%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE001+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 11:39:59 AM UTC 2026
% Result : Theorem 5.50s 2.00s
% Output : Refutation 5.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 6 unt; 1 def)
% Number of atoms : 26 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 4 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ~ leq(addition(X0,X2),addition(X0,X2))
& leq(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
( ~ leq(addition(sK0,sK2),addition(sK0,sK2))
& leq(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f19,plain,
~ leq(addition(sK0,sK2),addition(sK0,sK2)),
inference(cnf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f33,definition,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ3_eqProxy])],[equality_proxy_definition]) ).
fof(f34,plain,
! [X0,X1] :
( ~ sQ3_eqProxy(addition(X0,X1),X1)
| leq(X0,X1) ),
inference(equality_proxy_replacement,[],[f21,f33]) ).
fof(f38,plain,
! [X0] : sQ3_eqProxy(addition(X0,X0),X0),
inference(equality_proxy_replacement,[],[f24,f33]) ).
fof(f49,plain,
! [X0] : leq(X0,X0),
inference(resolution,[],[f34,f38]) ).
fof(f52,plain,
$false,
inference(resolution,[],[f49,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n013.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 12:57:21 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 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
% 5.50/2.00 % (205467)Detected formulas, will run a generic FOF schedule.
% 5.50/2.00 % (205479)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3587671446:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.50/2.00 % (205479)Refutation not found, incomplete strategy
% 5.50/2.00 % (205479)------------------------------
% 5.50/2.00 % (205479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/2.00 % (205479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/2.00 % (205479)CaDiCaL version: 2.1.3
% 5.50/2.00 % (205479)Termination reason: Refutation not found, incomplete strategy
% 5.50/2.00 % (205479)Time elapsed: 0.001 s
% 5.50/2.00 % (205479)Peak memory usage: 88 MB
% 5.50/2.00 % (205476)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=3133398139:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.50/2.00 % (205482)dis-21_1_sil=8000:lcm=predicate:random_seed=2807131889: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)
% 5.50/2.00 % (205482)First to succeed.
% 5.50/2.00 % (205482)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-205467"
% 5.50/2.00 % (205478)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=2929845613:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.50/2.00 % (205477)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=3181121136:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.50/2.00 % (205481)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3097198702:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.50/2.00 % (205480)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1586310362:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.50/2.00 % (205480)Also succeeded, but the first one will report.
% 5.50/2.00 % (205481)Also succeeded, but the first one will report.
% 5.50/2.00 % (205479)------------------------------
% 5.50/2.00 % (205479)------------------------------
% 5.50/2.00 % (205490)lrs+10_1_sil=8000:sp=occurrence:random_seed=3131246644:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 5.50/2.00 % (205490)Also succeeded, but the first one will report.
% 5.50/2.00 % (205482)Refutation found. Thanks to Tanya!
% 5.50/2.00 % SZS status Theorem for theBenchmark
% 5.50/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 5.50/2.00 % (205482)------------------------------
% 5.50/2.00 % (205482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/2.00 % (205482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/2.00 % (205482)CaDiCaL version: 2.1.3
% 5.50/2.00 % (205482)Termination reason: Refutation
% 5.50/2.00 % (205482)Time elapsed: 0.003 s
% 5.50/2.00 % (205482)Peak memory usage: 88 MB
% 5.50/2.00 % (205482)Instructions burned: 1 (million)
% 5.50/2.00 % (205482)------------------------------
% 5.50/2.00 % (205482)------------------------------
% 5.50/2.00 % (205467)Success in time 0.662 s
% 5.50/2.00 % Vampire exiting
%------------------------------------------------------------------------------