%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS261+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 : n026.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 11:41:59 AM UTC 2026
% Result : Theorem 3.38s 1.38s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 187 ( 65 ~; 81 |; 34 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 114 ( 93 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ! [X2] :
( model(X2,X0)
=> model(X2,X1) )
<=> status(X0,X1,thm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
fof(f9,axiom,
! [X0,X1] :
( ( ? [X2] : model(X2,X0)
& ? [X3] : ~ model(X3,X0)
& ! [X4] :
( model(X4,X0)
<=> model(X4,X1) ) )
<=> status(X0,X1,eth) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eth) ).
fof(f20,axiom,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& status(X2,X3,X1) )
<=> mighta(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta) ).
fof(f32,axiom,
? [X0,X1,X2] :
( model(X0,X1)
& ~ model(X0,X2)
& ? [X3] : model(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_thm_spt) ).
fof(f33,conjecture,
mighta(eth,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta_eth_thm) ).
fof(f34,negated_conjecture,
~ mighta(eth,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ mighta(eth,thm),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
& status(X2,X3,X1) )
=> mighta(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f37,plain,
! [X0,X1] :
( mighta(X0,X1)
| ! [X2,X3] :
( ~ status(X2,X3,X0)
| ~ status(X2,X3,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
<=> status(X0,X1,thm) ),
inference(ennf_transformation,[],[f5]) ).
fof(f40,plain,
! [X0,X1] :
( ( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
| ~ status(X0,X1,thm) )
& ( status(X0,X1,thm)
| ? [X2] :
( ~ model(X2,X1)
& model(X2,X0) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f41,plain,
! [X0,X1] :
( ( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
| ~ status(X0,X1,thm) )
& ( status(X0,X1,thm)
| ? [X3] :
( ~ model(X3,X1)
& model(X3,X0) ) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( ! [X2] :
( model(X2,X1)
| ~ model(X2,X0) )
| ~ status(X0,X1,thm) )
& ( status(X0,X1,thm)
| ( ~ model(sK0(X0,X1),X1)
& model(sK0(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ? [X3] : ~ model(X3,X0)
& ! [X4] :
( ( model(X4,X0)
| ~ model(X4,X1) )
& ( model(X4,X1)
| ~ model(X4,X0) ) ) )
| ~ status(X0,X1,eth) )
& ( status(X0,X1,eth)
| ! [X2] : ~ model(X2,X0)
| ! [X3] : model(X3,X0)
| ? [X4] :
( ( ~ model(X4,X1)
| ~ model(X4,X0) )
& ( model(X4,X1)
| model(X4,X0) ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ? [X3] : ~ model(X3,X0)
& ! [X4] :
( ( model(X4,X0)
| ~ model(X4,X1) )
& ( model(X4,X1)
| ~ model(X4,X0) ) ) )
| ~ status(X0,X1,eth) )
& ( status(X0,X1,eth)
| ! [X2] : ~ model(X2,X0)
| ! [X3] : model(X3,X0)
| ? [X4] :
( ( ~ model(X4,X1)
| ~ model(X4,X0) )
& ( model(X4,X1)
| model(X4,X0) ) ) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ? [X3] : ~ model(X3,X0)
& ! [X4] :
( ( model(X4,X0)
| ~ model(X4,X1) )
& ( model(X4,X1)
| ~ model(X4,X0) ) ) )
| ~ status(X0,X1,eth) )
& ( status(X0,X1,eth)
| ! [X5] : ~ model(X5,X0)
| ! [X6] : model(X6,X0)
| ? [X7] :
( ( ~ model(X7,X1)
| ~ model(X7,X0) )
& ( model(X7,X1)
| model(X7,X0) ) ) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( model(sK1(X0),X0)
& ~ model(sK2(X0),X0)
& ! [X4] :
( ( model(X4,X0)
| ~ model(X4,X1) )
& ( model(X4,X1)
| ~ model(X4,X0) ) ) )
| ~ status(X0,X1,eth) )
& ( status(X0,X1,eth)
| ! [X5] : ~ model(X5,X0)
| ! [X6] : model(X6,X0)
| ( ( ~ model(sK3(X0,X1),X1)
| ~ model(sK3(X0,X1),X0) )
& ( model(sK3(X0,X1),X1)
| model(sK3(X0,X1),X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0)),skolemize(X3,sK2(X0)),skolemize(X7,sK3(X0,X1))],[f45]) ).
fof(f47,plain,
( model(sK4,sK5)
& ~ model(sK4,sK6)
& model(sK7,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f32]) ).
fof(f53,plain,
~ mighta(eth,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ status(X2,X3,X1)
| ~ status(X2,X3,X0)
| mighta(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X0,X1] :
( model(sK0(X0,X1),X0)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f42]) ).
fof(f56,plain,
! [X0,X1] :
( ~ model(sK0(X0,X1),X1)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
! [X0,X1,X6,X5] :
( model(sK3(X0,X1),X1)
| ~ model(X5,X0)
| model(X6,X0)
| status(X0,X1,eth)
| model(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X0,X1,X6,X5] :
( ~ model(sK3(X0,X1),X1)
| ~ model(X5,X0)
| model(X6,X0)
| status(X0,X1,eth)
| ~ model(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f64,plain,
model(sK7,sK6),
inference(cnf_transformation,[],[f47]) ).
fof(f65,plain,
~ model(sK4,sK6),
inference(cnf_transformation,[],[f47]) ).
fof(f82,plain,
! [X0] :
( status(X0,X0,thm)
| status(X0,X0,thm) ),
inference(resolution,[],[f56,f55]) ).
fof(f85,plain,
! [X0] : status(X0,X0,thm),
inference(duplicate_literal_removal,[],[f82]) ).
fof(f94,plain,
! [X0,X1] :
( ~ status(X0,X0,X1)
| mighta(X1,thm) ),
inference(resolution,[],[f54,f85]) ).
fof(f105,plain,
! [X0,X1] :
( ~ model(sK3(X0,X0),X0)
| model(X1,X0)
| status(X0,X0,eth)
| ~ model(sK3(X0,X0),X0) ),
inference(factoring,[],[f59]) ).
fof(f107,plain,
! [X0,X1] :
( ~ model(sK3(X0,X0),X0)
| model(X1,X0)
| status(X0,X0,eth) ),
inference(duplicate_literal_removal,[],[f105]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( model(X0,X1)
| status(X1,X1,eth)
| ~ model(X2,X1)
| model(X3,X1)
| status(X1,X1,eth)
| model(sK3(X1,X1),X1) ),
inference(resolution,[],[f107,f58]) ).
fof(f112,plain,
! [X2,X3,X0,X1] :
( model(X0,X1)
| status(X1,X1,eth)
| ~ model(X2,X1)
| model(X3,X1)
| model(sK3(X1,X1),X1) ),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( status(X1,X1,eth)
| model(X0,X1)
| ~ model(X2,X1)
| model(X3,X1) ),
inference(forward_subsumption_resolution,[],[f112,f107]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( model(X0,X1)
| ~ model(X2,X1)
| model(X3,X1)
| mighta(eth,thm) ),
inference(resolution,[],[f113,f94]) ).
fof(f150,plain,
! [X2,X3,X0,X1] :
( model(X3,X1)
| ~ model(X2,X1)
| model(X0,X1) ),
inference(forward_subsumption_resolution,[],[f147,f53]) ).
fof(f162,plain,
! [X0,X1] :
( model(X1,sK6)
| ~ model(X0,sK6) ),
inference(resolution,[],[f150,f65]) ).
fof(f176,plain,
! [X0] : ~ model(X0,sK6),
inference(resolution,[],[f162,f65]) ).
fof(f184,plain,
$false,
inference(resolution,[],[f176,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS261+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 13:50:42 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.38/1.38 % (2861275)Detected formulas, will run a generic FOF schedule.
% 3.38/1.38 % (2861280)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=632850047:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.38/1.38 % (2861285)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1850391491:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.38/1.38 % (2861284)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3733102252:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.38/1.38 % (2861283)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3029786057:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.38/1.38 % (2861282)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=2378799018:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.38/1.38 % (2861281)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=662316270:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.38/1.38 % (2861283)Refutation not found, incomplete strategy
% 3.38/1.38 % (2861283)------------------------------
% 3.38/1.38 % (2861283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.38 % (2861283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.38 % (2861283)CaDiCaL version: 2.1.3
% 3.38/1.38 % (2861283)Termination reason: Refutation not found, incomplete strategy
% 3.38/1.38 % (2861283)Time elapsed: 0.001 s
% 3.38/1.38 % (2861283)Peak memory usage: 88 MB
% 3.38/1.38 % (2861283)Instructions burned: 1 (million)
% 3.38/1.38 % (2861284)First to succeed.
% 3.38/1.38 % (2861284)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2861275"
% 3.38/1.38 % (2861286)dis-21_1_sil=8000:lcm=predicate:random_seed=1421298335:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.38/1.38 % (2861285)Also succeeded, but the first one will report.
% 3.38/1.38 % (2861286)Also succeeded, but the first one will report.
% 3.38/1.38 % (2861283)------------------------------
% 3.38/1.38 % (2861283)------------------------------
% 3.38/1.38 % (2861284)Refutation found. Thanks to Tanya!
% 3.38/1.38 % SZS status Theorem for theBenchmark
% 3.38/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.38 % (2861284)------------------------------
% 3.38/1.38 % (2861284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.38 % (2861284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.38 % (2861284)CaDiCaL version: 2.1.3
% 3.38/1.38 % (2861284)Termination reason: Refutation
% 3.38/1.38 % (2861284)Time elapsed: 0.004 s
% 3.38/1.38 % (2861284)Peak memory usage: 88 MB
% 3.38/1.38 % (2861284)Instructions burned: 5 (million)
% 3.38/1.38 % (2861284)------------------------------
% 3.38/1.38 % (2861284)------------------------------
% 3.38/1.38 % (2861275)Success in time 0.41 s
% 3.38/1.38 % Vampire exiting
%------------------------------------------------------------------------------