%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP642+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 : 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 : Tue Sep 29 10:15:14 AM UTC 2026
% Result : Theorem 4.69s 2.16s
% Output : Refutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 11 unt; 1 def)
% Number of atoms : 119 ( 14 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 141 ( 54 ~; 47 |; 33 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
! [X0] :
( X0 = k1_xboole_0
<=> ! [X1] : ~ r2_hidden(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f13983,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) )
=> r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_latsubgr) ).
fof(f13984,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) )
=> k1_funct_1(k1_latsubgr(X0),X1) != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_latsubgr) ).
fof(f13985,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) )
=> k1_funct_1(k1_latsubgr(X0),X1) != k1_xboole_0 ) ),
inference(negated_conjecture,[status(cth)],[f13984]) ).
fof(f13987,plain,
? [X0] :
( ? [X1] :
( k1_xboole_0 = 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,[],[f13985]) ).
fof(f13988,plain,
? [X0] :
( ? [X1] :
( k1_xboole_0 = 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,[],[f13987]) ).
fof(f14034,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,[],[f13983]) ).
fof(f14035,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,[],[f14034]) ).
fof(f14042,plain,
( k1_xboole_0 = 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)],[f13988]) ).
fof(f14045,plain,
! [X0] :
( ( X0 = k1_xboole_0
| ? [X1] : r2_hidden(X1,X0) )
& ( ! [X1] : ~ r2_hidden(X1,X0)
| k1_xboole_0 != X0 ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f14046,plain,
! [X0] :
( ( X0 = k1_xboole_0
| ? [X1] : r2_hidden(X1,X0) )
& ( ! [X2] : ~ r2_hidden(X2,X0)
| k1_xboole_0 != X0 ) ),
inference(rectify,[],[f14045]) ).
fof(f14047,plain,
! [X0] :
( ( X0 = k1_xboole_0
| r2_hidden(sK3(X0),X0) )
& ( ! [X2] : ~ r2_hidden(X2,X0)
| k1_xboole_0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f14046]) ).
fof(f14060,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f14042]) ).
fof(f14061,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f14042]) ).
fof(f14062,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f14042]) ).
fof(f14063,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f14042]) ).
fof(f14064,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f14042]) ).
fof(f14065,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f14042]) ).
fof(f14066,plain,
k1_xboole_0 = k1_funct_1(k1_latsubgr(sK0),sK1),
inference(cnf_transformation,[],[f14042]) ).
fof(f14091,plain,
! [X2,X0] :
( ~ r2_hidden(X2,X0)
| k1_xboole_0 != X0 ),
inference(cnf_transformation,[],[f14047]) ).
fof(f14122,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(cnf_transformation,[],[f14035]) ).
fof(f14140,definition,
~ sP17(k1_xboole_0),
introduced(definition,[new_symbols(definition,[sP17])],[inequality_splitting_name_introduction]) ).
fof(f14141,plain,
! [X2,X0] :
( ~ r2_hidden(X2,X0)
| sP17(X0) ),
inference(inequality_splitting,[],[f14091,f14140]) ).
fof(f14187,plain,
( r2_hidden(k2_group_1(sK0),k1_xboole_0)
| ~ 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(superposition,[],[f14122,f14066]) ).
fof(f14197,plain,
( r2_hidden(k2_group_1(sK0),k1_xboole_0)
| ~ 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,[],[f14187,f14065]) ).
fof(f14200,plain,
( r2_hidden(k2_group_1(sK0),k1_xboole_0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14197,f14064]) ).
fof(f14203,plain,
( r2_hidden(k2_group_1(sK0),k1_xboole_0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14200,f14063]) ).
fof(f14206,plain,
( r2_hidden(k2_group_1(sK0),k1_xboole_0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14203,f14062]) ).
fof(f14209,plain,
( r2_hidden(k2_group_1(sK0),k1_xboole_0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f14206,f14061]) ).
fof(f14212,plain,
r2_hidden(k2_group_1(sK0),k1_xboole_0),
inference(forward_subsumption_resolution,[],[f14209,f14060]) ).
fof(f14221,plain,
sP17(k1_xboole_0),
inference(resolution,[],[f14212,f14141]) ).
fof(f14224,plain,
$false,
inference(forward_subsumption_resolution,[],[f14221,f14140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n011.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 10:21:48 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 4.69/2.16 % (2188022)Detected formulas, will run a generic FOF schedule.
% 4.69/2.16 % (2188032)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1216425642:s2a=on:i=139:gtg=position_2992 on theBenchmark for (2992ds/139Mi)
% 4.69/2.16 % (2188032)Instruction limit reached!
% 4.69/2.16 % (2188032)------------------------------
% 4.69/2.16 % (2188032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/2.16 % (2188032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/2.16 % (2188032)CaDiCaL version: 2.1.3
% 4.69/2.16 % (2188032)Termination reason: Instruction limit
% 4.69/2.16 % (2188032)Termination phase: Property scanning
% 4.69/2.16 % (2188032)Time elapsed: 0.033 s
% 4.69/2.16 % (2188032)Peak memory usage: 103 MB
% 4.69/2.16 % (2188032)Instructions burned: 141 (million)
% 4.69/2.16 % (2188031)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=23321142:i=119:av=off:ss=axioms_2992 on theBenchmark for (2992ds/119Mi)
% 4.69/2.16 % (2188030)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=458045744:i=109:sd=1:ins=1:gsp=on:ss=axioms_2992 on theBenchmark for (2992ds/109Mi)
% 4.69/2.16 % (2188029)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=4083429636:i=141695:sd=1:nm=32:gsp=on:ss=included_2992 on theBenchmark for (2992ds/141695Mi)
% 4.69/2.16 % (2188027)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=2723992135:i=141193_2992 on theBenchmark for (2992ds/141193Mi)
% 4.69/2.16 % (2188028)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=3120010599:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2992 on theBenchmark for (2992ds/134677Mi)
% 4.69/2.16 % (2188033)dis-21_1_sil=8000:lcm=predicate:random_seed=2533239052: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)
% 4.69/2.16 % (2188030)First to succeed.
% 4.69/2.16 % (2188030)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2188022"
% 4.69/2.16 % (2188036)lrs+10_1_sil=8000:sp=occurrence:random_seed=3523024332:i=285:sd=3:ss=axioms:sgt=8_2991 on theBenchmark for (2991ds/285Mi)
% 4.69/2.16 % (2188031)Instruction limit reached!
% 4.69/2.16 % (2188031)------------------------------
% 4.69/2.16 % (2188031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/2.16 % (2188031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/2.16 % (2188031)CaDiCaL version: 2.1.3
% 4.69/2.16 % (2188031)Termination reason: Instruction limit
% 4.69/2.16 % (2188031)Termination phase: Saturation
% 4.69/2.16 % (2188031)Time elapsed: 0.095 s
% 4.69/2.16 % (2188031)Peak memory usage: 107 MB
% 4.69/2.16 % (2188031)Instructions burned: 119 (million)
% 4.69/2.16 % (2188033)Instruction limit reached!
% 4.69/2.16 % (2188033)------------------------------
% 4.69/2.16 % (2188033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/2.16 % (2188033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/2.16 % (2188033)CaDiCaL version: 2.1.3
% 4.69/2.16 % (2188033)Termination reason: Instruction limit
% 4.69/2.16 % (2188033)Termination phase: Preprocessing 1
% 4.69/2.16 % (2188033)Time elapsed: 0.100 s
% 4.69/2.16 % (2188033)Peak memory usage: 104 MB
% 4.69/2.16 % (2188033)Instructions burned: 129 (million)
% 4.69/2.16 % (2188036)Also succeeded, but the first one will report.
% 4.69/2.16 % (2188043)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2744831147:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2990 on theBenchmark for (2990ds/157Mi)
% 4.69/2.16 % (2188044)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1072772610:i=325:sd=1:ss=axioms:sgt=32_2990 on theBenchmark for (2990ds/325Mi)
% 4.69/2.16 % (2188043)Instruction limit reached!
% 4.69/2.16 % (2188043)------------------------------
% 4.69/2.16 % (2188043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/2.16 % (2188043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/2.16 % (2188043)CaDiCaL version: 2.1.3
% 4.69/2.16 % (2188043)Termination reason: Instruction limit
% 4.69/2.16 % (2188043)Termination phase: Property scanning
% 4.69/2.16 % (2188043)Time elapsed: 0.068 s
% 4.69/2.16 % (2188043)Peak memory usage: 103 MB
% 4.69/2.16 % (2188043)Instructions burned: 159 (million)
% 4.69/2.16 % (2188044)Also succeeded, but the first one will report.
% 4.69/2.16 % (2188030)Refutation found. Thanks to Tanya!
% 4.69/2.16 % SZS status Theorem for theBenchmark
% 4.69/2.16 % SZS output start Proof for theBenchmark
% See solution above
% 4.69/2.16 % (2188030)------------------------------
% 4.69/2.16 % (2188030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/2.16 % (2188030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/2.16 % (2188030)CaDiCaL version: 2.1.3
% 4.69/2.16 % (2188030)Termination reason: Refutation
% 4.69/2.16 % (2188030)Time elapsed: 0.074 s
% 4.69/2.16 % (2188030)Peak memory usage: 108 MB
% 4.69/2.16 % (2188030)Instructions burned: 90 (million)
% 4.69/2.16 % (2188030)------------------------------
% 4.69/2.16 % (2188030)------------------------------
% 4.69/2.16 % (2188022)Success in time 1.193 s
% 4.69/2.16 % Vampire exiting
%------------------------------------------------------------------------------