%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP642+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 10:15:14 AM UTC 2026
% Result : Theorem 3.67s 1.36s
% Output : Refutation 3.67s
% 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/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5658,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/sandbox/benchmark/theBenchmark.p',t19_latsubgr) ).
fof(f5659,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/sandbox/benchmark/theBenchmark.p',t20_latsubgr) ).
fof(f5660,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)],[f5659]) ).
fof(f5661,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,[],[f5660]) ).
fof(f5662,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,[],[f5661]) ).
fof(f5710,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,[],[f5658]) ).
fof(f5711,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,[],[f5710]) ).
fof(f5718,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)],[f5662]) ).
fof(f5721,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(f5722,plain,
! [X0] :
( ( X0 = k1_xboole_0
| ? [X1] : r2_hidden(X1,X0) )
& ( ! [X2] : ~ r2_hidden(X2,X0)
| k1_xboole_0 != X0 ) ),
inference(rectify,[],[f5721]) ).
fof(f5723,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))],[f5722]) ).
fof(f5738,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5739,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5740,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5741,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5742,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f5718]) ).
fof(f5743,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f5718]) ).
fof(f5744,plain,
k1_xboole_0 = k1_funct_1(k1_latsubgr(sK0),sK1),
inference(cnf_transformation,[],[f5718]) ).
fof(f5764,plain,
! [X2,X0] :
( ~ r2_hidden(X2,X0)
| k1_xboole_0 != X0 ),
inference(cnf_transformation,[],[f5723]) ).
fof(f5803,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,[],[f5711]) ).
fof(f5815,definition,
~ sP16(k1_xboole_0),
introduced(definition,[new_symbols(definition,[sP16])],[inequality_splitting_name_introduction]) ).
fof(f5816,plain,
! [X2,X0] :
( ~ r2_hidden(X2,X0)
| sP16(X0) ),
inference(inequality_splitting,[],[f5764,f5815]) ).
fof(f5864,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,[],[f5803,f5744]) ).
fof(f5874,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,[],[f5864,f5743]) ).
fof(f5877,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,[],[f5874,f5742]) ).
fof(f5880,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,[],[f5877,f5741]) ).
fof(f5883,plain,
( r2_hidden(k2_group_1(sK0),k1_xboole_0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f5880,f5740]) ).
fof(f5886,plain,
( r2_hidden(k2_group_1(sK0),k1_xboole_0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f5883,f5739]) ).
fof(f5889,plain,
r2_hidden(k2_group_1(sK0),k1_xboole_0),
inference(forward_subsumption_resolution,[],[f5886,f5738]) ).
fof(f5898,plain,
sP16(k1_xboole_0),
inference(resolution,[],[f5889,f5816]) ).
fof(f5901,plain,
$false,
inference(forward_subsumption_resolution,[],[f5898,f5815]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Sun Sep 27 10:21:47 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.67/1.36 % (3786427)Detected formulas, will run a generic FOF schedule.
% 3.67/1.36 % (3786437)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3481852385:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 3.67/1.36 % (3786436)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2935712211:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 3.67/1.36 % (3786438)dis-21_1_sil=8000:lcm=predicate:random_seed=3987359098: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)
% 3.67/1.36 % (3786432)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=1563484562:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 3.67/1.36 % (3786435)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1773934462:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 3.67/1.36 % (3786434)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=3235705615:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 3.67/1.36 % (3786433)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=3271721865:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 3.67/1.36 % (3786435)First to succeed.
% 3.67/1.36 % (3786435)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3786427"
% 3.67/1.36 % (3786437)Instruction limit reached!
% 3.67/1.36 % (3786437)------------------------------
% 3.67/1.36 % (3786437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.36 % (3786437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.36 % (3786437)CaDiCaL version: 2.1.3
% 3.67/1.36 % (3786437)Termination reason: Instruction limit
% 3.67/1.36 % (3786437)Termination phase: Unused predicate definition removal
% 3.67/1.36 % (3786437)Time elapsed: 0.047 s
% 3.67/1.36 % (3786437)Peak memory usage: 93 MB
% 3.67/1.36 % (3786437)Instructions burned: 139 (million)
% 3.67/1.36 % (3786436)Instruction limit reached!
% 3.67/1.36 % (3786436)------------------------------
% 3.67/1.36 % (3786436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.36 % (3786436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.36 % (3786436)CaDiCaL version: 2.1.3
% 3.67/1.36 % (3786436)Termination reason: Instruction limit
% 3.67/1.36 % (3786436)Termination phase: Saturation
% 3.67/1.36 % (3786436)Time elapsed: 0.082 s
% 3.67/1.36 % (3786436)Peak memory usage: 96 MB
% 3.67/1.36 % (3786436)Instructions burned: 120 (million)
% 3.67/1.36 % (3786438)Instruction limit reached!
% 3.67/1.36 % (3786438)------------------------------
% 3.67/1.36 % (3786438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.36 % (3786438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.36 % (3786438)CaDiCaL version: 2.1.3
% 3.67/1.36 % (3786438)Termination reason: Instruction limit
% 3.67/1.36 % (3786438)Termination phase: Preprocessing 3
% 3.67/1.36 % (3786438)Time elapsed: 0.099 s
% 3.67/1.36 % (3786438)Peak memory usage: 97 MB
% 3.67/1.36 % (3786438)Instructions burned: 130 (million)
% 3.67/1.36 % (3786446)lrs+10_1_sil=8000:sp=occurrence:random_seed=4274037661:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.67/1.36 % (3786446)Also succeeded, but the first one will report.
% 3.67/1.36 % (3786447)lrs+10_1_sil=32000:urr=on:br=off:random_seed=379015979:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.67/1.36 % (3786448)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3324982189:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.67/1.36 % (3786435)Refutation found. Thanks to Tanya!
% 3.67/1.36 % SZS status Theorem for theBenchmark
% 3.67/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.36 % (3786435)------------------------------
% 3.67/1.36 % (3786435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.36 % (3786435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.36 % (3786435)CaDiCaL version: 2.1.3
% 3.67/1.36 % (3786435)Termination reason: Refutation
% 3.67/1.36 % (3786435)Time elapsed: 0.029 s
% 3.67/1.36 % (3786435)Peak memory usage: 95 MB
% 3.67/1.36 % (3786435)Instructions burned: 38 (million)
% 3.67/1.36 % (3786435)------------------------------
% 3.67/1.36 % (3786435)------------------------------
% 3.67/1.36 % (3786427)Success in time 0.545 s
% 3.67/1.36 % Vampire exiting
%------------------------------------------------------------------------------