%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE066+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 11:40:14 AM UTC 2026
% Result : Theorem 3.39s 1.40s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 21 unt; 1 def)
% Number of atoms : 29 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f18,conjecture,
! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( zero != multiplication(X0,X1)
& multiplication(X0,domain(X1)) = zero ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( zero != multiplication(sK0,sK1)
& zero = multiplication(sK0,domain(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
zero = multiplication(sK0,domain(sK1)),
inference(cnf_transformation,[],[f21]) ).
fof(f23,plain,
zero != multiplication(sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f24,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f34,definition,
~ sP2(zero),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f35,plain,
sP2(multiplication(sK0,sK1)),
inference(inequality_splitting,[],[f23,f34]) ).
fof(f36,plain,
domain(zero) = domain(multiplication(sK0,sK1)),
inference(superposition,[],[f32,f22]) ).
fof(f39,plain,
zero = domain(multiplication(sK0,sK1)),
inference(forward_demodulation,[],[f36,f24]) ).
fof(f40,plain,
multiplication(zero,multiplication(sK0,sK1)) = addition(multiplication(sK0,sK1),multiplication(zero,multiplication(sK0,sK1))),
inference(superposition,[],[f33,f39]) ).
fof(f43,plain,
zero = addition(multiplication(sK0,sK1),zero),
inference(forward_demodulation,[],[f40,f25]) ).
fof(f45,plain,
zero = multiplication(sK0,sK1),
inference(forward_demodulation,[],[f43,f27]) ).
fof(f47,plain,
sP2(zero),
inference(superposition,[],[f35,f45]) ).
fof(f50,plain,
$false,
inference(forward_subsumption_resolution,[],[f47,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE066+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 13:08:38 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 3.39/1.40 % (3505671)Detected formulas, will run a generic FOF schedule.
% 3.39/1.40 % (3505735)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=4018465097:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/1.40 % (3505737)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=905624638:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/1.40 % (3505732)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=3191816140:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/1.40 % (3505734)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=4219652813:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/1.40 % (3505737)First to succeed.
% 3.39/1.40 % (3505737)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3505671"
% 3.39/1.40 % (3505740)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1894150545:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/1.40 % (3505739)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=865143063:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/1.40 % (3505741)dis-21_1_sil=8000:lcm=predicate:random_seed=2390231703: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)
% 3.39/1.40 % (3505741)Refutation not found, incomplete strategy
% 3.39/1.40 % (3505741)------------------------------
% 3.39/1.40 % (3505741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.40 % (3505741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.40 % (3505741)CaDiCaL version: 2.1.3
% 3.39/1.40 % (3505741)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.40 % (3505741)Time elapsed: 0.001 s
% 3.39/1.40 % (3505741)Peak memory usage: 88 MB
% 3.39/1.40 % (3505741)Instructions burned: 1 (million)
% 3.39/1.40 % (3505739)Also succeeded, but the first one will report.
% 3.39/1.40 % (3505740)Also succeeded, but the first one will report.
% 3.39/1.40 % (3505737)Refutation found. Thanks to Tanya!
% 3.39/1.40 % SZS status Theorem for theBenchmark
% 3.39/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.40 % (3505737)------------------------------
% 3.51/1.40 % (3505737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.40 % (3505737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.40 % (3505737)CaDiCaL version: 2.1.3
% 3.51/1.40 % (3505737)Termination reason: Refutation
% 3.51/1.40 % (3505737)Time elapsed: 0.003 s
% 3.51/1.40 % (3505737)Peak memory usage: 88 MB
% 3.51/1.40 % (3505737)Instructions burned: 1 (million)
% 3.51/1.40 % (3505737)------------------------------
% 3.51/1.40 % (3505737)------------------------------
% 3.51/1.40 % (3505671)Success in time 0.423 s
% 3.51/1.40 % Vampire exiting
%------------------------------------------------------------------------------