%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN088+1 : TPTP v9.3.1. Released v7.3.0.
% 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 12:26:47 PM UTC 2026
% Result : Theorem 3.40s 1.35s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 1 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 24 ~; 15 |; 6 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 21 ( 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0,X1] :
( ! [X2] :
( ~ id(X2,X1)
| ~ r1(X2) )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
fof(f19,conjecture,
! [X0] :
( ! [X1] :
( ~ id(X1,X0)
| ~ r1(X1) )
| ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerounidone) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( ~ id(X1,X0)
| ~ r1(X1) )
| ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
( ? [X1] :
( id(X1,X0)
& r1(X1) )
& ? [X2] :
( r1(X2)
& r2(X2,X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
( id(sK1,sK0)
& r1(sK1)
& r1(sK2)
& r2(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f21]) ).
fof(f26,plain,
r2(sK2,sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f28,plain,
r1(sK1),
inference(cnf_transformation,[],[f22]) ).
fof(f29,plain,
id(sK1,sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ id(X2,X1)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f55,plain,
! [X2,X1] :
( ~ id(X2,X1)
| ~ r1(X2)
| sP8(X1) ),
inference(cnf_transformation,[],[f55_D]) ).
fof(f55_D,definition,
! [X1] :
( ! [X2] :
( ~ id(X2,X1)
| ~ r1(X2) )
<=> ~ sP8(X1) ),
introduced(definition,[new_symbols(definition,[sP8])],[general_splitting_component_introduction]) ).
fof(f56,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ~ sP8(X1) ),
inference(general_splitting,[],[f33,f55_D]) ).
fof(f71,plain,
~ sP8(sK0),
inference(resolution,[],[f26,f56]) ).
fof(f78,plain,
( ~ r1(sK1)
| sP8(sK0) ),
inference(resolution,[],[f29,f55]) ).
fof(f80,plain,
sP8(sK0),
inference(forward_subsumption_resolution,[],[f78,f28]) ).
fof(f82,plain,
$false,
inference(forward_subsumption_resolution,[],[f80,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN088+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 22:02:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 3.40/1.35 % (3253013)Detected formulas, will run a generic FOF schedule.
% 3.40/1.35 % (3253020)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=3851650585:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.35 % (3253019)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=515394262:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.35 % (3253021)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=790617305:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.35 % (3253018)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=4107445193:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.35 % (3253021)First to succeed.
% 3.40/1.35 % (3253021)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3253013"
% 3.40/1.35 % (3253024)dis-21_1_sil=8000:lcm=predicate:random_seed=3682136147: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)
% 3.40/1.35 % (3253022)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=264492366:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.35 % (3253023)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=464806189:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.35 % (3253022)Also succeeded, but the first one will report.
% 3.40/1.35 % (3253024)Also succeeded, but the first one will report.
% 3.40/1.35 % (3253023)Also succeeded, but the first one will report.
% 3.40/1.35 % (3253021)Refutation found. Thanks to Tanya!
% 3.40/1.35 % SZS status Theorem for theBenchmark
% 3.40/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.35 % (3253021)------------------------------
% 3.40/1.35 % (3253021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.35 % (3253021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.35 % (3253021)CaDiCaL version: 2.1.3
% 3.40/1.35 % (3253021)Termination reason: Refutation
% 3.40/1.35 % (3253021)Time elapsed: 0.003 s
% 3.40/1.35 % (3253021)Peak memory usage: 88 MB
% 3.40/1.35 % (3253021)Instructions burned: 2 (million)
% 3.40/1.35 % (3253021)------------------------------
% 3.40/1.35 % (3253021)------------------------------
% 3.40/1.35 % (3253013)Success in time 0.41 s
% 3.40/1.35 % Vampire exiting
%------------------------------------------------------------------------------