%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN069+2 : 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 : n018.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 3.44s 1.46s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 5 unt; 1 def)
% Number of atoms : 44 ( 12 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 45 ( 18 ~; 10 |; 16 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 21 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f5,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f12,conjecture,
? [X0] :
( X0 = X0
& ? [X1] :
( r1(X1)
& r2(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneeqone) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( X0 = X0
& ? [X1] :
( r1(X1)
& r2(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( X0 != X0
| ! [X1] :
( ~ r1(X1)
| ~ r2(X1,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK14(X0,X1))
& r3(X0,sK14(X0,X1),sK13(X0,X1))
& sK12(X0,X1) = sK13(X0,X1)
& r2(sK15(X0,X1),sK12(X0,X1))
& r3(X0,X1,sK15(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1)),skolemize(X4,sK14(X0,X1)),skolemize(X5,sK15(X0,X1))],[f5]) ).
fof(f23,plain,
! [X1] :
( ( ~ r1(X1)
& sK19 != X1 )
| ( r1(X1)
& sK19 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f1]) ).
fof(f24,plain,
! [X0,X1] :
( X0 != X0
| ~ r1(X1)
| ~ r2(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f47,plain,
! [X0,X1] : r2(X1,sK14(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f61,plain,
! [X1] :
( sK19 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f75,plain,
r1(sK19),
inference(equality_resolution,[],[f61]) ).
fof(f77,definition,
! [X0,X1] :
( sQ20_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ20_eqProxy])],[equality_proxy_definition]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sQ20_eqProxy(X0,X0)
| ~ r1(X1)
| ~ r2(X1,X0) ),
inference(equality_proxy_replacement,[],[f24,f77]) ).
fof(f92,plain,
! [X0] : sQ20_eqProxy(X0,X0),
inference(equality_proxy_axiom,[],[f77]) ).
fof(f99,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ r2(X0,X1) ),
inference(resolution,[],[f92,f78]) ).
fof(f103,plain,
! [X0] : ~ r2(sK19,X0),
inference(resolution,[],[f99,f75]) ).
fof(f110,plain,
$false,
inference(resolution,[],[f103,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN069+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n018.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:55:24 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.44/1.46 % (2768990)Detected formulas, will run a generic FOF schedule.
% 3.44/1.46 % (2768997)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=42453055:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.46 % (2768998)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3002283518:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.46 % (2768996)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=2745313769:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.46 % (2768995)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=4062398020:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.46 % (2768998)Refutation not found, incomplete strategy
% 3.44/1.46 % (2768998)------------------------------
% 3.44/1.46 % (2768998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.46 % (2768998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.46 % (2768998)CaDiCaL version: 2.1.3
% 3.44/1.46 % (2768998)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.46 % (2768998)Time elapsed: 0.001 s
% 3.44/1.46 % (2768998)Peak memory usage: 88 MB
% 3.44/1.46 % (2769000)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4170687636:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.46 % (2769001)dis-21_1_sil=8000:lcm=predicate:random_seed=312698310: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)
% 3.44/1.46 % (2769000)Also succeeded, but the first one will report.
% 3.44/1.46 % (2769001)First to succeed.
% 3.44/1.46 % (2769001)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2768990"
% 3.44/1.46 % (2768999)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1247431445:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.46 % (2768999)Also succeeded, but the first one will report.
% 3.44/1.46 % (2768998)------------------------------
% 3.44/1.46 % (2768998)------------------------------
% 3.44/1.46 % (2769001)Refutation found. Thanks to Tanya!
% 3.44/1.46 % SZS status Theorem for theBenchmark
% 3.44/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.46 % (2769001)------------------------------
% 3.44/1.46 % (2769001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.46 % (2769001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.46 % (2769001)CaDiCaL version: 2.1.3
% 3.44/1.46 % (2769001)Termination reason: Refutation
% 3.44/1.46 % (2769001)Time elapsed: 0.002 s
% 3.44/1.46 % (2769001)Peak memory usage: 88 MB
% 3.44/1.46 % (2769001)Instructions burned: 2 (million)
% 3.44/1.46 % (2769001)------------------------------
% 3.44/1.46 % (2769001)------------------------------
% 3.44/1.46 % (2768990)Success in time 0.405 s
% 3.44/1.46 % Vampire exiting
%------------------------------------------------------------------------------