%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP632+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 07:30:34 AM UTC 2026
% Result : Theorem 3.06s 0.83s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 105 ( 30 unt; 0 def)
% Number of atoms : 311 ( 68 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 340 ( 134 ~; 144 |; 46 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-6 aty)
% Number of variables : 123 ( 2 sgn 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_funct_2,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ( ( v1_partfun1(C,A,B)
& v1_funct_1(C) )
=> ( v1_funct_2(C,A,B)
& v1_funct_1(C) ) ) ),
file('theBenchmark.p',cc1_funct_2) ).
fof(dt_k4_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k4_autgroup) ).
fof(dt_k6_partfun1,axiom,
! [A] :
( m2_relset_1(k6_partfun1(A),A,A)
& v1_partfun1(k6_partfun1(A),A,A) ),
file('theBenchmark.p',dt_k6_partfun1) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_m2_fraenkel,axiom,
! [A,B,C] :
( ( m1_fraenkel(C,A,B)
& ~ v1_xboole_0(B) )
=> ! [D] :
( m2_fraenkel(D,A,B,C)
=> ( m2_relset_1(D,A,B)
& v1_funct_2(D,A,B)
& v1_funct_1(D) ) ) ),
file('theBenchmark.p',dt_m2_fraenkel) ).
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(fc2_funct_1,axiom,
! [A] :
( v1_funct_1(k6_relat_1(A))
& v1_relat_1(k6_relat_1(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(redefinition_k6_partfun1,axiom,
! [A] : k6_partfun1(A) = k6_relat_1(A),
file('theBenchmark.p',redefinition_k6_partfun1) ).
fof(redefinition_k7_funct_2,axiom,
! [A,B,C,D,E] :
( ( m1_relset_1(E,B,C)
& v1_funct_2(E,B,C)
& v1_funct_1(E)
& m1_relset_1(D,A,B)
& v1_funct_2(D,A,B)
& v1_funct_1(D)
& ~ v1_xboole_0(B) )
=> k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ),
file('theBenchmark.p',redefinition_k7_funct_2) ).
fof(redefinition_k7_relset_1,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(F,C,D)
& m1_relset_1(E,A,B) )
=> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ),
file('theBenchmark.p',redefinition_k7_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(t23_funct_2,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> ( k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C
& k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C ) ),
file('theBenchmark.p',t23_funct_2) ).
fof(t24_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> k6_autgroup(A,k2_group_1(A)) = k6_partfun1(u1_struct_0(A)) ),
file('theBenchmark.p',t24_autgroup) ).
fof(t30_autgroup,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,k6_autgroup(A,k2_group_1(A))) = B
& k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),B) = B ) ) ),
file('theBenchmark.p',t30_autgroup) ).
fof(t30_autgroup_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,k6_autgroup(A,k2_group_1(A))) = B
& k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),B) = B ) ) ),
inference(assume_negation,[status(cth)],[t30_autgroup]) ).
cnf(c_84,plain,
( m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k4_autgroup]) ).
cnf(c_90,plain,
( k6_partfun1(u1_struct_0(A)) = k6_autgroup(A,k2_group_1(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t24_autgroup]) ).
fof(nnf_81,plain,
? [A] :
( ? [B] :
( ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,k6_autgroup(A,k2_group_1(A))) != B
| k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),B) != B )
& m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t30_autgroup_neg]) ).
fof(sk_t30_autgroup_neg,plain,
( ( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0))) != sK1
| k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),sK1) != sK1 )
& m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_81]) ).
cnf(c_91,negated_conjecture,
v1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t30_autgroup_neg]) ).
cnf(c_94,negated_conjecture,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(split_conjunct,[status(thm)],[sk_t30_autgroup_neg]) ).
cnf(c_101,plain,
( m2_relset_1(D,C,A)
| ~ m2_fraenkel(D,C,A,B)
| ~ m1_fraenkel(B,C,A)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[dt_m2_fraenkel]) ).
cnf(c_102,plain,
( v1_funct_2(D,C,A)
| ~ m2_fraenkel(D,C,A,B)
| ~ m1_fraenkel(B,C,A)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[dt_m2_fraenkel]) ).
cnf(c_103,plain,
( v1_funct_1(D)
| ~ m2_fraenkel(D,C,A,B)
| ~ m1_fraenkel(B,C,A)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[dt_m2_fraenkel]) ).
cnf(c_129,plain,
m2_relset_1(k6_partfun1(A),A,A),
inference(clausify,[status(thm)],[dt_k6_partfun1]) ).
cnf(c_132,negated_conjecture,
( m2_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_101,c_94]) ).
cnf(c_140,plain,
( m1_relset_1(A,B,C)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_142,plain,
( k7_relset_1(B,B,B,C,k6_partfun1(B),A) = A
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[t23_funct_2]) ).
cnf(c_143,plain,
( k7_relset_1(B,C,C,C,A,k6_partfun1(C)) = A
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[t23_funct_2]) ).
cnf(c_147,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc1_struct_0]) ).
cnf(c_149,plain,
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(clausify,[status(thm)],[dt_l1_group_1]) ).
cnf(c_156,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| v3_struct_0(A)
| ~ l1_group_1(A) ),
inference(resolve,[status(thm)],[c_149,c_147]) ).
cnf(c_183,negated_conjecture,
( v1_funct_1(sK1)
| ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_103,c_94]) ).
cnf(c_193,negated_conjecture,
( v1_funct_2(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_102,c_94]) ).
cnf(c_208,plain,
( v1_funct_2(A,B,C)
| ~ v1_partfun1(A,B,C)
| ~ v1_funct_1(A)
| ~ m1_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[cc1_funct_2]) ).
cnf(c_216,plain,
v1_partfun1(k6_partfun1(A),A,A),
inference(clausify,[status(thm)],[dt_k6_partfun1]) ).
cnf(c_230,plain,
v1_funct_1(k6_relat_1(A)),
inference(clausify,[status(thm)],[fc2_funct_1]) ).
cnf(c_270,plain,
k6_relat_1(A) = k6_partfun1(A),
inference(clausify,[status(thm)],[redefinition_k6_partfun1]) ).
cnf(c_271,plain,
( k5_relat_1(B,D) = k7_funct_2(C,A,E,B,D)
| ~ m1_relset_1(D,A,E)
| ~ v1_funct_2(D,A,E)
| ~ v1_funct_1(D)
| ~ m1_relset_1(B,C,A)
| ~ v1_funct_2(B,C,A)
| ~ v1_funct_1(B)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[redefinition_k7_funct_2]) ).
cnf(c_272,plain,
( k7_funct_2(C,A,E,B,D) = k5_relat_1(B,D)
| ~ m1_relset_1(D,A,E)
| ~ v1_funct_2(D,A,E)
| ~ v1_funct_1(D)
| ~ m1_relset_1(B,C,A)
| ~ v1_funct_2(B,C,A)
| ~ v1_funct_1(B)
| v1_xboole_0(A) ),
inference(copy,[status(thm)],[c_271]) ).
cnf(c_273,plain,
( k7_relset_1(B,C,E,F,A,D) = k5_relat_1(A,D)
| ~ m1_relset_1(D,E,F)
| ~ m1_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_k7_relset_1]) ).
cnf(c_281,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t30_autgroup_neg]) ).
cnf(c_282,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t30_autgroup_neg]) ).
cnf(c_283,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t30_autgroup_neg]) ).
cnf(c_284,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t30_autgroup_neg]) ).
cnf(c_285,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0))) != sK1
| k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),sK1) != sK1 ),
inference(split_conjunct,[status(thm)],[sk_t30_autgroup_neg]) ).
cnf(c_310,negated_conjecture,
( k6_partfun1(u1_struct_0(sK0)) = k6_autgroup(sK0,k2_group_1(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_91,c_90]) ).
cnf(c_3207,negated_conjecture,
( k6_autgroup(sK0,k2_group_1(sK0)) = k6_partfun1(u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(copy,[status(thm)],[c_310]) ).
cnf(c_3208,negated_conjecture,
( k6_autgroup(sK0,k2_group_1(sK0)) = k6_partfun1(u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_281,c_3207]) ).
cnf(c_3209,negated_conjecture,
( k6_autgroup(sK0,k2_group_1(sK0)) = k6_partfun1(u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_282,c_3208]) ).
cnf(c_3210,negated_conjecture,
( k6_autgroup(sK0,k2_group_1(sK0)) = k6_partfun1(u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_283,c_3209]) ).
cnf(c_311,negated_conjecture,
k6_autgroup(sK0,k2_group_1(sK0)) = k6_partfun1(u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_284,c_3210]) ).
cnf(c_312,negated_conjecture,
( m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_91,c_84]) ).
cnf(c_3211,negated_conjecture,
( m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_281,c_312]) ).
cnf(c_3212,negated_conjecture,
( m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_282,c_3211]) ).
cnf(c_3213,negated_conjecture,
( m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_283,c_3212]) ).
cnf(c_313,negated_conjecture,
m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_284,c_3213]) ).
cnf(c_344,plain,
m1_relset_1(k6_partfun1(A),A,A),
inference(resolve,[status(thm)],[c_140,c_129]) ).
cnf(c_349,negated_conjecture,
( ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_140,c_132]) ).
cnf(c_350,negated_conjecture,
( v1_xboole_0(u1_struct_0(sK0))
| m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_313,c_349]) ).
cnf(c_371,negated_conjecture,
( ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(u1_struct_0(sK0)),sK1) = sK1 ),
inference(resolve,[status(thm)],[c_142,c_132]) ).
cnf(c_372,negated_conjecture,
( v1_xboole_0(u1_struct_0(sK0))
| k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(u1_struct_0(sK0)),sK1) = sK1 ),
inference(resolve,[status(thm)],[c_313,c_371]) ).
cnf(c_391,negated_conjecture,
( ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) = sK1 ),
inference(resolve,[status(thm)],[c_143,c_132]) ).
cnf(c_392,negated_conjecture,
( v1_xboole_0(u1_struct_0(sK0))
| k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) = sK1 ),
inference(resolve,[status(thm)],[c_313,c_391]) ).
cnf(c_429,plain,
v1_funct_1(k6_partfun1(A)),
inference(paramod,[status(thm)],[c_270,c_230]) ).
cnf(c_3214,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_autgroup(sK0,k2_group_1(sK0))) != sK1
| k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(u1_struct_0(sK0)),sK1) != sK1 ),
inference(paramod,[status(thm)],[c_311,c_285]) ).
cnf(c_437,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) != sK1
| k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(u1_struct_0(sK0)),sK1) != sK1 ),
inference(paramod,[status(thm)],[c_311,c_3214]) ).
cnf(c_439,negated_conjecture,
( v1_funct_2(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_313,c_193]) ).
cnf(c_440,negated_conjecture,
( v1_funct_1(sK1)
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_313,c_183]) ).
cnf(c_3215,plain,
( v1_funct_2(k6_partfun1(A),A,A)
| ~ v1_funct_1(k6_partfun1(A))
| ~ m1_relset_1(k6_partfun1(A),A,A) ),
inference(resolve,[status(thm)],[c_216,c_208]) ).
cnf(c_3216,plain,
( v1_funct_2(k6_partfun1(A),A,A)
| ~ v1_funct_1(k6_partfun1(A)) ),
inference(resolve,[status(thm)],[c_344,c_3215]) ).
cnf(c_458,plain,
v1_funct_2(k6_partfun1(A),A,A),
inference(resolve,[status(thm)],[c_429,c_3216]) ).
cnf(c_3217,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_284,c_156]) ).
cnf(c_762,negated_conjecture,
~ v1_xboole_0(u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_281,c_3217]) ).
cnf(c_765,negated_conjecture,
v1_funct_1(sK1),
inference(resolve,[status(thm)],[c_762,c_440]) ).
cnf(c_766,negated_conjecture,
v1_funct_2(sK1,u1_struct_0(sK0),u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_762,c_439]) ).
cnf(c_772,negated_conjecture,
k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) = sK1,
inference(resolve,[status(thm)],[c_762,c_392]) ).
cnf(c_774,negated_conjecture,
k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(u1_struct_0(sK0)),sK1) = sK1,
inference(resolve,[status(thm)],[c_762,c_372]) ).
cnf(c_776,negated_conjecture,
m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_762,c_350]) ).
cnf(c_3218,plain,
( k7_relset_1(D,D,B,C,k6_partfun1(D),A) = k5_relat_1(k6_partfun1(D),A)
| ~ m1_relset_1(A,B,C) ),
inference(resolve,[status(thm)],[c_273,c_344]) ).
cnf(c_3122,negated_conjecture,
k7_relset_1(A,A,u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(A),sK1) = k5_relat_1(k6_partfun1(A),sK1),
inference(resolve,[status(thm)],[c_3218,c_776]) ).
cnf(c_3219,negated_conjecture,
( k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),B,C,sK1,A) = k5_relat_1(sK1,A)
| ~ m1_relset_1(A,B,C) ),
inference(resolve,[status(thm)],[c_273,c_776]) ).
cnf(c_3129,negated_conjecture,
k7_relset_1(u1_struct_0(sK0),u1_struct_0(sK0),A,A,sK1,k6_partfun1(A)) = k5_relat_1(sK1,k6_partfun1(A)),
inference(resolve,[status(thm)],[c_3219,c_344]) ).
cnf(c_3220,plain,
( k7_funct_2(C,A,E,k6_partfun1(B),D) = k5_relat_1(k6_partfun1(B),D)
| ~ m1_relset_1(D,A,E)
| ~ v1_funct_2(D,A,E)
| ~ v1_funct_1(D)
| ~ m1_relset_1(k6_partfun1(B),C,A)
| ~ v1_funct_2(k6_partfun1(B),C,A)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_272,c_429]) ).
cnf(c_3221,plain,
( k7_funct_2(A,A,C,k6_partfun1(A),B) = k5_relat_1(k6_partfun1(A),B)
| ~ m1_relset_1(B,A,C)
| ~ v1_funct_2(B,A,C)
| ~ v1_funct_1(B)
| ~ m1_relset_1(k6_partfun1(A),A,A)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_3220,c_458]) ).
cnf(c_3222,plain,
( k7_funct_2(A,A,C,k6_partfun1(A),B) = k5_relat_1(k6_partfun1(A),B)
| ~ m1_relset_1(B,A,C)
| ~ v1_funct_2(B,A,C)
| ~ v1_funct_1(B)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_3221,c_344]) ).
cnf(c_3223,negated_conjecture,
( k7_funct_2(A,A,B,k6_partfun1(A),sK1) = k5_relat_1(k6_partfun1(A),sK1)
| ~ m1_relset_1(sK1,A,B)
| ~ v1_funct_2(sK1,A,B)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_3222,c_765]) ).
cnf(c_3224,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(u1_struct_0(sK0)),sK1) = k5_relat_1(k6_partfun1(u1_struct_0(sK0)),sK1)
| ~ m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_3223,c_766]) ).
cnf(c_3225,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(u1_struct_0(sK0)),sK1) = k5_relat_1(k6_partfun1(u1_struct_0(sK0)),sK1)
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_3224,c_776]) ).
cnf(c_3136,negated_conjecture,
k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_partfun1(u1_struct_0(sK0)),sK1) = k5_relat_1(k6_partfun1(u1_struct_0(sK0)),sK1),
inference(resolve,[status(thm)],[c_762,c_3225]) ).
cnf(c_3226,negated_conjecture,
( k7_funct_2(B,A,D,sK1,C) = k5_relat_1(sK1,C)
| ~ m1_relset_1(C,A,D)
| ~ v1_funct_2(C,A,D)
| ~ v1_funct_1(C)
| ~ m1_relset_1(sK1,B,A)
| ~ v1_funct_2(sK1,B,A)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_272,c_765]) ).
cnf(c_3227,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),B,sK1,A) = k5_relat_1(sK1,A)
| ~ m1_relset_1(A,u1_struct_0(sK0),B)
| ~ v1_funct_2(A,u1_struct_0(sK0),B)
| ~ v1_funct_1(A)
| ~ m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_3226,c_766]) ).
cnf(c_3228,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),B,sK1,A) = k5_relat_1(sK1,A)
| ~ m1_relset_1(A,u1_struct_0(sK0),B)
| ~ v1_funct_2(A,u1_struct_0(sK0),B)
| ~ v1_funct_1(A)
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_3227,c_776]) ).
cnf(c_3229,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),B,sK1,k6_partfun1(A)) = k5_relat_1(sK1,k6_partfun1(A))
| ~ m1_relset_1(k6_partfun1(A),u1_struct_0(sK0),B)
| ~ v1_funct_2(k6_partfun1(A),u1_struct_0(sK0),B)
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_3228,c_429]) ).
cnf(c_3230,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) = k5_relat_1(sK1,k6_partfun1(u1_struct_0(sK0)))
| ~ m1_relset_1(k6_partfun1(u1_struct_0(sK0)),u1_struct_0(sK0),u1_struct_0(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_3229,c_458]) ).
cnf(c_3231,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) = k5_relat_1(sK1,k6_partfun1(u1_struct_0(sK0)))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_3230,c_344]) ).
cnf(c_3139,negated_conjecture,
k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) = k5_relat_1(sK1,k6_partfun1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_762,c_3231]) ).
cnf(c_3152,negated_conjecture,
k5_relat_1(k6_partfun1(u1_struct_0(sK0)),sK1) = sK1,
inference(paramod,[status(thm)],[c_3122,c_774]) ).
cnf(c_3181,negated_conjecture,
k5_relat_1(sK1,k6_partfun1(u1_struct_0(sK0))) = sK1,
inference(paramod,[status(thm)],[c_3129,c_772]) ).
cnf(c_3232,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) != sK1
| k5_relat_1(k6_partfun1(u1_struct_0(sK0)),sK1) != sK1 ),
inference(paramod,[status(thm)],[c_3136,c_437]) ).
cnf(c_3233,negated_conjecture,
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK1,k6_partfun1(u1_struct_0(sK0))) != sK1
| sK1 != sK1 ),
inference(paramod,[status(thm)],[c_3152,c_3232]) ).
cnf(c_3234,negated_conjecture,
( k5_relat_1(sK1,k6_partfun1(u1_struct_0(sK0))) != sK1
| sK1 != sK1 ),
inference(paramod,[status(thm)],[c_3139,c_3233]) ).
cnf(c_3235,negated_conjecture,
( sK1 != sK1
| sK1 != sK1 ),
inference(paramod,[status(thm)],[c_3181,c_3234]) ).
cnf(c_3236,negated_conjecture,
sK1 != sK1,
inference(copy,[status(thm)],[c_3235]) ).
cnf(c_3206,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_3236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP632+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 15:13:20 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2276441 was started by sandbox on n018,
% 0.11/0.37 % Fri Sep 25 15:13:20 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 3.06/0.83
% 3.06/0.83 % SZS status Theorem for theBenchmark
% 3.06/0.83
% 3.06/0.83 % Proof 1 at 0.34 (+ 0.09) seconds.
% 3.06/0.83 % Length of proof is 72.
% 3.06/0.83 % Level of proof is 8.
% 3.06/0.83 % Maximum clause weight is 48.000.
% 3.06/0.83 % Given clauses 288.
% 3.06/0.83
% 3.06/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------