
v8_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_16,negated_conjecture,
l3_vectsp_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_17,negated_conjecture,
~ v3_struct_0(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_18,negated_conjecture,
v3_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_19,negated_conjecture,
v4_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_20,negated_conjecture,
v5_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_21,negated_conjecture,
v6_rlvect_1(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_22,negated_conjecture,
v5_vectsp_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_23,negated_conjecture,
l1_vectsp_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_24,negated_conjecture,
m1_subset_1(sK3,u1_struct_0(sK2)),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_25,negated_conjecture,
k1_rlvect_1(sK1) != k2_group_1(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_26,negated_conjecture,
( v1_rmod_5(k8_rlvect_2(sK2,k1_rlvect_1(sK2),sK3),sK1,sK2)
| v1_rmod_5(k8_rlvect_2(sK2,sK3,k1_rlvect_1(sK2)),sK1,sK2) ),
inference(clausify,[status(thm)],[f_1_6]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_4,U_3] :
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ r2_hidden(U_3,U_4)
| ~ r2_hidden(U_4,U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_3_2,plain,
$true,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_4_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_5_2,plain,
! [U_6,U_5] :
( m1_subset_1(U_6,U_5)
| ~ r2_hidden(U_6,U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( m1_subset_1(U_6,U_5)
| ~ r2_hidden(U_6,U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_6_2,plain,
! [U_9,U_8,U_7] :
( m1_subset_1(U_9,U_7)
| ~ m1_subset_1(U_8,k1_zfmisc_1(U_7))
| ~ r2_hidden(U_9,U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( m1_subset_1(U_9,U_7)
| ~ m1_subset_1(U_8,k1_zfmisc_1(U_7))
| ~ r2_hidden(U_9,U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_7_2,plain,
! [U_12,U_11,U_10] :
( ~ v1_xboole_0(U_10)
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_10))
| ~ r2_hidden(U_12,U_11) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_12,U_11] :
( ! [U_10] :
( ~ v1_xboole_0(U_10)
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_10)) )
| ~ r2_hidden(U_12,U_11) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( ~ v1_xboole_0(U_10)
| ~ m1_subset_1(U_11,k1_zfmisc_1(U_10))
| ~ r2_hidden(U_12,U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_8_2,plain,
! [U_14,U_13] : r1_tarski(U_14,U_14),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_14] : r1_tarski(U_14,U_14),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
r1_tarski(U_14,U_14),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
? [A] : l1_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_vectsp_1]) ).
fof(f_9_2,plain,
? [U_15] : l1_vectsp_1(U_15),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
l1_vectsp_1(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_15,sK4)],[f_9_2]) ).
cnf(f_9_4,plain,
l1_vectsp_1(sK4),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] :
( l1_group_1(A)
| ~ l1_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_vectsp_1]) ).
fof(f_10_2,plain,
! [U_16] :
( l1_group_1(U_16)
| ~ l1_vectsp_1(U_16) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( l1_group_1(U_16)
| ~ l1_vectsp_1(U_16) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_11_2,plain,
! [U_18] :
( ? [U_17] :
( ~ v1_xboole_0(U_17)
& m1_subset_1(U_17,k1_zfmisc_1(U_18)) )
| v1_xboole_0(U_18) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_18] :
( ( ~ v1_xboole_0(sK5(U_18))
& m1_subset_1(sK5(U_18),k1_zfmisc_1(U_18)) )
| v1_xboole_0(U_18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_17,sK5(U_18))],[f_11_2]) ).
cnf(f_11_4,plain,
( m1_subset_1(sK5(U_18),k1_zfmisc_1(U_18))
| v1_xboole_0(U_18) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( ~ v1_xboole_0(sK5(U_18))
| v1_xboole_0(U_18) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_12_2,plain,
? [U_19] : v1_xboole_0(U_19),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
v1_xboole_0(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_19,sK6)],[f_12_2]) ).
cnf(f_12_4,plain,
v1_xboole_0(sK6),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] :
( ? [B] :
( v1_finset_1(B)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc2_rlvect_2]) ).
fof(f_13_2,plain,
! [U_21] :
( ? [U_20] :
( v1_finset_1(U_20)
& ~ v1_xboole_0(U_20)
& m1_subset_1(U_20,k1_zfmisc_1(u1_struct_0(U_21))) )
| ~ l1_struct_0(U_21)
| v3_struct_0(U_21) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_21] :
( ( v1_finset_1(sK7(U_21))
& ~ v1_xboole_0(sK7(U_21))
& m1_subset_1(sK7(U_21),k1_zfmisc_1(u1_struct_0(U_21))) )
| ~ l1_struct_0(U_21)
| v3_struct_0(U_21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_20,sK7(U_21))],[f_13_2]) ).
cnf(f_13_4,plain,
( m1_subset_1(sK7(U_21),k1_zfmisc_1(u1_struct_0(U_21)))
| ~ l1_struct_0(U_21)
| v3_struct_0(U_21) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( ~ v1_xboole_0(sK7(U_21))
| ~ l1_struct_0(U_21)
| v3_struct_0(U_21) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( v1_finset_1(sK7(U_21))
| ~ l1_struct_0(U_21)
| v3_struct_0(U_21) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_14_2,plain,
! [U_23] :
? [U_22] :
( v1_xboole_0(U_22)
& m1_subset_1(U_22,k1_zfmisc_1(U_23)) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_23] :
( v1_xboole_0(sK8(U_23))
& m1_subset_1(sK8(U_23),k1_zfmisc_1(U_23)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_22,sK8(U_23))],[f_14_2]) ).
cnf(f_14_4,plain,
m1_subset_1(sK8(U_23),k1_zfmisc_1(U_23)),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
v1_xboole_0(sK8(U_23)),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_15_2,plain,
? [U_24] : ~ v1_xboole_0(U_24),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
~ v1_xboole_0(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_24,sK9)],[f_15_2]) ).
cnf(f_15_4,plain,
~ v1_xboole_0(sK9),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_16_2,plain,
! [U_26] :
( ? [U_25] :
( ~ v1_xboole_0(U_25)
& m1_subset_1(U_25,k1_zfmisc_1(u1_struct_0(U_26))) )
| ~ l1_struct_0(U_26)
| v3_struct_0(U_26) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_26] :
( ( ~ v1_xboole_0(sK10(U_26))
& m1_subset_1(sK10(U_26),k1_zfmisc_1(u1_struct_0(U_26))) )
| ~ l1_struct_0(U_26)
| v3_struct_0(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_25,sK10(U_26))],[f_16_2]) ).
cnf(f_16_4,plain,
( m1_subset_1(sK10(U_26),k1_zfmisc_1(u1_struct_0(U_26)))
| ~ l1_struct_0(U_26)
| v3_struct_0(U_26) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( ~ v1_xboole_0(sK10(U_26))
| ~ l1_struct_0(U_26)
| v3_struct_0(U_26) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_17_2,plain,
! [U_28,U_27] :
( r2_hidden(U_28,U_27)
| v1_xboole_0(U_27)
| ~ m1_subset_1(U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( r2_hidden(U_28,U_27)
| v1_xboole_0(U_27)
| ~ m1_subset_1(U_28,U_27) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_18_2,plain,
! [U_29] :
( U_29 = k1_xboole_0
| ~ v1_xboole_0(U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( U_29 = k1_xboole_0
| ~ v1_xboole_0(U_29) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_19_2,plain,
! [U_31,U_30] :
( ~ v1_xboole_0(U_30)
| ~ r2_hidden(U_31,U_30) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( ~ v1_xboole_0(U_30)
| ~ r2_hidden(U_31,U_30) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_20_2,plain,
! [U_33,U_32] :
( ~ v1_xboole_0(U_32)
| U_33 = U_32
| ~ v1_xboole_0(U_33) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_33] :
( ! [U_32] :
( ~ v1_xboole_0(U_32)
| U_33 = U_32 )
| ~ v1_xboole_0(U_33) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( ~ v1_xboole_0(U_32)
| U_33 = U_32
| ~ v1_xboole_0(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] : k2_tarski(A,B) = k2_tarski(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_21_2,plain,
! [U_35,U_34] : k2_tarski(U_35,U_34) = k2_tarski(U_34,U_35),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
k2_tarski(U_35,U_34) = k2_tarski(U_34,U_35),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_22_2,plain,
? [U_36] : l1_group_1(U_36),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
l1_group_1(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_36,sK11)],[f_22_2]) ).
cnf(f_22_4,plain,
l1_group_1(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] : l1_rlvect_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_rlvect_1]) ).
fof(f_23_2,plain,
? [U_37] : l1_rlvect_1(U_37),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
l1_rlvect_1(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_37,sK12)],[f_23_2]) ).
cnf(f_23_4,plain,
l1_rlvect_1(sK12),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_24_2,plain,
? [U_38] : l1_struct_0(U_38),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
l1_struct_0(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_38,sK13)],[f_24_2]) ).
cnf(f_24_4,plain,
l1_struct_0(sK13),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] : l2_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l2_struct_0]) ).
fof(f_25_2,plain,
? [U_39] : l2_struct_0(U_39),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
l2_struct_0(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_39,sK14)],[f_25_2]) ).
cnf(f_25_4,plain,
l2_struct_0(sK14),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : l2_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l2_vectsp_1]) ).
fof(f_26_2,plain,
? [U_40] : l2_vectsp_1(U_40),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
l2_vectsp_1(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_40,sK15)],[f_26_2]) ).
cnf(f_26_4,plain,
l2_vectsp_1(sK15),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_27_2,plain,
$true,
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_28_2,plain,
$true,
inference(clausify,[status(thm)],[f_28_1]) ).
fof(f_29_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_29_2,plain,
! [U_41] :
( l1_struct_0(U_41)
| ~ l1_group_1(U_41) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( l1_struct_0(U_41)
| ~ l1_group_1(U_41) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A] :
( l2_struct_0(A)
| ~ l1_rlvect_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1]) ).
fof(f_30_2,plain,
! [U_42] :
( l2_struct_0(U_42)
| ~ l1_rlvect_1(U_42) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( l2_struct_0(U_42)
| ~ l1_rlvect_1(U_42) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_31_2,plain,
$true,
inference(clausify,[status(thm)],[f_31_1]) ).
fof(f_32_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_struct_0]) ).
fof(f_32_2,plain,
! [U_43] :
( l1_struct_0(U_43)
| ~ l2_struct_0(U_43) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( l1_struct_0(U_43)
| ~ l2_struct_0(U_43) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A] :
( ( l2_struct_0(A)
& l1_vectsp_1(A) )
| ~ l2_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_vectsp_1]) ).
fof(f_33_2,plain,
! [U_44] :
( ( l2_struct_0(U_44)
& l1_vectsp_1(U_44) )
| ~ l2_vectsp_1(U_44) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( l1_vectsp_1(U_44)
| ~ l2_vectsp_1(U_44) ),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( l2_struct_0(U_44)
| ~ l2_vectsp_1(U_44) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_34_2,plain,
! [U_45] :
( ~ v1_xboole_0(u1_struct_0(U_45))
| ~ l1_struct_0(U_45)
| v3_struct_0(U_45) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_45))
| ~ l1_struct_0(U_45)
| v3_struct_0(U_45) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_35_2,plain,
! [U_46] : ~ v1_xboole_0(k1_zfmisc_1(U_46)),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_46)),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_36_2,plain,
! [U_48,U_47] : ~ v1_xboole_0(k2_tarski(U_48,U_47)),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
~ v1_xboole_0(k2_tarski(U_48,U_47)),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_37_2,plain,
? [U_49] :
( ~ v3_struct_0(U_49)
& l1_struct_0(U_49) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ~ v3_struct_0(sK16)
& l1_struct_0(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_49,sK16)],[f_37_2]) ).
cnf(f_37_4,plain,
l1_struct_0(sK16),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
~ v3_struct_0(sK16),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc4_struct_0]) ).
fof(f_38_2,plain,
? [U_50] :
( ~ v3_struct_0(U_50)
& l2_struct_0(U_50) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ~ v3_struct_0(sK17)
& l2_struct_0(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_50,sK17)],[f_38_2]) ).
cnf(f_38_4,plain,
l2_struct_0(sK17),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
~ v3_struct_0(sK17),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A] :
( ? [B] :
( ~ v3_struct_0(B)
& l1_vectsp_2(B,A) )
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc9_vectsp_2]) ).
fof(f_39_2,plain,
! [U_52] :
( ? [U_51] :
( ~ v3_struct_0(U_51)
& l1_vectsp_2(U_51,U_52) )
| ~ l1_struct_0(U_52) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_52] :
( ( ~ v3_struct_0(sK18(U_52))
& l1_vectsp_2(sK18(U_52),U_52) )
| ~ l1_struct_0(U_52) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_51,sK18(U_52))],[f_39_2]) ).
cnf(f_39_4,plain,
( l1_vectsp_2(sK18(U_52),U_52)
| ~ l1_struct_0(U_52) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ v3_struct_0(sK18(U_52))
| ~ l1_struct_0(U_52) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(B))
| ~ r1_tarski(A,B) )
& ( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_40_2,plain,
! [U_54,U_53] :
( ( m1_subset_1(U_54,k1_zfmisc_1(U_53))
| ~ r1_tarski(U_54,U_53) )
& ( r1_tarski(U_54,U_53)
| ~ m1_subset_1(U_54,k1_zfmisc_1(U_53)) ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_58,U_56] :
( m1_subset_1(U_58,k1_zfmisc_1(U_56))
| ~ r1_tarski(U_58,U_56) )
& ! [U_57,U_55] :
( r1_tarski(U_57,U_55)
| ~ m1_subset_1(U_57,k1_zfmisc_1(U_55)) ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( r1_tarski(U_57,U_55)
| ~ m1_subset_1(U_57,k1_zfmisc_1(U_55)) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
( m1_subset_1(U_58,k1_zfmisc_1(U_56))
| ~ r1_tarski(U_58,U_56) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B,C] :
( k8_rlvect_2(A,B,C) = k8_rlvect_2(A,C,B)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[commutativity_k8_rlvect_2]) ).
fof(f_41_2,plain,
! [U_61,U_60,U_59] :
( k8_rlvect_2(U_61,U_60,U_59) = k8_rlvect_2(U_61,U_59,U_60)
| ~ m1_subset_1(U_59,u1_struct_0(U_61))
| ~ m1_subset_1(U_60,u1_struct_0(U_61))
| ~ l1_struct_0(U_61)
| v3_struct_0(U_61) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( k8_rlvect_2(U_61,U_60,U_59) = k8_rlvect_2(U_61,U_59,U_60)
| ~ m1_subset_1(U_59,u1_struct_0(U_61))
| ~ m1_subset_1(U_60,u1_struct_0(U_61))
| ~ l1_struct_0(U_61)
| v3_struct_0(U_61) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A] :
( ? [B] : l1_vectsp_2(B,A)
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_l1_vectsp_2]) ).
fof(f_42_2,plain,
! [U_63] :
( ? [U_62] : l1_vectsp_2(U_62,U_63)
| ~ l1_struct_0(U_63) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_63] :
( l1_vectsp_2(sK19(U_63),U_63)
| ~ l1_struct_0(U_63) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_62,sK19(U_63))],[f_42_2]) ).
cnf(f_42_4,plain,
( l1_vectsp_2(sK19(U_63),U_63)
| ~ l1_struct_0(U_63) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
? [A] : l3_vectsp_1(A),
inference(fof_nnf,[status(thm)],[existence_l3_vectsp_1]) ).
fof(f_43_2,plain,
? [U_64] : l3_vectsp_1(U_64),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
l3_vectsp_1(sK20),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_64,sK20)],[f_43_2]) ).
cnf(f_43_4,plain,
l3_vectsp_1(sK20),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_44_2,plain,
! [U_66] :
? [U_65] : m1_subset_1(U_65,U_66),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_66] : m1_subset_1(sK21(U_66),U_66),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_65,sK21(U_66))],[f_44_2]) ).
cnf(f_44_4,plain,
m1_subset_1(sK21(U_66),U_66),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B,C] :
( k8_rlvect_2(A,B,C) = k2_tarski(B,C)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k8_rlvect_2]) ).
fof(f_45_2,plain,
! [U_69,U_68,U_67] :
( k8_rlvect_2(U_69,U_68,U_67) = k2_tarski(U_68,U_67)
| ~ m1_subset_1(U_67,u1_struct_0(U_69))
| ~ m1_subset_1(U_68,u1_struct_0(U_69))
| ~ l1_struct_0(U_69)
| v3_struct_0(U_69) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( k8_rlvect_2(U_69,U_68,U_67) = k2_tarski(U_68,U_67)
| ~ m1_subset_1(U_67,u1_struct_0(U_69))
| ~ m1_subset_1(U_68,u1_struct_0(U_69))
| ~ l1_struct_0(U_69)
| v3_struct_0(U_69) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A] :
( m1_subset_1(k1_rlvect_1(A),u1_struct_0(A))
| ~ l2_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_rlvect_1]) ).
fof(f_46_2,plain,
! [U_70] :
( m1_subset_1(k1_rlvect_1(U_70),u1_struct_0(U_70))
| ~ l2_struct_0(U_70) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( m1_subset_1(k1_rlvect_1(U_70),u1_struct_0(U_70))
| ~ l2_struct_0(U_70) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A] :
( m1_subset_1(k2_group_1(A),u1_struct_0(A))
| ~ l1_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_group_1]) ).
fof(f_47_2,plain,
! [U_71] :
( m1_subset_1(k2_group_1(U_71),u1_struct_0(U_71))
| ~ l1_group_1(U_71)
| v3_struct_0(U_71) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( m1_subset_1(k2_group_1(U_71),u1_struct_0(U_71))
| ~ l1_group_1(U_71)
| v3_struct_0(U_71) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [A,B,C] :
( ( m1_subset_1(k8_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A)))
& v1_finset_1(k8_rlvect_2(A,B,C)) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k8_rlvect_2]) ).
fof(f_48_2,plain,
! [U_74,U_73,U_72] :
( ( m1_subset_1(k8_rlvect_2(U_74,U_73,U_72),k1_zfmisc_1(u1_struct_0(U_74)))
& v1_finset_1(k8_rlvect_2(U_74,U_73,U_72)) )
| ~ m1_subset_1(U_72,u1_struct_0(U_74))
| ~ m1_subset_1(U_73,u1_struct_0(U_74))
| ~ l1_struct_0(U_74)
| v3_struct_0(U_74) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( v1_finset_1(k8_rlvect_2(U_74,U_73,U_72))
| ~ m1_subset_1(U_72,u1_struct_0(U_74))
| ~ m1_subset_1(U_73,u1_struct_0(U_74))
| ~ l1_struct_0(U_74)
| v3_struct_0(U_74) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( m1_subset_1(k8_rlvect_2(U_74,U_73,U_72),k1_zfmisc_1(u1_struct_0(U_74)))
| ~ m1_subset_1(U_72,u1_struct_0(U_74))
| ~ m1_subset_1(U_73,u1_struct_0(U_74))
| ~ l1_struct_0(U_74)
| v3_struct_0(U_74) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [A] :
( ! [B] :
( l1_rlvect_1(B)
| ~ l1_vectsp_2(B,A) )
| ~ l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_vectsp_2]) ).
fof(f_49_2,plain,
! [U_76] :
( ! [U_75] :
( l1_rlvect_1(U_75)
| ~ l1_vectsp_2(U_75,U_76) )
| ~ l1_struct_0(U_76) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( l1_rlvect_1(U_75)
| ~ l1_vectsp_2(U_75,U_76)
| ~ l1_struct_0(U_76) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [A] :
( ( l2_vectsp_1(A)
& l1_rlvect_1(A) )
| ~ l3_vectsp_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1]) ).
fof(f_50_2,plain,
! [U_77] :
( ( l2_vectsp_1(U_77)
& l1_rlvect_1(U_77) )
| ~ l3_vectsp_1(U_77) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( l1_rlvect_1(U_77)
| ~ l3_vectsp_1(U_77) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( l2_vectsp_1(U_77)
| ~ l3_vectsp_1(U_77) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_51_2,plain,
$true,
inference(clausify,[status(thm)],[f_51_1]) ).
fof(f_52_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_52_2,plain,
$true,
inference(clausify,[status(thm)],[f_52_1]) ).
fof(f_53_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( D != k1_rlvect_1(B)
& C != k1_rlvect_1(B) )
| k1_rlvect_1(A) = k2_group_1(A)
| ~ v1_rmod_5(k8_rlvect_2(B,C,D),A,B)
| ~ m1_subset_1(D,u1_struct_0(B)) )
| ~ m1_subset_1(C,u1_struct_0(B)) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t5_rmod_5]) ).
fof(f_53_2,plain,
! [U_81] :
( ! [U_80] :
( ! [U_79] :
( ! [U_78] :
( ( U_78 != k1_rlvect_1(U_80)
& U_79 != k1_rlvect_1(U_80) )
| k1_rlvect_1(U_81) = k2_group_1(U_81)
| ~ v1_rmod_5(k8_rlvect_2(U_80,U_79,U_78),U_81,U_80)
| ~ m1_subset_1(U_78,u1_struct_0(U_80)) )
| ~ m1_subset_1(U_79,u1_struct_0(U_80)) )
| ~ l1_vectsp_2(U_80,U_81)
| ~ v5_vectsp_2(U_80,U_81)
| ~ v6_rlvect_1(U_80)
| ~ v5_rlvect_1(U_80)
| ~ v4_rlvect_1(U_80)
| ~ v3_rlvect_1(U_80)
| v3_struct_0(U_80) )
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( U_79 != k1_rlvect_1(U_80)
| k1_rlvect_1(U_81) = k2_group_1(U_81)
| ~ v1_rmod_5(k8_rlvect_2(U_80,U_79,U_78),U_81,U_80)
| ~ m1_subset_1(U_78,u1_struct_0(U_80))
| ~ m1_subset_1(U_79,u1_struct_0(U_80))
| ~ l1_vectsp_2(U_80,U_81)
| ~ v5_vectsp_2(U_80,U_81)
| ~ v6_rlvect_1(U_80)
| ~ v5_rlvect_1(U_80)
| ~ v4_rlvect_1(U_80)
| ~ v3_rlvect_1(U_80)
| v3_struct_0(U_80)
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( U_78 != k1_rlvect_1(U_80)
| k1_rlvect_1(U_81) = k2_group_1(U_81)
| ~ v1_rmod_5(k8_rlvect_2(U_80,U_79,U_78),U_81,U_80)
| ~ m1_subset_1(U_78,u1_struct_0(U_80))
| ~ m1_subset_1(U_79,u1_struct_0(U_80))
| ~ l1_vectsp_2(U_80,U_81)
| ~ v5_vectsp_2(U_80,U_81)
| ~ v6_rlvect_1(U_80)
| ~ v5_rlvect_1(U_80)
| ~ v4_rlvect_1(U_80)
| ~ v3_rlvect_1(U_80)
| v3_struct_0(U_80)
| ~ l3_vectsp_1(U_81)
| ~ v8_vectsp_1(U_81)
| ~ v7_vectsp_1(U_81)
| ~ v6_vectsp_1(U_81)
| ~ v4_group_1(U_81)
| ~ v6_rlvect_1(U_81)
| ~ v5_rlvect_1(U_81)
| ~ v4_rlvect_1(U_81)
| ~ v3_rlvect_1(U_81)
| v3_struct_0(U_81) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_3_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_2]) ).
cnf(f_27_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_2]) ).
cnf(f_28_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_2]) ).
cnf(f_31_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_31_2]) ).
cnf(f_51_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_51_2]) ).
cnf(f_52_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_52_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k1_rlvect_1(Eq_x_0) = k1_rlvect_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k2_group_1(Eq_x_0) = k2_group_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( k8_rlvect_2(Eq_x_0,Eq_x_1,Eq_x_2) = k8_rlvect_2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( k2_tarski(Eq_x_0,Eq_x_1) = k2_tarski(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK21(Eq_x_0) = sK21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( v3_struct_0(Eq_y_0)
| ~ v3_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( v3_rlvect_1(Eq_y_0)
| ~ v3_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( v4_rlvect_1(Eq_y_0)
| ~ v4_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( v5_rlvect_1(Eq_y_0)
| ~ v5_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( v6_rlvect_1(Eq_y_0)
| ~ v6_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( v4_group_1(Eq_y_0)
| ~ v4_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( v6_vectsp_1(Eq_y_0)
| ~ v6_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( v7_vectsp_1(Eq_y_0)
| ~ v7_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( v8_vectsp_1(Eq_y_0)
| ~ v8_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( l3_vectsp_1(Eq_y_0)
| ~ l3_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( v5_vectsp_2(Eq_y_0,Eq_y_1)
| ~ v5_vectsp_2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( l1_vectsp_2(Eq_y_0,Eq_y_1)
| ~ l1_vectsp_2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( m1_subset_1(Eq_y_0,Eq_y_1)
| ~ m1_subset_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( v1_rmod_5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_rmod_5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( r2_hidden(Eq_y_0,Eq_y_1)
| ~ r2_hidden(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( l1_vectsp_1(Eq_y_0)
| ~ l1_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( l1_group_1(Eq_y_0)
| ~ l1_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( l1_struct_0(Eq_y_0)
| ~ l1_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( v1_finset_1(Eq_y_0)
| ~ v1_finset_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( l1_rlvect_1(Eq_y_0)
| ~ l1_rlvect_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( l2_struct_0(Eq_y_0)
| ~ l2_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( l2_vectsp_1(Eq_y_0)
| ~ l2_vectsp_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.69 % Computer : n002.cluster.edu
% 0.19/0.69 % Model : x86_64 x86_64
% 0.19/0.69 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.69 % Memory : 8046.5625MB
% 0.19/0.69 % OS : Linux 6.8.0-71-generic
% 0.19/0.69 % CPULimit : 300
% 0.19/0.69 % WCLimit : 300
% 0.19/0.69 % DateTime : Sun Sep 20 09:52:50 UTC 2026
% 0.22/0.70 % CPUTime :
% 195.78/196.39 % SZS status Theorem for theBenchmark
% 195.78/196.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------