%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP641+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Tue Sep 29 10:15:13 AM UTC 2026
% Result : Theorem 4.81s 2.25s
% Output : Refutation 4.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 215 ( 87 ~; 80 |; 35 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7470,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_group_1(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f8757,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> r1_rlvect_1(X1,k2_group_1(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_group_2) ).
fof(f13982,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_group_1(X1)
& m1_group_2(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
<=> r1_rlvect_1(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_latsubgr) ).
fof(f13983,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_group_1(X1)
& m1_group_2(X1,X0) )
=> r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_latsubgr) ).
fof(f13984,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_group_1(X1)
& m1_group_2(X1,X0) )
=> r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
inference(negated_conjecture,[status(cth)],[f13983]) ).
fof(f13986,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1))
& v1_group_1(X1)
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f13984]) ).
fof(f13987,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1))
& v1_group_1(X1)
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f13986]) ).
fof(f14023,plain,
! [X0] :
( ! [X1] :
( r1_rlvect_1(X1,k2_group_1(X0))
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f8757]) ).
fof(f14024,plain,
! [X0] :
( ! [X1] :
( r1_rlvect_1(X1,k2_group_1(X0))
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f14023]) ).
fof(f14029,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f7470]) ).
fof(f14030,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f14029]) ).
fof(f14035,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
<=> r1_rlvect_1(X1,X2) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f13982]) ).
fof(f14036,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
<=> r1_rlvect_1(X1,X2) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f14035]) ).
fof(f14041,plain,
( ~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1))
& v1_group_1(sK1)
& m1_group_2(sK1,sK0)
& ~ v3_struct_0(sK0)
& v3_group_1(sK0)
& v4_group_1(sK0)
& l1_group_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13987]) ).
fof(f14054,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
| ~ r1_rlvect_1(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)) )
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(nnf_transformation,[],[f14036]) ).
fof(f14058,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f14041]) ).
fof(f14059,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f14041]) ).
fof(f14060,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f14041]) ).
fof(f14061,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f14041]) ).
fof(f14062,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f14041]) ).
fof(f14063,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f14041]) ).
fof(f14064,plain,
~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f14041]) ).
fof(f14103,plain,
! [X0,X1] :
( r1_rlvect_1(X1,k2_group_1(X0))
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f14024]) ).
fof(f14106,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f14030]) ).
fof(f14112,plain,
! [X2,X0,X1] :
( r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
| ~ r1_rlvect_1(X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f14054]) ).
fof(f14165,plain,
( ~ r1_rlvect_1(sK1,k2_group_1(sK0))
| ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0))
| ~ v1_group_1(sK1)
| ~ m1_group_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f14064,f14112]) ).
fof(f14171,plain,
( ~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK0))
| ~ v1_group_1(sK1)
| ~ m1_group_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14165,f14103]) ).
fof(f14173,plain,
( ~ v1_group_1(sK1)
| ~ m1_group_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14171,f14106]) ).
fof(f14175,plain,
( ~ m1_group_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14173,f14063]) ).
fof(f14177,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14175,f14062]) ).
fof(f14178,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14177,f14061]) ).
fof(f14179,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14178,f14060]) ).
fof(f14180,plain,
~ l1_group_1(sK0),
inference(forward_subsumption_resolution,[],[f14179,f14059]) ).
fof(f14181,plain,
$false,
inference(forward_subsumption_resolution,[],[f14180,f14058]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP641+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:22:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.81/2.25 % (3299759)Detected formulas, will run a generic FOF schedule.
% 4.81/2.25 % (3299769)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=421048123:s2a=on:i=139:gtg=position_2992 on theBenchmark for (2992ds/139Mi)
% 4.81/2.25 % (3299769)Instruction limit reached!
% 4.81/2.25 % (3299769)------------------------------
% 4.81/2.25 % (3299769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/2.25 % (3299765)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2550741950:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2992 on theBenchmark for (2992ds/134677Mi)
% 4.81/2.25 % (3299764)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=110526825:i=141193_2992 on theBenchmark for (2992ds/141193Mi)
% 4.81/2.25 % (3299766)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1962447439:i=141695:sd=1:nm=32:gsp=on:ss=included_2992 on theBenchmark for (2992ds/141695Mi)
% 4.81/2.25 % (3299767)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=658892548:i=109:sd=1:ins=1:gsp=on:ss=axioms_2992 on theBenchmark for (2992ds/109Mi)
% 4.81/2.25 % (3299768)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3561393804:i=119:av=off:ss=axioms_2992 on theBenchmark for (2992ds/119Mi)
% 4.81/2.25 % (3299769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/2.25 % (3299769)CaDiCaL version: 2.1.3
% 4.81/2.25 % (3299769)Termination reason: Instruction limit
% 4.81/2.25 % (3299769)Termination phase: Property scanning
% 4.81/2.25 % (3299769)Time elapsed: 0.033 s
% 4.81/2.25 % (3299769)Peak memory usage: 103 MB
% 4.81/2.25 % (3299769)Instructions burned: 142 (million)
% 4.81/2.25 % (3299770)dis-21_1_sil=8000:lcm=predicate:random_seed=1405428556:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2992 on theBenchmark for (2992ds/129Mi)
% 4.81/2.25 % (3299767)First to succeed.
% 4.81/2.25 % (3299767)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3299759"
% 4.81/2.25 % (3299768)Instruction limit reached!
% 4.81/2.25 % (3299768)------------------------------
% 4.81/2.25 % (3299768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/2.25 % (3299768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/2.25 % (3299768)CaDiCaL version: 2.1.3
% 4.81/2.25 % (3299768)Termination reason: Instruction limit
% 4.81/2.25 % (3299768)Termination phase: Saturation
% 4.81/2.25 % (3299768)Time elapsed: 0.093 s
% 4.81/2.25 % (3299768)Peak memory usage: 107 MB
% 4.81/2.25 % (3299768)Instructions burned: 120 (million)
% 4.81/2.25 % (3299770)Instruction limit reached!
% 4.81/2.25 % (3299770)------------------------------
% 4.81/2.25 % (3299770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/2.25 % (3299770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/2.25 % (3299770)CaDiCaL version: 2.1.3
% 4.81/2.25 % (3299770)Termination reason: Instruction limit
% 4.81/2.25 % (3299770)Termination phase: Preprocessing 1
% 4.81/2.25 % (3299770)Time elapsed: 0.100 s
% 4.81/2.25 % (3299770)Peak memory usage: 104 MB
% 4.81/2.25 % (3299770)Instructions burned: 129 (million)
% 4.81/2.25 % (3299777)lrs+10_1_sil=8000:sp=occurrence:random_seed=2432192523:i=285:sd=3:ss=axioms:sgt=8_2991 on theBenchmark for (2991ds/285Mi)
% 4.81/2.25 % (3299777)Also succeeded, but the first one will report.
% 4.81/2.25 % (3299779)lrs+10_1_sil=32000:urr=on:br=off:random_seed=830016097:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2990 on theBenchmark for (2990ds/157Mi)
% 4.81/2.25 % (3299781)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3811221432:i=325:sd=1:ss=axioms:sgt=32_2990 on theBenchmark for (2990ds/325Mi)
% 4.81/2.25 % (3299767)Refutation found. Thanks to Tanya!
% 4.81/2.25 % SZS status Theorem for theBenchmark
% 4.81/2.25 % SZS output start Proof for theBenchmark
% See solution above
% 4.81/2.25 % (3299767)------------------------------
% 4.81/2.25 % (3299767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.81/2.25 % (3299767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.81/2.25 % (3299767)CaDiCaL version: 2.1.3
% 4.81/2.25 % (3299767)Termination reason: Refutation
% 4.81/2.25 % (3299767)Time elapsed: 0.073 s
% 4.81/2.25 % (3299767)Peak memory usage: 108 MB
% 4.81/2.25 % (3299767)Instructions burned: 89 (million)
% 4.81/2.25 % (3299767)------------------------------
% 4.81/2.25 % (3299767)------------------------------
% 4.81/2.25 % (3299759)Success in time 1.199 s
% 4.81/2.25 % Vampire exiting
%------------------------------------------------------------------------------