%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN069+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:26:43 PM UTC 2026
% Result : Theorem 2.55s 1.32s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 33 ( 10 ~; 5 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 30 ( 19 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f13,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( id(X3,X2)
& ? [X4] :
( r2(X1,X4)
& r4(X0,X4,X3) ) )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
fof(f16,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( id(X1,X3)
& r1(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f19,conjecture,
? [X0] :
( id(X0,X0)
& ? [X1] :
( r1(X1)
& r2(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneidone) ).
fof(f20,negated_conjecture,
~ ? [X0] :
( id(X0,X0)
& ? [X1] :
( r1(X1)
& r2(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0] :
( ~ id(X0,X0)
| ! [X1] :
( ~ r1(X1)
| ~ r2(X1,X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f23,plain,
! [X0] :
( r1(sK4(X0))
& r4(X0,sK4(X0),sK3(X0))
& id(sK3(X0),sK5(X0))
& r1(sK5(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0)),skolemize(X3,sK5(X0))],[f16]) ).
fof(f25,plain,
! [X0,X1] :
( id(sK9(X0,X1),sK8(X0,X1))
& r2(X1,sK10(X0,X1))
& r4(X0,sK10(X0,X1),sK9(X0,X1))
& r3(sK11(X0,X1),X0,sK8(X0,X1))
& r4(X0,X1,sK11(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f13]) ).
fof(f31,plain,
! [X0,X1] :
( ~ r1(X1)
| ~ id(X0,X0)
| ~ r2(X1,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0] : r1(sK5(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f48,plain,
! [X0,X1] : r2(X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f25]) ).
fof(f73,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f90,plain,
! [X0,X1] :
( ~ r2(sK5(X1),X0)
| ~ id(X0,X0) ),
inference(resolution,[],[f37,f31]) ).
fof(f93,plain,
! [X0,X1] : ~ id(sK10(X0,sK5(X1)),sK10(X0,sK5(X1))),
inference(resolution,[],[f48,f90]) ).
fof(f99,plain,
$false,
inference(resolution,[],[f93,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN069+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 21:53:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.55/1.32 % (2795725)Detected formulas, will run a generic FOF schedule.
% 2.55/1.32 % (2795736)dis-21_1_sil=8000:lcm=predicate:random_seed=3440619068: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)
% 2.55/1.32 % (2795736)First to succeed.
% 2.55/1.32 % (2795736)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2795725"
% 2.55/1.32 % (2795733)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1886012310:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.32 % (2795734)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1822304465:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.32 % (2795730)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=1859406125:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.32 % (2795731)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=1716553766:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.32 % (2795732)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=4292249632:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.32 % (2795735)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1476913403:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.32 % (2795734)Also succeeded, but the first one will report.
% 2.55/1.32 % (2795735)Also succeeded, but the first one will report.
% 2.55/1.32 % (2795733)Instruction limit reached!
% 2.55/1.32 % (2795733)------------------------------
% 2.55/1.32 % (2795733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.32 % (2795733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.32 % (2795733)CaDiCaL version: 2.1.3
% 2.55/1.32 % (2795733)Termination reason: Instruction limit
% 2.55/1.32 % (2795733)Termination phase: Saturation
% 2.55/1.32 % (2795733)Time elapsed: 0.065 s
% 2.55/1.32 % (2795733)Peak memory usage: 88 MB
% 2.55/1.32 % (2795733)Instructions burned: 111 (million)
% 2.55/1.32 % (2795736)Refutation found. Thanks to Tanya!
% 2.55/1.32 % SZS status Theorem for theBenchmark
% 2.55/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.32 % (2795736)------------------------------
% 2.55/1.32 % (2795736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.32 % (2795736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.32 % (2795736)CaDiCaL version: 2.1.3
% 2.55/1.32 % (2795736)Termination reason: Refutation
% 2.55/1.32 % (2795736)Time elapsed: 0.001 s
% 2.55/1.32 % (2795736)Peak memory usage: 88 MB
% 2.55/1.32 % (2795736)Instructions burned: 2 (million)
% 2.55/1.32 % (2795736)------------------------------
% 2.55/1.32 % (2795736)------------------------------
% 2.55/1.32 % (2795725)Success in time 0.275 s
% 2.55/1.32 % Vampire exiting
%------------------------------------------------------------------------------