%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE003+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 : 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 11:40:00 AM UTC 2026
% Result : Theorem 2.69s 1.36s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 7 unt; 2 def)
% Number of atoms : 31 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 11 ~; 9 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f13,conjecture,
( ! [X0] : addition(X0,X0) = X0
<=> addition(one,one) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f14,negated_conjecture,
~ ( ! [X0] : addition(X0,X0) = X0
<=> addition(one,one) = one ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
( ! [X0] : addition(X0,X0) = X0
<~> addition(one,one) = one ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
( ( one != addition(one,one)
| ? [X0] : addition(X0,X0) != X0 )
& ( addition(one,one) = one
| ! [X0] : addition(X0,X0) = X0 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f17,plain,
( ( one != addition(one,one)
| ? [X0] : addition(X0,X0) != X0 )
& ( addition(one,one) = one
| ! [X1] : addition(X1,X1) = X1 ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
( ( one != addition(one,one)
| sK0 != addition(sK0,sK0) )
& ( addition(one,one) = one
| ! [X1] : addition(X1,X1) = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f17]) ).
fof(f20,plain,
( one != addition(one,one)
| sK0 != addition(sK0,sK0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f21,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f26,definition,
~ sP1(one),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
fof(f27,definition,
~ sP2(sK0),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f28,plain,
( sP1(addition(one,one))
| sP2(addition(sK0,sK0)) ),
inference(inequality_splitting,[],[f20,f27,f26]) ).
fof(f29,plain,
( sP1(one)
| sP2(addition(sK0,sK0)) ),
inference(forward_demodulation,[],[f28,f21]) ).
fof(f30,plain,
sP2(addition(sK0,sK0)),
inference(forward_subsumption_resolution,[],[f29,f26]) ).
fof(f31,plain,
sP2(sK0),
inference(forward_demodulation,[],[f30,f21]) ).
fof(f32,plain,
$false,
inference(forward_subsumption_resolution,[],[f31,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE003+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 12:58:00 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.69/1.36 % (2380272)Detected formulas, will run a generic FOF schedule.
% 2.69/1.36 % (2380380)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=820278865:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.36 % (2380380)First to succeed.
% 2.69/1.36 % (2380380)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2380272"
% 2.69/1.36 % (2380377)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=2246446857:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.36 % (2380378)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=1691250952:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.36 % (2380379)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=3581788932:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.36 % (2380383)dis-21_1_sil=8000:lcm=predicate:random_seed=1879305921: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)
% 2.69/1.36 % (2380382)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1401263680:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.36 % (2380381)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2379165229:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.36 % (2380381)Also succeeded, but the first one will report.
% 2.69/1.36 % (2380382)Also succeeded, but the first one will report.
% 2.69/1.36 % (2380383)Also succeeded, but the first one will report.
% 2.69/1.36 % (2380380)Refutation found. Thanks to Tanya!
% 2.69/1.36 % SZS status Theorem for theBenchmark
% 2.69/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.36 % (2380380)------------------------------
% 2.69/1.36 % (2380380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.36 % (2380380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.36 % (2380380)CaDiCaL version: 2.1.3
% 2.69/1.36 % (2380380)Termination reason: Refutation
% 2.69/1.36 % (2380380)Time elapsed: 0.001 s
% 2.69/1.36 % (2380380)Peak memory usage: 88 MB
% 2.69/1.36 % (2380380)------------------------------
% 2.69/1.36 % (2380380)------------------------------
% 2.69/1.36 % (2380272)Success in time 0.311 s
% 2.69/1.36 % Vampire exiting
%------------------------------------------------------------------------------