%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS180+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 11:41:50 AM UTC 2026
% Result : Theorem 2.40s 1.21s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 10 unt; 3 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 148 ( 63 ~; 52 |; 13 &)
% ( 7 <=>; 10 =>; 0 <=; 3 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 88 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
=> status(X2,X3,X1) )
<=> isa(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa) ).
fof(f3,axiom,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& ~ status(X2,X3,X1) )
<=> nota(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nota) ).
fof(f4,axiom,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
=> ~ status(X2,X3,X1) )
<=> nevera(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nevera) ).
fof(f5,axiom,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
<~> status(X2,X3,X1) )
<=> xora(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xora) ).
fof(f14,conjecture,
! [X0,X1] :
? [X2,X3] :
( status(X2,X3,X0)
=> ~ ( isa(X0,X1)
& ( nota(X0,X1)
| nevera(X0,X1)
| xora(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_exclusive) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
? [X2,X3] :
( status(X2,X3,X0)
=> ~ ( isa(X0,X1)
& ( nota(X0,X1)
| nevera(X0,X1)
| xora(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( xora(X0,X1)
=> ! [X2,X3] :
( status(X2,X3,X0)
<~> status(X2,X3,X1) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f17,plain,
! [X0,X1] :
( nevera(X0,X1)
=> ! [X2,X3] :
( status(X2,X3,X0)
=> ~ status(X2,X3,X1) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f18,plain,
! [X0,X1] :
( nota(X0,X1)
=> ? [X2,X3] :
( status(X2,X3,X0)
& ~ status(X2,X3,X1) ) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( isa(X0,X1)
=> ! [X2,X3] :
( status(X2,X3,X0)
=> status(X2,X3,X1) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f20,plain,
? [X0,X1] :
! [X2,X3] :
( isa(X0,X1)
& ( nota(X0,X1)
| nevera(X0,X1)
| xora(X0,X1) )
& status(X2,X3,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0,X1] :
! [X2,X3] :
( isa(X0,X1)
& ( nota(X0,X1)
| nevera(X0,X1)
| xora(X0,X1) )
& status(X2,X3,X0) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
<~> status(X2,X3,X1) )
| ~ xora(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( ! [X2,X3] :
( ~ status(X2,X3,X1)
| ~ status(X2,X3,X0) )
| ~ nevera(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& ~ status(X2,X3,X1) )
| ~ nota(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f25,plain,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X1)
| ~ status(X2,X3,X0) )
| ~ isa(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f26,plain,
! [X2,X3] :
( isa(sK0,sK1)
& ( nota(sK0,sK1)
| nevera(sK0,sK1)
| xora(sK0,sK1) )
& status(X2,X3,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
fof(f27,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( ~ status(X2,X3,X1)
| ~ status(X2,X3,X0) )
& ( status(X2,X3,X1)
| status(X2,X3,X0) ) )
| ~ xora(X0,X1) ),
inference(nnf_transformation,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( ( status(sK2(X0,X1),sK3(X0,X1),X0)
& ~ status(sK2(X0,X1),sK3(X0,X1),X1) )
| ~ nota(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f24]) ).
fof(f29,plain,
! [X2,X3] : status(X2,X3,sK0),
inference(cnf_transformation,[],[f26]) ).
fof(f30,plain,
( nota(sK0,sK1)
| nevera(sK0,sK1)
| xora(sK0,sK1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f31,plain,
isa(sK0,sK1),
inference(cnf_transformation,[],[f26]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ xora(X0,X1)
| ~ status(X2,X3,X0)
| ~ status(X2,X3,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ nevera(X0,X1)
| ~ status(X2,X3,X0)
| ~ status(X2,X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X0,X1] :
( ~ nota(X0,X1)
| ~ status(sK2(X0,X1),sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ isa(X0,X1)
| ~ status(X2,X3,X0)
| status(X2,X3,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,definition,
( spl4_1
<=> xora(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f40,plain,
( xora(sK0,sK1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,definition,
( spl4_2
<=> nevera(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f43,plain,
( nevera(sK0,sK1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,definition,
( spl4_3
<=> nota(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f46,plain,
( nota(sK0,sK1)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f30,f45,f42,f39]) ).
fof(f48,plain,
( ! [X0,X1] :
( ~ status(X0,X1,sK1)
| ~ status(X0,X1,sK0) )
| ~ spl4_2 ),
inference(resolution,[],[f34,f43]) ).
fof(f49,plain,
! [X0,X1] :
( status(X0,X1,sK1)
| ~ status(X0,X1,sK0) ),
inference(resolution,[],[f37,f31]) ).
fof(f50,plain,
( ! [X0,X1] :
( ~ status(X0,X1,sK0)
| ~ status(X0,X1,sK0) )
| ~ spl4_2 ),
inference(resolution,[],[f49,f48]) ).
fof(f51,plain,
( ! [X0,X1] : ~ status(X0,X1,sK0)
| ~ spl4_2 ),
inference(duplicate_literal_removal,[],[f50]) ).
fof(f52,plain,
( $false
| ~ spl4_2 ),
inference(resolution,[],[f51,f29]) ).
fof(f53,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f52]) ).
fof(f55,plain,
( ~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK1)
| ~ spl4_3 ),
inference(resolution,[],[f46,f35]) ).
fof(f56,plain,
( ~ status(sK2(sK0,sK1),sK3(sK0,sK1),sK0)
| ~ spl4_3 ),
inference(resolution,[],[f55,f49]) ).
fof(f57,plain,
( $false
| ~ spl4_3 ),
inference(resolution,[],[f56,f29]) ).
fof(f58,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f57]) ).
fof(f59,plain,
( ! [X0,X1] :
( ~ status(X0,X1,sK1)
| ~ status(X0,X1,sK0) )
| ~ spl4_1 ),
inference(resolution,[],[f40,f33]) ).
fof(f61,plain,
( ! [X0,X1] :
( ~ status(X0,X1,sK0)
| ~ status(X0,X1,sK0) )
| ~ spl4_1 ),
inference(resolution,[],[f59,f49]) ).
fof(f62,plain,
( ! [X0,X1] : ~ status(X0,X1,sK0)
| ~ spl4_1 ),
inference(duplicate_literal_removal,[],[f61]) ).
fof(f63,plain,
( $false
| ~ spl4_1 ),
inference(resolution,[],[f62,f29]) ).
fof(f64,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f63]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
~ spl4_3,
inference(sat_conversion,[],[f58]) ).
cnf(s4,plain,
~ spl4_1,
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s2,s4]) ).
fof(f65,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS180+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n014.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 13:34:17 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.40/1.21 % (821830)Detected formulas, will run a generic FOF schedule.
% 2.40/1.21 % (821848)dis-21_1_sil=8000:lcm=predicate:random_seed=109923539:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 2.40/1.21 % (821848)First to succeed.
% 2.40/1.21 % (821848)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-821830"
% 2.40/1.21 % (821846)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1402440810:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.40/1.21 % (821847)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=249326946:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.40/1.21 % (821842)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=406127896:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.40/1.21 % (821843)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=803830507:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.40/1.21 % (821845)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=765297480:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.40/1.21 % (821844)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=725708179:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.40/1.21 % (821847)Also succeeded, but the first one will report.
% 2.40/1.21 % (821845)Also succeeded, but the first one will report.
% 2.40/1.21 % (821846)Also succeeded, but the first one will report.
% 2.40/1.21 % (821848)Refutation found. Thanks to Tanya!
% 2.40/1.21 % SZS status Theorem for theBenchmark
% 2.40/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 2.40/1.21 % (821848)------------------------------
% 2.40/1.21 % (821848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/1.21 % (821848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/1.21 % (821848)CaDiCaL version: 2.1.3
% 2.40/1.21 % (821848)Termination reason: Refutation
% 2.40/1.21 % (821848)Time elapsed: 0.002 s
% 2.40/1.21 % (821848)Peak memory usage: 89 MB
% 2.40/1.21 % (821848)Instructions burned: 2 (million)
% 2.40/1.21 % (821848)------------------------------
% 2.40/1.21 % (821848)------------------------------
% 2.40/1.21 % (821830)Success in time 0.252 s
% 2.40/1.21 % Vampire exiting
%------------------------------------------------------------------------------