%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS186+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 11:41:51 AM UTC 2026
% Result : Theorem 3.44s 1.35s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 6 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 133 ( 45 ~; 54 |; 25 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 63 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ! [X2] :
( model(X2,X0)
=> model(X2,X1) )
<=> status(X0,X1,thm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
fof(f6,axiom,
! [X0,X1] :
( ( ? [X2] : model(X2,X0)
& ! [X3] :
( model(X3,X0)
<=> model(X3,X1) ) )
<=> status(X0,X1,eqv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqv) ).
fof(f21,axiom,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
=> status(X2,X3,X1) )
<=> isa(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa) ).
fof(f33,conjecture,
isa(eqv,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa_eqv_thm) ).
fof(f34,negated_conjecture,
~ isa(eqv,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ isa(eqv,thm),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
=> status(X2,X3,X1) )
=> isa(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f37,plain,
! [X0,X1] :
( isa(X0,X1)
| ? [X2,X3] :
( ~ status(X2,X3,X1)
& status(X2,X3,X0) ) ),
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] :
( isa(X0,X1)
| ( ~ status(sK0(X0,X1),sK1(X0,X1),X1)
& status(sK0(X0,X1),sK1(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f37]) ).
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(sK2(X0,X1),X1)
& model(sK2(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ! [X3] :
( ( model(X3,X0)
| ~ model(X3,X1) )
& ( model(X3,X1)
| ~ model(X3,X0) ) ) )
| ~ status(X0,X1,eqv) )
& ( status(X0,X1,eqv)
| ! [X2] : ~ model(X2,X0)
| ? [X3] :
( ( ~ model(X3,X1)
| ~ model(X3,X0) )
& ( model(X3,X1)
| model(X3,X0) ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ! [X3] :
( ( model(X3,X0)
| ~ model(X3,X1) )
& ( model(X3,X1)
| ~ model(X3,X0) ) ) )
| ~ status(X0,X1,eqv) )
& ( status(X0,X1,eqv)
| ! [X2] : ~ model(X2,X0)
| ? [X3] :
( ( ~ model(X3,X1)
| ~ model(X3,X0) )
& ( model(X3,X1)
| model(X3,X0) ) ) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ? [X2] : model(X2,X0)
& ! [X3] :
( ( model(X3,X0)
| ~ model(X3,X1) )
& ( model(X3,X1)
| ~ model(X3,X0) ) ) )
| ~ status(X0,X1,eqv) )
& ( status(X0,X1,eqv)
| ! [X4] : ~ model(X4,X0)
| ? [X5] :
( ( ~ model(X5,X1)
| ~ model(X5,X0) )
& ( model(X5,X1)
| model(X5,X0) ) ) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( ( model(sK3(X0),X0)
& ! [X3] :
( ( model(X3,X0)
| ~ model(X3,X1) )
& ( model(X3,X1)
| ~ model(X3,X0) ) ) )
| ~ status(X0,X1,eqv) )
& ( status(X0,X1,eqv)
| ! [X4] : ~ model(X4,X0)
| ( ( ~ model(sK4(X0,X1),X1)
| ~ model(sK4(X0,X1),X0) )
& ( model(sK4(X0,X1),X1)
| model(sK4(X0,X1),X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3(X0)),skolemize(X5,sK4(X0,X1))],[f46]) ).
fof(f54,plain,
~ isa(eqv,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f55,plain,
! [X0,X1] :
( status(sK0(X0,X1),sK1(X0,X1),X0)
| isa(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f56,plain,
! [X0,X1] :
( ~ status(sK0(X0,X1),sK1(X0,X1),X1)
| isa(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f57,plain,
! [X0,X1] :
( model(sK2(X0,X1),X0)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f43]) ).
fof(f58,plain,
! [X0,X1] :
( ~ model(sK2(X0,X1),X1)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f43]) ).
fof(f62,plain,
! [X3,X0,X1] :
( ~ status(X0,X1,eqv)
| ~ model(X3,X0)
| model(X3,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f95,plain,
! [X0,X1] :
( model(X1,sK1(eqv,X0))
| ~ model(X1,sK0(eqv,X0))
| isa(eqv,X0) ),
inference(resolution,[],[f55,f62]) ).
fof(f142,plain,
! [X0,X1] :
( ~ model(sK2(X0,sK1(eqv,X1)),sK0(eqv,X1))
| isa(eqv,X1)
| status(X0,sK1(eqv,X1),thm) ),
inference(resolution,[],[f95,f58]) ).
fof(f157,plain,
! [X0] :
( isa(eqv,X0)
| status(sK0(eqv,X0),sK1(eqv,X0),thm)
| status(sK0(eqv,X0),sK1(eqv,X0),thm) ),
inference(resolution,[],[f142,f57]) ).
fof(f160,plain,
! [X0] :
( status(sK0(eqv,X0),sK1(eqv,X0),thm)
| isa(eqv,X0) ),
inference(duplicate_literal_removal,[],[f157]) ).
fof(f161,plain,
( isa(eqv,thm)
| isa(eqv,thm) ),
inference(resolution,[],[f160,f56]) ).
fof(f163,plain,
isa(eqv,thm),
inference(duplicate_literal_removal,[],[f161]) ).
fof(f164,plain,
$false,
inference(forward_subsumption_resolution,[],[f163,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS186+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n011.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 13:35:45 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 3.44/1.35 % (2414354)Detected formulas, will run a generic FOF schedule.
% 3.44/1.35 % (2414359)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=4152435269:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.35 % (2414360)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=2958131315:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.35 % (2414365)dis-21_1_sil=8000:lcm=predicate:random_seed=811670004: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)
% 3.44/1.35 % (2414361)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=3186786008:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.35 % (2414362)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3235354799:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.35 % (2414362)Refutation not found, incomplete strategy
% 3.44/1.35 % (2414362)------------------------------
% 3.44/1.35 % (2414362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.35 % (2414362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.35 % (2414362)CaDiCaL version: 2.1.3
% 3.44/1.35 % (2414362)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.35 % (2414362)Time elapsed: 0.001 s
% 3.44/1.35 % (2414362)Peak memory usage: 88 MB
% 3.44/1.35 % (2414362)Instructions burned: 1 (million)
% 3.44/1.35 % (2414364)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2630536795:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.35 % (2414363)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=765094107:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.35 % (2414363)First to succeed.
% 3.44/1.35 % (2414363)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2414354"
% 3.44/1.35 % (2414364)Also succeeded, but the first one will report.
% 3.44/1.35 % (2414365)Also succeeded, but the first one will report.
% 3.44/1.35 % (2414362)------------------------------
% 3.44/1.35 % (2414362)------------------------------
% 3.44/1.35 % (2414363)Refutation found. Thanks to Tanya!
% 3.44/1.35 % SZS status Theorem for theBenchmark
% 3.44/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.35 % (2414363)------------------------------
% 3.44/1.35 % (2414363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.35 % (2414363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.35 % (2414363)CaDiCaL version: 2.1.3
% 3.44/1.35 % (2414363)Termination reason: Refutation
% 3.44/1.35 % (2414363)Time elapsed: 0.004 s
% 3.44/1.35 % (2414363)Peak memory usage: 88 MB
% 3.44/1.35 % (2414363)Instructions burned: 4 (million)
% 3.44/1.35 % (2414363)------------------------------
% 3.44/1.35 % (2414363)------------------------------
% 3.44/1.35 % (2414354)Success in time 0.417 s
% 3.44/1.35 % Vampire exiting
%------------------------------------------------------------------------------