%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN085+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 : n015.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 3.66s 1.47s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 16 unt; 0 def)
% Number of atoms : 88 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 39 ~; 27 |; 26 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 60 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r3(X0,X1,X3)
& X3 != X2 )
| ( r3(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
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(f11,axiom,
! [X0,X1] :
( ! [X2] :
( ~ r1(X2)
| X2 != X1 )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
fof(f12,conjecture,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r3(X2,X1,X0) )
| ! [X3] :
( ~ r1(X3)
| ~ r2(X3,X1) ) )
| ! [X4] :
( X0 != X4
| ~ r1(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneidzero) ).
fof(f13,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r3(X2,X1,X0) )
| ! [X3] :
( ~ r1(X3)
| ~ r2(X3,X1) ) )
| ! [X4] :
( X0 != X4
| ~ r1(X4) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r3(X2,X1,X0) )
& ? [X3] :
( r1(X3)
& r2(X3,X1) ) )
& ? [X4] :
( X0 = X4
& r1(X4) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
( r1(sK2)
& r3(sK2,sK1,sK0)
& r1(sK3)
& r2(sK3,sK1)
& sK0 = sK4
& r1(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f14]) ).
fof(f18,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK9(X0) != X2 )
| ( r2(X0,X2)
& sK9(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f2]) ).
fof(f20,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(f21,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK16(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK16(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16(X0,X1))],[f3]) ).
fof(f22,plain,
r1(sK4),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
sK0 = sK4,
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
r2(sK3,sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
r3(sK2,sK1,sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f40,plain,
! [X2,X0] :
( sK9(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f46,plain,
! [X0,X1] : r2(sK15(X0,X1),sK12(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f47,plain,
! [X0,X1] : sK12(X0,X1) = sK13(X0,X1),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] : r3(X0,sK14(X0,X1),sK13(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
! [X0,X1] : r2(X1,sK14(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f52,plain,
! [X3,X0,X1] :
( sK16(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f54,plain,
r3(sK2,sK1,sK4),
inference(definition_unfolding,[],[f26,f23]) ).
fof(f55,plain,
! [X0,X1] : r2(sK15(X0,X1),sK13(X0,X1)),
inference(definition_unfolding,[],[f46,f47]) ).
fof(f56,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f28]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ r2(X1,X2)
| X0 = X2
| ~ r2(X1,X0) ),
inference(superposition,[],[f40,f40]) ).
fof(f73,plain,
! [X0,X1] : ~ r1(sK13(X0,X1)),
inference(resolution,[],[f55,f56]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( ~ r3(X1,X2,X3)
| X0 = X3
| ~ r3(X1,X2,X0) ),
inference(superposition,[],[f52,f52]) ).
fof(f143,plain,
! [X0] :
( ~ r2(sK3,X0)
| sK1 = X0 ),
inference(resolution,[],[f70,f24]) ).
fof(f156,plain,
! [X0] : sK1 = sK14(X0,sK3),
inference(resolution,[],[f143,f49]) ).
fof(f166,plain,
! [X0] : r3(X0,sK1,sK13(X0,sK3)),
inference(superposition,[],[f48,f156]) ).
fof(f197,plain,
! [X0] :
( ~ r3(sK2,sK1,X0)
| sK4 = X0 ),
inference(resolution,[],[f83,f54]) ).
fof(f205,plain,
sK4 = sK13(sK2,sK3),
inference(resolution,[],[f197,f166]) ).
fof(f247,plain,
~ r1(sK4),
inference(superposition,[],[f73,f205]) ).
fof(f249,plain,
$false,
inference(forward_subsumption_resolution,[],[f247,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN085+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n015.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 22:00:46 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 3.66/1.47 % (2050845)Detected formulas, will run a generic FOF schedule.
% 3.66/1.47 % (2050853)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4082852850:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.47 % (2050853)Refutation not found, incomplete strategy
% 3.66/1.47 % (2050853)------------------------------
% 3.66/1.47 % (2050853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.47 % (2050853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.47 % (2050853)CaDiCaL version: 2.1.3
% 3.66/1.47 % (2050853)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.47 % (2050853)Time elapsed: 0.001 s
% 3.66/1.47 % (2050853)Peak memory usage: 88 MB
% 3.66/1.47 % (2050853)Instructions burned: 1 (million)
% 3.66/1.47 % (2050852)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=3253327470:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.47 % (2050850)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=4173788745:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.47 % (2050854)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1284946640:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.47 % (2050856)dis-21_1_sil=8000:lcm=predicate:random_seed=1853095286: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)
% 3.66/1.47 % (2050851)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=1343202862:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.47 % (2050855)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1946905017:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.47 % (2050856)Refutation not found, incomplete strategy
% 3.66/1.47 % (2050856)------------------------------
% 3.66/1.47 % (2050856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.47 % (2050856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.47 % (2050856)CaDiCaL version: 2.1.3
% 3.66/1.47 % (2050856)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.47 % (2050856)Time elapsed: 0.002 s
% 3.66/1.47 % (2050856)Peak memory usage: 88 MB
% 3.66/1.47 % (2050856)Instructions burned: 2 (million)
% 3.66/1.47 % (2050855)Also succeeded, but the first one will report.
% 3.66/1.47 % (2050854)First to succeed.
% 3.66/1.47 % (2050854)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2050845"
% 3.66/1.47 % (2050853)------------------------------
% 3.66/1.47 % (2050853)------------------------------
% 3.66/1.47 % (2050864)lrs+10_1_sil=8000:sp=occurrence:random_seed=244330173:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.66/1.47 % (2050856)------------------------------
% 3.66/1.47 % (2050856)------------------------------
% 3.66/1.47 % (2050864)Also succeeded, but the first one will report.
% 3.66/1.47 % (2050854)Refutation found. Thanks to Tanya!
% 3.66/1.47 % SZS status Theorem for theBenchmark
% 3.66/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.47 % (2050854)------------------------------
% 3.66/1.47 % (2050854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.47 % (2050854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.47 % (2050854)CaDiCaL version: 2.1.3
% 3.66/1.47 % (2050854)Termination reason: Refutation
% 3.66/1.47 % (2050854)Time elapsed: 0.007 s
% 3.66/1.47 % (2050854)Peak memory usage: 88 MB
% 3.66/1.47 % (2050854)Instructions burned: 8 (million)
% 3.66/1.47 % (2050854)------------------------------
% 3.66/1.47 % (2050854)------------------------------
% 3.66/1.47 % (2050845)Success in time 0.436 s
% 3.66/1.47 % Vampire exiting
%------------------------------------------------------------------------------