%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP643+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 07:30:38 AM UTC 2026
% Result : Theorem 0.14s 10.48s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 54 ( 17 unt; 0 def)
% Number of atoms : 243 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 317 ( 128 ~; 128 |; 41 &)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k1_group_1,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k1_group_1) ).
fof(t18_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_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) ) ) ) ),
file('theBenchmark.p',t18_latsubgr) ).
fof(t59_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_group_2(D,A)
=> ( ( r1_rlvect_1(D,C)
& r1_rlvect_1(D,B) )
=> r1_rlvect_1(D,k1_group_1(A,B,C)) ) ) ) ) ),
file('theBenchmark.p',t59_group_2) ).
fof(t21_latsubgr,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(D,k1_funct_1(k1_latsubgr(A),B))
& r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) )
=> r2_hidden(k1_group_1(A,C,D),k1_funct_1(k1_latsubgr(A),B)) ) ) ) ) ),
file('theBenchmark.p',t21_latsubgr) ).
fof(t21_latsubgr_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(D,k1_funct_1(k1_latsubgr(A),B))
& r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) )
=> r2_hidden(k1_group_1(A,C,D),k1_funct_1(k1_latsubgr(A),B)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t21_latsubgr]) ).
fof(nnf_54,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ r2_hidden(k1_group_1(A,C,D),k1_funct_1(k1_latsubgr(A),B))
& r2_hidden(D,k1_funct_1(k1_latsubgr(A),B))
& r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
& m1_subset_1(D,u1_struct_0(A)) )
& m1_subset_1(C,u1_struct_0(A)) )
& m1_group_2(B,A)
& v1_group_1(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t21_latsubgr_neg]) ).
fof(sk_t21_latsubgr_neg,plain,
( ~ r2_hidden(k1_group_1(sK0,sK2,sK3),k1_funct_1(k1_latsubgr(sK0),sK1))
& r2_hidden(sK3,k1_funct_1(k1_latsubgr(sK0),sK1))
& r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1))
& m1_subset_1(sK3,u1_struct_0(sK0))
& m1_subset_1(sK2,u1_struct_0(sK0))
& m1_group_2(sK1,sK0)
& v1_group_1(sK1)
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_54]) ).
cnf(c_55,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_56,plain,
( r1_rlvect_1(D,k1_group_1(A,B,C))
| ~ r1_rlvect_1(D,C)
| ~ r1_rlvect_1(D,B)
| ~ m1_group_2(D,A)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t59_group_2]) ).
cnf(c_57,plain,
( ~ r1_rlvect_1(B,C)
| r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_group_2(B,A)
| ~ v1_group_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t18_latsubgr]) ).
cnf(c_58,plain,
( r1_rlvect_1(B,C)
| ~ r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_group_2(B,A)
| ~ v1_group_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t18_latsubgr]) ).
cnf(c_63,negated_conjecture,
v1_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_64,negated_conjecture,
( ~ r1_rlvect_1(A,B)
| r2_hidden(B,k1_funct_1(k1_latsubgr(sK0),A))
| ~ m1_subset_1(B,u1_struct_0(sK0))
| ~ m1_group_2(A,sK0)
| ~ v1_group_1(A)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_57]) ).
cnf(c_65,negated_conjecture,
( r1_rlvect_1(A,B)
| ~ r2_hidden(B,k1_funct_1(k1_latsubgr(sK0),A))
| ~ m1_subset_1(B,u1_struct_0(sK0))
| ~ m1_group_2(A,sK0)
| ~ v1_group_1(A)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_58]) ).
cnf(c_153,negated_conjecture,
( r1_rlvect_1(C,k1_group_1(sK0,A,B))
| ~ r1_rlvect_1(C,B)
| ~ r1_rlvect_1(C,A)
| ~ m1_group_2(C,sK0)
| ~ m1_subset_1(B,u1_struct_0(sK0))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_56]) ).
cnf(c_154,negated_conjecture,
~ r2_hidden(k1_group_1(sK0,sK2,sK3),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_155,negated_conjecture,
r2_hidden(sK3,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_156,negated_conjecture,
r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_157,negated_conjecture,
m1_subset_1(sK3,u1_struct_0(sK0)),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_158,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_159,negated_conjecture,
m1_group_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_160,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_161,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_162,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t21_latsubgr_neg]) ).
cnf(c_191,plain,
( m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k1_group_1]) ).
cnf(c_193,negated_conjecture,
( ~ r1_rlvect_1(sK1,A)
| r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_group_2(sK1,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_63,c_64]) ).
cnf(c_369,negated_conjecture,
( ~ r1_rlvect_1(sK1,A)
| r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_group_2(sK1,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_162,c_193]) ).
cnf(c_370,negated_conjecture,
( ~ r1_rlvect_1(sK1,A)
| r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_group_2(sK1,sK0)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_161,c_369]) ).
cnf(c_371,negated_conjecture,
( ~ r1_rlvect_1(sK1,A)
| r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_group_2(sK1,sK0) ),
inference(resolve,[status(thm)],[c_160,c_370]) ).
cnf(c_194,negated_conjecture,
( ~ r1_rlvect_1(sK1,A)
| r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_159,c_371]) ).
cnf(c_195,negated_conjecture,
( r1_rlvect_1(sK1,A)
| ~ r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_group_2(sK1,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_63,c_65]) ).
cnf(c_372,negated_conjecture,
( r1_rlvect_1(sK1,A)
| ~ r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_group_2(sK1,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_162,c_195]) ).
cnf(c_373,negated_conjecture,
( r1_rlvect_1(sK1,A)
| ~ r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_group_2(sK1,sK0)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_161,c_372]) ).
cnf(c_374,negated_conjecture,
( r1_rlvect_1(sK1,A)
| ~ r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_group_2(sK1,sK0) ),
inference(resolve,[status(thm)],[c_160,c_373]) ).
cnf(c_196,negated_conjecture,
( r1_rlvect_1(sK1,A)
| ~ r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_159,c_374]) ).
cnf(c_375,negated_conjecture,
( r1_rlvect_1(C,k1_group_1(sK0,A,B))
| ~ r1_rlvect_1(C,B)
| ~ r1_rlvect_1(C,A)
| ~ m1_group_2(C,sK0)
| ~ m1_subset_1(B,u1_struct_0(sK0))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_162,c_153]) ).
cnf(c_376,negated_conjecture,
( r1_rlvect_1(C,k1_group_1(sK0,A,B))
| ~ r1_rlvect_1(C,B)
| ~ r1_rlvect_1(C,A)
| ~ m1_group_2(C,sK0)
| ~ m1_subset_1(B,u1_struct_0(sK0))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_161,c_375]) ).
cnf(c_217,negated_conjecture,
( r1_rlvect_1(C,k1_group_1(sK0,A,B))
| ~ r1_rlvect_1(C,B)
| ~ r1_rlvect_1(C,A)
| ~ m1_group_2(C,sK0)
| ~ m1_subset_1(B,u1_struct_0(sK0))
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_160,c_376]) ).
cnf(c_377,negated_conjecture,
( m1_subset_1(k1_group_1(sK0,A,B),u1_struct_0(sK0))
| ~ m1_subset_1(B,u1_struct_0(sK0))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_191,c_160]) ).
cnf(c_378,negated_conjecture,
( m1_subset_1(k1_group_1(sK0,sK2,A),u1_struct_0(sK0))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_377,c_158]) ).
cnf(c_379,negated_conjecture,
( m1_subset_1(k1_group_1(sK0,sK2,sK3),u1_struct_0(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_378,c_157]) ).
cnf(c_288,negated_conjecture,
m1_subset_1(k1_group_1(sK0,sK2,sK3),u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_162,c_379]) ).
cnf(c_380,negated_conjecture,
( r1_rlvect_1(sK1,sK2)
| ~ m1_subset_1(sK2,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_196,c_156]) ).
cnf(c_294,negated_conjecture,
r1_rlvect_1(sK1,sK2),
inference(resolve,[status(thm)],[c_158,c_380]) ).
cnf(c_381,negated_conjecture,
( r1_rlvect_1(sK1,sK3)
| ~ m1_subset_1(sK3,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_196,c_155]) ).
cnf(c_295,negated_conjecture,
r1_rlvect_1(sK1,sK3),
inference(resolve,[status(thm)],[c_157,c_381]) ).
cnf(c_382,negated_conjecture,
( r1_rlvect_1(B,k1_group_1(sK0,sK2,A))
| ~ r1_rlvect_1(B,A)
| ~ r1_rlvect_1(B,sK2)
| ~ m1_group_2(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_217,c_158]) ).
cnf(c_383,negated_conjecture,
( r1_rlvect_1(A,k1_group_1(sK0,sK2,sK3))
| ~ r1_rlvect_1(A,sK3)
| ~ r1_rlvect_1(A,sK2)
| ~ m1_group_2(A,sK0) ),
inference(resolve,[status(thm)],[c_382,c_157]) ).
cnf(c_384,negated_conjecture,
( r1_rlvect_1(sK1,k1_group_1(sK0,sK2,sK3))
| ~ r1_rlvect_1(sK1,sK3)
| ~ r1_rlvect_1(sK1,sK2) ),
inference(resolve,[status(thm)],[c_383,c_159]) ).
cnf(c_385,negated_conjecture,
( r1_rlvect_1(sK1,k1_group_1(sK0,sK2,sK3))
| ~ r1_rlvect_1(sK1,sK3) ),
inference(resolve,[status(thm)],[c_384,c_294]) ).
cnf(c_319,negated_conjecture,
r1_rlvect_1(sK1,k1_group_1(sK0,sK2,sK3)),
inference(resolve,[status(thm)],[c_385,c_295]) ).
cnf(c_386,negated_conjecture,
( r2_hidden(k1_group_1(sK0,sK2,sK3),k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(k1_group_1(sK0,sK2,sK3),u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_194]) ).
cnf(c_387,negated_conjecture,
r2_hidden(k1_group_1(sK0,sK2,sK3),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(resolve,[status(thm)],[c_288,c_386]) ).
cnf(c_368,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_154,c_387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP643+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.39 % Computer : n011.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Fri Sep 25 15:20:09 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 2350323 was started by sandbox2 on n011,
% 0.11/10.39 % Fri Sep 25 15:20:09 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/10.41
% 0.14/10.41 % From the command line: assign(max_seconds, 300).
% 0.14/10.48
% 0.14/10.48 % SZS status Theorem for theBenchmark
% 0.14/10.48
% 0.14/10.48 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/10.48 % Length of proof is 32.
% 0.14/10.48 % Level of proof is 7.
% 0.14/10.48 % Maximum clause weight is 39.000.
% 0.14/10.48 % Given clauses 141.
% 0.14/10.48
% 0.14/10.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------