%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN081+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 : n002.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 12:26:46 PM UTC 2026
% Result : Theorem 3.66s 1.49s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 82 ( 33 ~; 23 |; 26 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 66 ( 45 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( id(X1,X0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f12,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( id(X3,X2)
& ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f15,axiom,
! [X0] :
? [X1] :
( id(X1,X0)
& ? [X2] :
( r1(X2)
& r3(X0,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f19,conjecture,
? [X0,X1,X2] :
( r3(X0,X1,X2)
& ? [X3] :
( id(X2,X3)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xplusyidthree) ).
fof(f20,negated_conjecture,
~ ? [X0,X1,X2] :
( r3(X0,X1,X2)
& ? [X3] :
( id(X2,X3)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ r3(X0,X1,X2)
| ! [X3] :
( ~ id(X2,X3)
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r1(X6)
| ~ r2(X6,X5) ) ) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f23,plain,
! [X1] :
( ( id(X1,sK3)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f1]) ).
fof(f25,plain,
! [X0] :
( id(sK5(X0),X0)
& r1(sK6(X0))
& r3(X0,sK6(X0),sK5(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f15]) ).
fof(f26,plain,
! [X0,X1] :
( id(sK8(X0,X1),sK7(X0,X1))
& r2(X1,sK9(X0,X1))
& r3(X0,sK9(X0,X1),sK8(X0,X1))
& r2(sK10(X0,X1),sK7(X0,X1))
& r3(X0,X1,sK10(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1)),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f12]) ).
fof(f28,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r3(X0,X1,X2)
| ~ id(X2,X3)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X1] :
( ~ id(X1,sK3)
| r1(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0] : r3(X0,sK6(X0),sK5(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
! [X0] : id(sK5(X0),X0),
inference(cnf_transformation,[],[f25]) ).
fof(f60,plain,
! [X0,X1] : r2(X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f71,plain,
r1(sK5(sK3)),
inference(resolution,[],[f41,f56]) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4] :
( ~ id(sK5(X0),X1)
| ~ r2(X2,X1)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3) ),
inference(resolution,[],[f54,f28]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r1(X3)
| ~ r2(X0,X1) ),
inference(resolution,[],[f77,f56]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( ~ r2(sK9(X0,X1),X2)
| ~ r1(X1)
| ~ r2(X2,X3) ),
inference(resolution,[],[f78,f60]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( ~ r2(sK9(X1,sK9(X2,X0)),X3)
| ~ r1(X0) ),
inference(resolution,[],[f83,f60]) ).
fof(f108,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f106,f60]) ).
fof(f116,plain,
$false,
inference(resolution,[],[f108,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN081+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:01:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.66/1.49 % (3928981)Detected formulas, will run a generic FOF schedule.
% 3.66/1.49 % (3929083)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=1727553755:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.49 % (3929084)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=131820043:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.49 % (3929085)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2741741722:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.49 % (3929082)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=1726711397:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.49 % (3929086)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2888236650:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.49 % (3929087)dis-21_1_sil=8000:lcm=predicate:random_seed=1741500610: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)
% 3.66/1.49 % (3929085)First to succeed.
% 3.66/1.49 % (3929087)Also succeeded, but the first one will report.
% 3.66/1.49 % (3929085)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3928981"
% 3.66/1.49 % (3929086)Also succeeded, but the first one will report.
% 3.66/1.49 % (3929084)Also succeeded, but the first one will report.
% 3.66/1.49 % (3929081)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=3225378122:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.49 % (3929085)Refutation found. Thanks to Tanya!
% 3.66/1.49 % SZS status Theorem for theBenchmark
% 3.66/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.49 % (3929085)------------------------------
% 3.66/1.49 % (3929085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.49 % (3929085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.49 % (3929085)CaDiCaL version: 2.1.3
% 3.66/1.49 % (3929085)Termination reason: Refutation
% 3.66/1.49 % (3929085)Time elapsed: 0.003 s
% 3.66/1.49 % (3929085)Peak memory usage: 88 MB
% 3.66/1.49 % (3929085)Instructions burned: 2 (million)
% 3.66/1.49 % (3929085)------------------------------
% 3.66/1.49 % (3929085)------------------------------
% 3.66/1.49 % (3928981)Success in time 0.437 s
% 3.66/1.49 % Vampire exiting
%------------------------------------------------------------------------------