%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS264+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 2.73s 1.35s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 222 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 272 ( 98 ~; 113 |; 52 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 152 ( 118 !; 34 ?)
% 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(f12,axiom,
! [X0,X1] :
( ( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X0)
=> model(X3,X1) )
& ? [X4] :
( model(X4,X1)
& ~ model(X4,X0) )
& ? [X5] : ~ model(X5,X1) )
<=> status(X0,X1,wth) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wth) ).
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(f31,axiom,
? [X0,X1] :
( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X0)
=> model(X3,X1) )
& ? [X4] :
( ~ model(X4,X0)
& model(X4,X1) )
& ? [X5] : ~ model(X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mixed_pair) ).
fof(f33,conjecture,
mighta(wth,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta_wth_thm) ).
fof(f34,negated_conjecture,
~ mighta(wth,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ mighta(wth,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(f39,plain,
! [X0,X1] :
( ( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X1)
| ~ model(X3,X0) )
& ? [X4] :
( model(X4,X1)
& ~ model(X4,X0) )
& ? [X5] : ~ model(X5,X1) )
<=> status(X0,X1,wth) ),
inference(ennf_transformation,[],[f12]) ).
fof(f40,plain,
? [X0,X1] :
( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X1)
| ~ model(X3,X0) )
& ? [X4] :
( ~ model(X4,X0)
& model(X4,X1) )
& ? [X5] : ~ model(X5,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f41,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(f42,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,[],[f41]) ).
fof(f43,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))],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X1)
| ~ model(X3,X0) )
& ? [X4] :
( model(X4,X1)
& ~ model(X4,X0) )
& ? [X5] : ~ model(X5,X1) )
| ~ status(X0,X1,wth) )
& ( status(X0,X1,wth)
| ! [X2] : ~ model(X2,X0)
| ? [X3] :
( ~ model(X3,X1)
& model(X3,X0) )
| ! [X4] :
( ~ model(X4,X1)
| model(X4,X0) )
| ! [X5] : model(X5,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X1)
| ~ model(X3,X0) )
& ? [X4] :
( model(X4,X1)
& ~ model(X4,X0) )
& ? [X5] : ~ model(X5,X1) )
| ~ status(X0,X1,wth) )
& ( status(X0,X1,wth)
| ! [X2] : ~ model(X2,X0)
| ? [X3] :
( ~ model(X3,X1)
& model(X3,X0) )
| ! [X4] :
( ~ model(X4,X1)
| model(X4,X0) )
| ! [X5] : model(X5,X1) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X1)
| ~ model(X3,X0) )
& ? [X4] :
( model(X4,X1)
& ~ model(X4,X0) )
& ? [X5] : ~ model(X5,X1) )
| ~ status(X0,X1,wth) )
& ( status(X0,X1,wth)
| ! [X6] : ~ model(X6,X0)
| ? [X7] :
( ~ model(X7,X1)
& model(X7,X0) )
| ! [X8] :
( ~ model(X8,X1)
| model(X8,X0) )
| ! [X9] : model(X9,X1) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( ( model(sK1(X0),X0)
& ! [X3] :
( model(X3,X1)
| ~ model(X3,X0) )
& model(sK2(X0,X1),X1)
& ~ model(sK2(X0,X1),X0)
& ~ model(sK3(X1),X1) )
| ~ status(X0,X1,wth) )
& ( status(X0,X1,wth)
| ! [X6] : ~ model(X6,X0)
| ( ~ model(sK4(X0,X1),X1)
& model(sK4(X0,X1),X0) )
| ! [X8] :
( ~ model(X8,X1)
| model(X8,X0) )
| ! [X9] : model(X9,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X2,sK1(X0)),skolemize(X4,sK2(X0,X1)),skolemize(X5,sK3(X1)),skolemize(X7,sK4(X0,X1))],[f46]) ).
fof(f49,plain,
( model(sK11,sK9)
& ! [X3] :
( model(X3,sK10)
| ~ model(X3,sK9) )
& ~ model(sK12,sK9)
& model(sK12,sK10)
& ~ model(sK13,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X4,sK12),skolemize(X5,sK13)],[f40]) ).
fof(f54,plain,
~ mighta(wth,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ status(X2,X3,X1)
| ~ status(X2,X3,X0)
| mighta(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
! [X0,X1] :
( model(sK0(X0,X1),X0)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X0,X1] :
( ~ model(sK0(X0,X1),X1)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X0,X1,X8,X6,X9] :
( model(sK4(X0,X1),X0)
| ~ model(X6,X0)
| status(X0,X1,wth)
| ~ model(X8,X1)
| model(X8,X0)
| model(X9,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f60,plain,
! [X0,X1,X8,X6,X9] :
( ~ model(sK4(X0,X1),X1)
| ~ model(X6,X0)
| status(X0,X1,wth)
| ~ model(X8,X1)
| model(X8,X0)
| model(X9,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f69,plain,
~ model(sK13,sK10),
inference(cnf_transformation,[],[f49]) ).
fof(f70,plain,
model(sK12,sK10),
inference(cnf_transformation,[],[f49]) ).
fof(f71,plain,
~ model(sK12,sK9),
inference(cnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X3] :
( model(X3,sK10)
| ~ model(X3,sK9) ),
inference(cnf_transformation,[],[f49]) ).
fof(f73,plain,
model(sK11,sK9),
inference(cnf_transformation,[],[f49]) ).
fof(f86,plain,
! [X0] :
( ~ model(sK0(X0,sK10),sK9)
| status(X0,sK10,thm) ),
inference(resolution,[],[f57,f72]) ).
fof(f96,plain,
( status(sK9,sK10,thm)
| status(sK9,sK10,thm) ),
inference(resolution,[],[f86,f56]) ).
fof(f97,plain,
status(sK9,sK10,thm),
inference(duplicate_literal_removal,[],[f96]) ).
fof(f103,plain,
! [X0] :
( ~ status(sK9,sK10,X0)
| mighta(X0,thm) ),
inference(resolution,[],[f97,f55]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( ~ model(sK4(X1,sK10),sK9)
| status(X1,sK10,wth)
| ~ model(X2,sK10)
| model(X2,X1)
| model(X3,sK10)
| ~ model(X0,X1) ),
inference(resolution,[],[f60,f72]) ).
fof(f125,plain,
! [X0,X1] :
( ~ model(sK4(sK9,sK10),sK9)
| status(sK9,sK10,wth)
| ~ model(X0,sK10)
| model(X0,sK9)
| model(X1,sK10) ),
inference(factoring,[],[f111]) ).
fof(f136,plain,
! [X2,X3,X0,X1,X4] :
( status(sK9,sK10,wth)
| ~ model(X0,sK10)
| model(X0,sK9)
| model(X1,sK10)
| ~ model(X2,sK9)
| status(sK9,sK10,wth)
| ~ model(X3,sK10)
| model(X3,sK9)
| model(X4,sK10) ),
inference(resolution,[],[f125,f59]) ).
fof(f137,plain,
! [X2,X3,X0,X1,X4] :
( status(sK9,sK10,wth)
| ~ model(X0,sK10)
| model(X0,sK9)
| model(X1,sK10)
| ~ model(X2,sK9)
| ~ model(X3,sK10)
| model(X3,sK9)
| model(X4,sK10) ),
inference(duplicate_literal_removal,[],[f136]) ).
fof(f152,plain,
! [X2,X3,X0,X1,X4] :
( ~ model(X0,sK10)
| model(X0,sK9)
| model(X1,sK10)
| ~ model(X2,sK9)
| ~ model(X3,sK10)
| model(X3,sK9)
| model(X4,sK10)
| mighta(wth,thm) ),
inference(resolution,[],[f137,f103]) ).
fof(f155,plain,
! [X2,X3,X0,X1,X4] :
( model(X4,sK10)
| model(X0,sK9)
| model(X1,sK10)
| ~ model(X2,sK9)
| ~ model(X3,sK10)
| model(X3,sK9)
| ~ model(X0,sK10) ),
inference(forward_subsumption_resolution,[],[f152,f54]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( model(X3,sK9)
| model(X1,sK10)
| ~ model(X2,sK9)
| ~ model(X3,sK10)
| model(X0,sK9)
| ~ model(X0,sK10) ),
inference(resolution,[],[f155,f69]) ).
fof(f168,plain,
! [X2,X0,X1] :
( model(X0,sK10)
| ~ model(X1,sK9)
| ~ model(sK12,sK10)
| model(X2,sK9)
| ~ model(X2,sK10) ),
inference(resolution,[],[f159,f71]) ).
fof(f170,plain,
! [X2,X0,X1] :
( model(X2,sK9)
| ~ model(X1,sK9)
| model(X0,sK10)
| ~ model(X2,sK10) ),
inference(forward_subsumption_resolution,[],[f168,f70]) ).
fof(f178,plain,
! [X0,X1] :
( ~ model(X0,sK9)
| model(X1,sK10)
| ~ model(sK12,sK10) ),
inference(resolution,[],[f170,f71]) ).
fof(f180,plain,
! [X0,X1] :
( model(X1,sK10)
| ~ model(X0,sK9) ),
inference(forward_subsumption_resolution,[],[f178,f70]) ).
fof(f185,plain,
! [X0] : ~ model(X0,sK9),
inference(resolution,[],[f180,f69]) ).
fof(f193,plain,
$false,
inference(resolution,[],[f185,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS264+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 13:51:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.73/1.35 % (2862507)Detected formulas, will run a generic FOF schedule.
% 2.73/1.35 % (2862516)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1901332210:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.35 % (2862516)First to succeed.
% 2.73/1.35 % (2862516)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2862507"
% 2.73/1.35 % (2862515)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1569848441:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.35 % (2862512)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=3877686368:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.35 % (2862518)dis-21_1_sil=8000:lcm=predicate:random_seed=3683396747: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)
% 2.73/1.35 % (2862514)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=122940107:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.35 % (2862513)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=4237086269:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.35 % (2862515)Refutation not found, incomplete strategy
% 2.73/1.35 % (2862515)------------------------------
% 2.73/1.35 % (2862515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (2862515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (2862515)CaDiCaL version: 2.1.3
% 2.73/1.35 % (2862515)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.35 % (2862515)Time elapsed: 0.002 s
% 2.73/1.35 % (2862515)Peak memory usage: 88 MB
% 2.73/1.35 % (2862515)Instructions burned: 1 (million)
% 2.73/1.35 % (2862517)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=883421166:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.35 % (2862517)Also succeeded, but the first one will report.
% 2.73/1.35 % (2862518)Instruction limit reached!
% 2.73/1.35 % (2862518)------------------------------
% 2.73/1.35 % (2862518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (2862518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (2862518)CaDiCaL version: 2.1.3
% 2.73/1.35 % (2862518)Termination reason: Instruction limit
% 2.73/1.35 % (2862518)Termination phase: Saturation
% 2.73/1.35 % (2862518)Time elapsed: 0.078 s
% 2.73/1.35 % (2862518)Peak memory usage: 90 MB
% 2.73/1.35 % (2862518)Instructions burned: 130 (million)
% 2.73/1.35 % (2862516)Refutation found. Thanks to Tanya!
% 2.73/1.35 % SZS status Theorem for theBenchmark
% 2.73/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.35 % (2862516)------------------------------
% 2.73/1.35 % (2862516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (2862516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (2862516)CaDiCaL version: 2.1.3
% 2.73/1.35 % (2862516)Termination reason: Refutation
% 2.73/1.35 % (2862516)Time elapsed: 0.003 s
% 2.73/1.35 % (2862516)Peak memory usage: 88 MB
% 2.73/1.35 % (2862516)Instructions burned: 8 (million)
% 2.73/1.35 % (2862516)------------------------------
% 2.73/1.35 % (2862516)------------------------------
% 2.73/1.35 % (2862507)Success in time 0.302 s
% 2.73/1.35 % Vampire exiting
%------------------------------------------------------------------------------