%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP641+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:34:56 PM UTC 2026
% Result : Theorem 18.24s 12.67s
% Output : CNFRefutation 19.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 198 ( 8 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 260 ( 110 ~; 104 |; 32 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 45 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18993,axiom,
! [A] :
( ( l1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k2_group_1(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21864,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> k2_group_1(B) = k2_group_1(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21866,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> r1_rlvect_1(B,k2_group_1(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36508,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36509,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) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36510,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) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
inference(negated_conjecture,[status(cth)],[f36509]) ).
fof(f97877,plain,
! [A] :
( m1_subset_1(k2_group_1(A),u1_struct_0(A))
| ~ l1_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18993]) ).
fof(f97878,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f97877]) ).
fof(f108047,plain,
! [A] :
( ! [B] :
( k2_group_1(B) = k2_group_1(A)
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21864]) ).
fof(f108048,plain,
! [X0,X1] :
( k2_group_1(X1) = k2_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f108047]) ).
fof(f108051,plain,
! [A] :
( ! [B] :
( r1_rlvect_1(B,k2_group_1(A))
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21866]) ).
fof(f108052,plain,
! [X0,X1] :
( r1_rlvect_1(X1,k2_group_1(X0))
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f108051]) ).
fof(f162767,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
<=> r1_rlvect_1(B,C) )
| ~ 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(pre_NNF_transformation,[status(thm)],[f36508]) ).
fof(f162768,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ r1_rlvect_1(B,C)
| r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) )
& ( 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(NNF_transformation,[status(thm)],[f162767]) ).
fof(f162770,plain,
! [X0,X1,X2] :
( ~ r1_rlvect_1(X1,X2)
| r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f162768]) ).
fof(f162771,plain,
? [A] :
( ? [B] :
( ~ r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B))
& 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(pre_NNF_transformation,[status(thm)],[f36510]) ).
fof(f162772,plain,
( ~ r2_hidden(k2_group_1(sK12737_skl),k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl))
& m1_group_2(sK12738_skl,sK12737_skl)
& v1_group_1(sK12738_skl)
& l1_group_1(sK12737_skl)
& v4_group_1(sK12737_skl)
& v3_group_1(sK12737_skl)
& ~ v3_struct_0(sK12737_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12737_skl,sK12738_skl]),skolemize(A,sK12737_skl),skolemize(B,sK12738_skl)],[f162771]) ).
fof(f162773,plain,
~ v3_struct_0(sK12737_skl),
inference(cnf_transformation,[status(thm)],[f162772]) ).
fof(f162774,plain,
v3_group_1(sK12737_skl),
inference(cnf_transformation,[status(thm)],[f162772]) ).
fof(f162775,plain,
v4_group_1(sK12737_skl),
inference(cnf_transformation,[status(thm)],[f162772]) ).
fof(f162776,plain,
l1_group_1(sK12737_skl),
inference(cnf_transformation,[status(thm)],[f162772]) ).
fof(f162777,plain,
v1_group_1(sK12738_skl),
inference(cnf_transformation,[status(thm)],[f162772]) ).
fof(f162778,plain,
m1_group_2(sK12738_skl,sK12737_skl),
inference(cnf_transformation,[status(thm)],[f162772]) ).
fof(f162779,plain,
~ r2_hidden(k2_group_1(sK12737_skl),k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl)),
inference(cnf_transformation,[status(thm)],[f162772]) ).
fof(f191183,plain,
! [X0] :
( k2_group_1(X0) = k2_group_1(sK12737_skl)
| ~ m1_group_2(X0,sK12737_skl)
| ~ l1_group_1(sK12737_skl)
| ~ v4_group_1(sK12737_skl)
| ~ v3_group_1(sK12737_skl) ),
inference(resolution,[status(thm)],[f108048,f162773]) ).
fof(f191185,plain,
! [X0] :
( k2_group_1(X0) = k2_group_1(sK12737_skl)
| ~ m1_group_2(X0,sK12737_skl)
| ~ l1_group_1(sK12737_skl)
| ~ v4_group_1(sK12737_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f191183,f162774]) ).
fof(f191260,plain,
! [X0] :
( k2_group_1(X0) = k2_group_1(sK12737_skl)
| ~ m1_group_2(X0,sK12737_skl)
| ~ l1_group_1(sK12737_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f191185,f162775]) ).
fof(f191261,plain,
! [X0] :
( k2_group_1(X0) = k2_group_1(sK12737_skl)
| ~ m1_group_2(X0,sK12737_skl) ),
inference(resolution,[status(thm)],[f191260,f162776]) ).
fof(f191300,plain,
k2_group_1(sK12738_skl) = k2_group_1(sK12737_skl),
inference(resolution,[status(thm)],[f191261,f162778]) ).
fof(f191308,plain,
~ r2_hidden(k2_group_1(sK12738_skl),k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl)),
inference(backward_demodulation,[status(thm)],[f191300,f162779]) ).
fof(f191309,plain,
! [X0] :
( r1_rlvect_1(X0,k2_group_1(sK12738_skl))
| ~ m1_group_2(X0,sK12737_skl)
| ~ l1_group_1(sK12737_skl)
| ~ v4_group_1(sK12737_skl)
| ~ v3_group_1(sK12737_skl)
| v3_struct_0(sK12737_skl) ),
inference(paramodulation,[status(thm)],[f191300,f108052]) ).
fof(f191310,plain,
( m1_subset_1(k2_group_1(sK12738_skl),u1_struct_0(sK12737_skl))
| ~ l1_group_1(sK12737_skl)
| v3_struct_0(sK12737_skl) ),
inference(paramodulation,[status(thm)],[f191300,f97878]) ).
fof(f191311,plain,
! [X0] :
( r1_rlvect_1(X0,k2_group_1(sK12738_skl))
| ~ m1_group_2(X0,sK12737_skl)
| ~ l1_group_1(sK12737_skl)
| ~ v4_group_1(sK12737_skl)
| ~ v3_group_1(sK12737_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f191309,f162773]) ).
fof(f191312,plain,
( m1_subset_1(k2_group_1(sK12738_skl),u1_struct_0(sK12737_skl))
| ~ l1_group_1(sK12737_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f191310,f162773]) ).
fof(f191390,plain,
m1_subset_1(k2_group_1(sK12738_skl),u1_struct_0(sK12737_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f191312,f162776]) ).
fof(f191439,plain,
! [X0] :
( r1_rlvect_1(X0,k2_group_1(sK12738_skl))
| ~ m1_group_2(X0,sK12737_skl)
| ~ l1_group_1(sK12737_skl)
| ~ v4_group_1(sK12737_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f191311,f162774]) ).
fof(f191488,plain,
! [X0,X1] :
( ~ r1_rlvect_1(sK12738_skl,X1)
| r2_hidden(X1,k1_funct_1(k1_latsubgr(X0),sK12738_skl))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_group_2(sK12738_skl,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f162770,f162777]) ).
fof(f192204,plain,
! [X0] :
( ~ r1_rlvect_1(sK12738_skl,X0)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK12737_skl))
| ~ m1_group_2(sK12738_skl,sK12737_skl)
| ~ l1_group_1(sK12737_skl)
| ~ v4_group_1(sK12737_skl)
| ~ v3_group_1(sK12737_skl) ),
inference(resolution,[status(thm)],[f191488,f162773]) ).
fof(f192206,plain,
! [X0] :
( ~ r1_rlvect_1(sK12738_skl,X0)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK12737_skl))
| ~ m1_group_2(sK12738_skl,sK12737_skl)
| ~ l1_group_1(sK12737_skl)
| ~ v4_group_1(sK12737_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f192204,f162774]) ).
fof(f192568,plain,
! [X0] :
( ~ r1_rlvect_1(sK12738_skl,X0)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK12737_skl))
| ~ m1_group_2(sK12738_skl,sK12737_skl)
| ~ l1_group_1(sK12737_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f192206,f162775]) ).
fof(f192569,plain,
! [X0] :
( ~ r1_rlvect_1(sK12738_skl,X0)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK12737_skl))
| ~ l1_group_1(sK12737_skl) ),
inference(resolution,[status(thm)],[f192568,f162778]) ).
fof(f192570,plain,
! [X0] :
( ~ r1_rlvect_1(sK12738_skl,X0)
| r2_hidden(X0,k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK12737_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f192569,f162776]) ).
fof(f192603,plain,
( ~ r1_rlvect_1(sK12738_skl,k2_group_1(sK12738_skl))
| r2_hidden(k2_group_1(sK12738_skl),k1_funct_1(k1_latsubgr(sK12737_skl),sK12738_skl)) ),
inference(resolution,[status(thm)],[f192570,f191390]) ).
fof(f192607,plain,
~ r1_rlvect_1(sK12738_skl,k2_group_1(sK12738_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f192603,f191308]) ).
fof(f192612,plain,
( ~ m1_group_2(sK12738_skl,sK12737_skl)
| ~ l1_group_1(sK12737_skl)
| ~ v4_group_1(sK12737_skl) ),
inference(resolution,[status(thm)],[f192607,f191439]) ).
fof(f192616,plain,
( ~ m1_group_2(sK12738_skl,sK12737_skl)
| ~ l1_group_1(sK12737_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f192612,f162775]) ).
fof(f192626,plain,
~ m1_group_2(sK12738_skl,sK12737_skl),
inference(forward_subsumption_resolution,[status(thm)],[f192616,f162776]) ).
fof(f192627,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f162778,f192626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP641+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n010.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 20 20:25:50 UTC 2026
% 0.19/0.45 % CPUTime :
% 11.22/11.56 % Drodi V4.1.1
% 18.24/12.67 % Refutation found
% 18.24/12.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.24/12.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 22.51/14.72 % Elapsed time: 13.716539 seconds
% 22.51/14.72 % CPU time: 22.221135 seconds
% 22.51/14.72 % Total memory used: 7.123 GB
% 22.51/14.72 % Net memory used: 7.089 GB
%------------------------------------------------------------------------------