%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP641+2 : 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 : n012.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 3.71s 1.23s
% Output : Refutation 3.71s
% 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(f3812,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(f4399,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(f5657,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(f5658,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(f5659,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)],[f5658]) ).
fof(f5663,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,[],[f5659]) ).
fof(f5664,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,[],[f5663]) ).
fof(f5700,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,[],[f4399]) ).
fof(f5701,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,[],[f5700]) ).
fof(f5706,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f3812]) ).
fof(f5707,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f5706]) ).
fof(f5712,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,[],[f5657]) ).
fof(f5713,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,[],[f5712]) ).
fof(f5718,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)],[f5664]) ).
fof(f5731,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,[],[f5713]) ).
fof(f5735,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5736,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5737,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5738,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5739,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5740,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f5718]) ).
fof(f5741,plain,
~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f5718]) ).
fof(f5780,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,[],[f5701]) ).
fof(f5783,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f5707]) ).
fof(f5789,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,[],[f5731]) ).
fof(f5842,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,[],[f5741,f5789]) ).
fof(f5848,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,[],[f5842,f5780]) ).
fof(f5850,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,[],[f5848,f5783]) ).
fof(f5852,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,[],[f5850,f5740]) ).
fof(f5854,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f5852,f5739]) ).
fof(f5855,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f5854,f5738]) ).
fof(f5856,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f5855,f5737]) ).
fof(f5857,plain,
~ l1_group_1(sK0),
inference(forward_subsumption_resolution,[],[f5856,f5736]) ).
fof(f5858,plain,
$false,
inference(forward_subsumption_resolution,[],[f5857,f5735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP641+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 10:22:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 3.71/1.23 % (2164731)Detected formulas, will run a generic FOF schedule.
% 3.71/1.23 % (2164738)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=183237415:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 3.71/1.23 % (2164737)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=1527120142:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 3.71/1.23 % (2164740)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2379676601:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 3.71/1.23 % (2164739)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=876189613:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 3.71/1.23 % (2164736)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=254610493:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 3.71/1.23 % (2164742)dis-21_1_sil=8000:lcm=predicate:random_seed=1401365367:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 3.71/1.23 % (2164741)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2347214881:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 3.71/1.23 % (2164739)First to succeed.
% 3.71/1.23 % (2164739)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2164731"
% 3.71/1.23 % (2164740)Instruction limit reached!
% 3.71/1.23 % (2164740)------------------------------
% 3.71/1.23 % (2164740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.23 % (2164740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.23 % (2164740)CaDiCaL version: 2.1.3
% 3.71/1.23 % (2164740)Termination reason: Instruction limit
% 3.71/1.23 % (2164740)Termination phase: Saturation
% 3.71/1.23 % (2164740)Time elapsed: 0.046 s
% 3.71/1.23 % (2164740)Peak memory usage: 95 MB
% 3.71/1.23 % (2164740)Instructions burned: 122 (million)
% 3.71/1.23 % (2164741)Instruction limit reached!
% 3.71/1.23 % (2164741)------------------------------
% 3.71/1.23 % (2164741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.23 % (2164741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.23 % (2164741)CaDiCaL version: 2.1.3
% 3.71/1.23 % (2164741)Termination reason: Instruction limit
% 3.71/1.23 % (2164741)Termination phase: Unused predicate definition removal
% 3.71/1.23 % (2164741)Time elapsed: 0.047 s
% 3.71/1.23 % (2164741)Peak memory usage: 92 MB
% 3.71/1.23 % (2164741)Instructions burned: 139 (million)
% 3.71/1.23 % (2164742)Instruction limit reached!
% 3.71/1.23 % (2164742)------------------------------
% 3.71/1.23 % (2164742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.23 % (2164742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.23 % (2164742)CaDiCaL version: 2.1.3
% 3.71/1.23 % (2164742)Termination reason: Instruction limit
% 3.71/1.23 % (2164742)Termination phase: Preprocessing 3
% 3.71/1.23 % (2164742)Time elapsed: 0.056 s
% 3.71/1.23 % (2164742)Peak memory usage: 96 MB
% 3.71/1.23 % (2164742)Instructions burned: 132 (million)
% 3.71/1.23 % (2164750)lrs+10_1_sil=8000:sp=occurrence:random_seed=570179946:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.71/1.23 % (2164751)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1128698604:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.71/1.23 % (2164752)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2358440767:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.71/1.23 % (2164751)Also succeeded, but the first one will report.
% 3.71/1.23 % (2164752)Also succeeded, but the first one will report.
% 3.71/1.23 % (2164750)Also succeeded, but the first one will report.
% 3.71/1.23 % (2164739)Refutation found. Thanks to Tanya!
% 3.71/1.23 % SZS status Theorem for theBenchmark
% 3.71/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.23 % (2164739)------------------------------
% 3.71/1.23 % (2164739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.23 % (2164739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.23 % (2164739)CaDiCaL version: 2.1.3
% 3.71/1.23 % (2164739)Termination reason: Refutation
% 3.71/1.23 % (2164739)Time elapsed: 0.017 s
% 3.71/1.23 % (2164739)Peak memory usage: 95 MB
% 3.71/1.23 % (2164739)Instructions burned: 37 (million)
% 3.71/1.23 % (2164739)------------------------------
% 3.71/1.23 % (2164739)------------------------------
% 3.71/1.23 % (2164731)Success in time 0.611 s
% 3.71/1.23 % Vampire exiting
%------------------------------------------------------------------------------