%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN081+2 : 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 : n019.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 0.17s 1.20s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 61 ( 12 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 74 ( 33 ~; 23 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-1 aty)
% Number of variables : 60 ( 43 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f12,conjecture,
? [X0,X1,X2] :
( r3(X0,X1,X2)
& ? [X3] :
( X2 = X3
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xplusyeqthree) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2] :
( r3(X0,X1,X2)
& ? [X3] :
( X2 = X3
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ r3(X0,X1,X2)
| ! [X3] :
( X2 != X3
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r1(X6)
| ~ r2(X6,X5) ) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK4(X0) != X2 )
| ( r2(X0,X2)
& sK4(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f2]) ).
fof(f18,plain,
! [X0] :
( r1(sK6(X0))
& r3(X0,sK6(X0),sK5(X0))
& sK5(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f8]) ).
fof(f21,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r3(X0,X1,X2)
| X2 != X3
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X2,X0] :
( sK4(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X0] : sK5(X0) = X0,
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X0] : r3(X0,sK6(X0),sK5(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0] : r1(sK6(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f49,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ r3(X0,X1,X3)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(equality_resolution,[],[f21]) ).
fof(f54,plain,
! [X0] : r2(X0,sK4(X0)),
inference(equality_resolution,[],[f33]) ).
fof(f62,plain,
! [X0] : r3(X0,sK6(X0),X0),
inference(forward_demodulation,[],[f37,f36]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r1(X3)
| ~ r2(X0,X1) ),
inference(resolution,[],[f62,f49]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ r2(sK4(X0),X1)
| ~ r1(X0)
| ~ r2(X1,X2) ),
inference(resolution,[],[f63,f54]) ).
fof(f69,plain,
! [X0,X1] :
( ~ r2(sK4(sK4(X0)),X1)
| ~ r1(X0) ),
inference(resolution,[],[f64,f54]) ).
fof(f72,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f69,f54]) ).
fof(f76,plain,
$false,
inference(resolution,[],[f72,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN081+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 21:58:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.17/1.20 % (3449217)Detected formulas, will run a generic FOF schedule.
% 0.17/1.20 % (3449228)dis-21_1_sil=8000:lcm=predicate:random_seed=1461393583: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)
% 0.17/1.20 % (3449224)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=3463837705:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.20 % (3449227)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3309400956:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.20 % (3449223)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=849739575:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.20 % (3449222)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=3257412337:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.20 % (3449226)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=349844938:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.20 % (3449225)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4203852584:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.20 % (3449226)First to succeed.
% 0.17/1.20 % (3449225)Also succeeded, but the first one will report.
% 0.17/1.20 % (3449226)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3449217"
% 0.17/1.20 % (3449227)Also succeeded, but the first one will report.
% 0.17/1.20 % (3449228)Instruction limit reached!
% 0.17/1.20 % (3449228)------------------------------
% 0.17/1.20 % (3449228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.20 % (3449228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.20 % (3449228)CaDiCaL version: 2.1.3
% 0.17/1.20 % (3449228)Termination reason: Instruction limit
% 0.17/1.20 % (3449228)Termination phase: Saturation
% 0.17/1.20 % (3449228)Time elapsed: 0.036 s
% 0.17/1.20 % (3449228)Peak memory usage: 88 MB
% 0.17/1.20 % (3449228)Instructions burned: 129 (million)
% 0.17/1.20 % (3449236)lrs+10_1_sil=8000:sp=occurrence:random_seed=1951796003:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.17/1.20 % (3449236)Also succeeded, but the first one will report.
% 0.17/1.20 % (3449226)Refutation found. Thanks to Tanya!
% 0.17/1.20 % SZS status Theorem for theBenchmark
% 0.17/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.20 % (3449226)------------------------------
% 0.17/1.20 % (3449226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.20 % (3449226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.20 % (3449226)CaDiCaL version: 2.1.3
% 0.17/1.20 % (3449226)Termination reason: Refutation
% 0.17/1.20 % (3449226)Time elapsed: 0.002 s
% 0.17/1.20 % (3449226)Peak memory usage: 88 MB
% 0.17/1.20 % (3449226)Instructions burned: 2 (million)
% 0.17/1.20 % (3449226)------------------------------
% 0.17/1.20 % (3449226)------------------------------
% 0.17/1.20 % (3449217)Success in time 0.397 s
% 0.17/1.20 % Vampire exiting
%------------------------------------------------------------------------------