%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP644+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 : n005.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 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 14 unt; 0 def)
% Number of atoms : 216 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 284 ( 117 ~; 115 |; 35 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k3_group_1,axiom,
! [A,B] :
( ( m1_subset_1(B,u1_struct_0(A))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k3_group_1(A,B),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k3_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(t60_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_group_2(C,A)
=> ( r1_rlvect_1(C,B)
=> r1_rlvect_1(C,k3_group_1(A,B)) ) ) ) ),
file('theBenchmark.p',t60_group_2) ).
fof(t22_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))
=> ( 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('theBenchmark.p',t22_latsubgr) ).
fof(t22_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))
=> ( r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
=> r2_hidden(k3_group_1(A,C),k1_funct_1(k1_latsubgr(A),B)) ) ) ) ),
inference(assume_negation,[status(cth)],[t22_latsubgr]) ).
fof(nnf_54,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ 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)) )
& 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)],[t22_latsubgr_neg]) ).
fof(sk_t22_latsubgr_neg,plain,
( ~ r2_hidden(k3_group_1(sK0,sK2),k1_funct_1(k1_latsubgr(sK0),sK1))
& r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1))
& 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]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_54]) ).
cnf(c_55,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
cnf(c_56,plain,
( 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))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t60_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_60,plain,
( m1_subset_1(k3_group_1(A,B),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)],[dt_k3_group_1]) ).
cnf(c_64,negated_conjecture,
v1_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
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_57]) ).
cnf(c_66,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,
( m1_subset_1(k3_group_1(sK0,A),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_60]) ).
cnf(c_155,negated_conjecture,
( r1_rlvect_1(B,k3_group_1(sK0,A))
| ~ r1_rlvect_1(B,A)
| ~ m1_group_2(B,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_156,negated_conjecture,
~ r2_hidden(k3_group_1(sK0,sK2),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
cnf(c_157,negated_conjecture,
r2_hidden(sK2,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
cnf(c_158,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
cnf(c_159,negated_conjecture,
m1_group_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
cnf(c_160,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
cnf(c_161,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
cnf(c_162,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_latsubgr_neg]) ).
cnf(c_192,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_64,c_65]) ).
cnf(c_318,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_192]) ).
cnf(c_319,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_318]) ).
cnf(c_320,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_319]) ).
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)) ),
inference(resolve,[status(thm)],[c_159,c_320]) ).
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))
| ~ m1_group_2(sK1,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_64,c_66]) ).
cnf(c_321,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_194]) ).
cnf(c_322,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_321]) ).
cnf(c_323,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_322]) ).
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)) ),
inference(resolve,[status(thm)],[c_159,c_323]) ).
cnf(c_324,negated_conjecture,
( r1_rlvect_1(B,k3_group_1(sK0,A))
| ~ r1_rlvect_1(B,A)
| ~ m1_group_2(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_162,c_155]) ).
cnf(c_325,negated_conjecture,
( r1_rlvect_1(B,k3_group_1(sK0,A))
| ~ r1_rlvect_1(B,A)
| ~ m1_group_2(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_161,c_324]) ).
cnf(c_215,negated_conjecture,
( r1_rlvect_1(B,k3_group_1(sK0,A))
| ~ r1_rlvect_1(B,A)
| ~ m1_group_2(B,sK0)
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_160,c_325]) ).
cnf(c_326,negated_conjecture,
( m1_subset_1(k3_group_1(sK0,A),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_327,negated_conjecture,
( m1_subset_1(k3_group_1(sK0,A),u1_struct_0(sK0))
| ~ m1_subset_1(A,u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_161,c_326]) ).
cnf(c_217,negated_conjecture,
( m1_subset_1(k3_group_1(sK0,A),u1_struct_0(sK0))
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_160,c_327]) ).
cnf(c_328,negated_conjecture,
( r1_rlvect_1(sK1,sK2)
| ~ m1_subset_1(sK2,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_195,c_157]) ).
cnf(c_272,negated_conjecture,
r1_rlvect_1(sK1,sK2),
inference(resolve,[status(thm)],[c_158,c_328]) ).
cnf(c_278,plain,
m1_subset_1(k3_group_1(sK0,sK2),u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_217,c_158]) ).
cnf(c_329,negated_conjecture,
( r1_rlvect_1(sK1,k3_group_1(sK0,sK2))
| ~ m1_group_2(sK1,sK0)
| ~ m1_subset_1(sK2,u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_272,c_215]) ).
cnf(c_330,negated_conjecture,
( r1_rlvect_1(sK1,k3_group_1(sK0,sK2))
| ~ m1_group_2(sK1,sK0) ),
inference(resolve,[status(thm)],[c_158,c_329]) ).
cnf(c_290,negated_conjecture,
r1_rlvect_1(sK1,k3_group_1(sK0,sK2)),
inference(resolve,[status(thm)],[c_159,c_330]) ).
cnf(c_331,negated_conjecture,
( r2_hidden(k3_group_1(sK0,sK2),k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ m1_subset_1(k3_group_1(sK0,sK2),u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_290,c_193]) ).
cnf(c_332,negated_conjecture,
r2_hidden(k3_group_1(sK0,sK2),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(resolve,[status(thm)],[c_278,c_331]) ).
cnf(c_317,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_156,c_332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP644+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 15:20:32 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 3822168 was started by sandbox on n005,
% 0.09/0.38 % Fri Sep 25 15:20:32 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.44
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44
% 0.09/0.44 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/0.44 % Length of proof is 31.
% 0.09/0.44 % Level of proof is 7.
% 0.09/0.44 % Maximum clause weight is 21.000.
% 0.09/0.44 % Given clauses 130.
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------