%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN087+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 : n007.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 3.55s 1.39s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 53 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 50 ( 21 ~; 13 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 34 ( 24 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
fof(f12,conjecture,
? [X0] :
( ? [X1] :
( r1(X1)
& r4(X1,X1,X0) )
& ? [X2] :
( r1(X2)
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimeszeroeqzero) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( r1(X1)
& r4(X1,X1,X0) )
& ? [X2] :
( r1(X2)
& X0 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( ~ r1(X1)
| ~ r4(X1,X1,X0) )
| ! [X2] :
( ~ r1(X2)
| X0 != X2 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( ~ r1(X1)
& sK0 != X1 )
| ( r1(X1)
& sK0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f22,plain,
! [X0] :
( r1(sK15(X0))
& r4(X0,sK15(X0),sK14(X0))
& r1(sK16(X0))
& sK14(X0) = sK16(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f9]) ).
fof(f25,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f54,plain,
! [X0] : sK14(X0) = sK16(X0),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f57,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r1(X1)
| ~ r4(X1,X1,X0)
| ~ r1(X2)
| X0 != X2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f74,plain,
! [X2,X1] :
( ~ r1(X1)
| ~ r4(X1,X1,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f75,plain,
! [X0] :
( ~ r1(X0)
| ~ r4(X0,X0,X0) ),
inference(factoring,[],[f74]) ).
fof(f76,plain,
~ r4(sK0,sK0,sK0),
inference(resolution,[],[f64,f75]) ).
fof(f86,plain,
! [X0] : sK0 = sK15(X0),
inference(resolution,[],[f26,f57]) ).
fof(f90,plain,
! [X0] : r1(sK14(X0)),
inference(superposition,[],[f55,f54]) ).
fof(f94,plain,
! [X0] : sK0 = sK14(X0),
inference(resolution,[],[f90,f26]) ).
fof(f138,plain,
! [X0] : r4(X0,sK15(X0),sK0),
inference(superposition,[],[f56,f94]) ).
fof(f144,plain,
! [X0] : r4(X0,sK0,sK0),
inference(forward_demodulation,[],[f138,f86]) ).
fof(f165,plain,
$false,
inference(resolution,[],[f144,f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN087+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 : n007.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 21:58:10 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
% 3.55/1.39 % (1816777)Detected formulas, will run a generic FOF schedule.
% 3.55/1.39 % (1816786)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3178440645:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.55/1.39 % (1816785)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2464118963:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.55/1.39 % (1816788)dis-21_1_sil=8000:lcm=predicate:random_seed=2794924646: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)
% 3.55/1.39 % (1816787)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2432316442:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.55/1.39 % (1816782)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=1007694082:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.55/1.39 % (1816783)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=2848447874:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.55/1.39 % (1816784)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=2720738093:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.55/1.39 % (1816785)Refutation not found, incomplete strategy
% 3.55/1.39 % (1816785)------------------------------
% 3.55/1.39 % (1816785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.39 % (1816785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.39 % (1816785)CaDiCaL version: 2.1.3
% 3.55/1.39 % (1816785)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.39 % (1816785)Time elapsed: 0.002 s
% 3.55/1.39 % (1816785)Peak memory usage: 88 MB
% 3.55/1.39 % (1816785)Instructions burned: 1 (million)
% 3.55/1.39 % (1816788)Refutation not found, incomplete strategy
% 3.55/1.39 % (1816788)------------------------------
% 3.55/1.39 % (1816788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.39 % (1816788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.39 % (1816788)CaDiCaL version: 2.1.3
% 3.55/1.39 % (1816788)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.39 % (1816788)Time elapsed: 0.002 s
% 3.55/1.39 % (1816788)Peak memory usage: 88 MB
% 3.55/1.39 % (1816788)Instructions burned: 2 (million)
% 3.55/1.39 % (1816787)First to succeed.
% 3.55/1.39 % (1816787)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1816777"
% 3.55/1.39 % (1816786)Instruction limit reached!
% 3.55/1.39 % (1816786)------------------------------
% 3.55/1.39 % (1816786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.39 % (1816786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.39 % (1816786)CaDiCaL version: 2.1.3
% 3.55/1.39 % (1816786)Termination reason: Instruction limit
% 3.55/1.39 % (1816786)Termination phase: Saturation
% 3.55/1.39 % (1816786)Time elapsed: 0.039 s
% 3.55/1.39 % (1816786)Peak memory usage: 88 MB
% 3.55/1.39 % (1816786)Instructions burned: 119 (million)
% 3.55/1.39 % (1816796)lrs+10_1_sil=8000:sp=occurrence:random_seed=3390264729:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.55/1.39 % (1816796)Also succeeded, but the first one will report.
% 3.55/1.39 % (1816788)------------------------------
% 3.55/1.39 % (1816788)------------------------------
% 3.55/1.39 % (1816785)------------------------------
% 3.55/1.39 % (1816785)------------------------------
% 3.55/1.39 % (1816787)Refutation found. Thanks to Tanya!
% 3.55/1.39 % SZS status Theorem for theBenchmark
% 3.55/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.39 % (1816787)------------------------------
% 3.55/1.39 % (1816787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.39 % (1816787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.39 % (1816787)CaDiCaL version: 2.1.3
% 3.55/1.39 % (1816787)Termination reason: Refutation
% 3.55/1.39 % (1816787)Time elapsed: 0.005 s
% 3.55/1.39 % (1816787)Peak memory usage: 88 MB
% 3.55/1.39 % (1816787)Instructions burned: 5 (million)
% 3.55/1.39 % (1816787)------------------------------
% 3.55/1.39 % (1816787)------------------------------
% 3.55/1.39 % (1816777)Success in time 0.437 s
% 3.55/1.39 % Vampire exiting
%------------------------------------------------------------------------------