%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n012.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 12:27:06 PM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 29 unt; 0 def)
% Number of atoms : 103 ( 36 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 40 ~; 25 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 72 ( 60 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',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/Axioms/NUM008+0.ax',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/Axioms/NUM008+0.ax',axiom_1a) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( ~ r1(X2)
| X2 != X1 )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',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,
! [X1] :
( ( ~ r1(X1)
& sK0 != X1 )
| ( r1(X1)
& sK0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f16,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK1(X0) != X2 )
| ( r2(X0,X2)
& sK1(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f17,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK2(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK2(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK6(X0,X1))
& r3(X0,sK6(X0,X1),sK5(X0,X1))
& sK4(X0,X1) = sK5(X0,X1)
& r2(sK7(X0,X1),sK4(X0,X1))
& r3(X0,X1,sK7(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f5]) ).
fof(f24,plain,
( r1(sK22)
& r3(sK22,sK21,sK20)
& r1(sK23)
& r2(sK23,sK21)
& sK20 = sK24
& r1(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24)],[f14]) ).
fof(f26,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f42,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
r1(sK24),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
sK20 = sK24,
inference(cnf_transformation,[],[f24]) ).
fof(f66,plain,
r2(sK23,sK21),
inference(cnf_transformation,[],[f24]) ).
fof(f67,plain,
r1(sK23),
inference(cnf_transformation,[],[f24]) ).
fof(f68,plain,
r3(sK22,sK21,sK20),
inference(cnf_transformation,[],[f24]) ).
fof(f69,plain,
r1(sK22),
inference(cnf_transformation,[],[f24]) ).
fof(f70,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f42,f43]) ).
fof(f73,plain,
r3(sK22,sK21,sK24),
inference(definition_unfolding,[],[f68,f65]) ).
fof(f74,plain,
r1(sK0),
inference(equality_resolution,[],[f26]) ).
fof(f83,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f103,plain,
sK0 = sK22,
inference(resolution,[],[f27,f69]) ).
fof(f104,plain,
sK0 = sK23,
inference(resolution,[],[f27,f67]) ).
fof(f105,plain,
sK0 = sK24,
inference(resolution,[],[f27,f64]) ).
fof(f160,plain,
sK21 = sK1(sK23),
inference(resolution,[],[f31,f66]) ).
fof(f162,plain,
! [X0,X1] : sK1(X0) = sK6(X1,X0),
inference(resolution,[],[f31,f45]) ).
fof(f165,plain,
sK21 = sK1(sK0),
inference(forward_demodulation,[],[f160,f104]) ).
fof(f213,plain,
! [X0,X1] : ~ r1(sK5(X0,X1)),
inference(resolution,[],[f70,f83]) ).
fof(f214,plain,
! [X0,X1] : r3(X0,sK1(X1),sK5(X0,X1)),
inference(forward_demodulation,[],[f44,f162]) ).
fof(f215,plain,
! [X0] : r3(X0,sK21,sK5(X0,sK0)),
inference(superposition,[],[f214,f165]) ).
fof(f233,plain,
sK24 = sK2(sK22,sK21),
inference(resolution,[],[f35,f73]) ).
fof(f235,plain,
! [X0] : sK5(X0,sK0) = sK2(X0,sK21),
inference(resolution,[],[f35,f215]) ).
fof(f236,plain,
sK24 = sK2(sK0,sK21),
inference(forward_demodulation,[],[f233,f103]) ).
fof(f237,plain,
sK0 = sK2(sK0,sK21),
inference(forward_demodulation,[],[f236,f105]) ).
fof(f257,plain,
! [X0] : ~ r1(sK2(X0,sK21)),
inference(superposition,[],[f213,f235]) ).
fof(f260,plain,
~ r1(sK0),
inference(superposition,[],[f257,f237]) ).
fof(f261,plain,
$false,
inference(forward_subsumption_resolution,[],[f260,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN085+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 21:57:05 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.32 Running first-order model finding
% 0.03/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % (2792709)Will run a generic schedule for satisfiability detection.
% 0.07/0.36 % (2792715)% WARNING: option uhcvi not known.
% 0.07/0.36 % (2792714)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3806246050_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.36 % (2792718)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1428440547:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.36 % (2792715)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=960516547:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.36 % (2792716)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=897663859:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.36 % (2792717)dis+10_1_sil=32000:sp=arity:random_seed=3197990:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.36 % (2792719)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3577581273:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.36 % (2792720)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2701313563:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.36 % TRYING [1]
% 0.07/0.36 % TRYING [2]
% 0.07/0.36 % TRYING [3]
% 0.07/0.36 % TRYING [4]
% 0.07/0.36 % (2792716) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2792709-2792716"...
% 0.07/0.36 % (2792718) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2792709-2792718"...
% 0.07/0.36 % (2792717) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2792709-2792717"...
% 0.07/0.36 % (2792720) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2792709-2792720"...
% 0.07/0.36 % (2792715) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2792709-2792715"...
% 0.07/0.36 % (2792716)...printing done.
% 0.07/0.36 % (2792718)...printing done.
% 0.07/0.36 % (2792717)...printing done.
% 0.07/0.36 % TRYING [5]
% 0.07/0.36 % (2792720)...printing done.
% 0.07/0.36 % (2792715)...printing done.
% 0.07/0.36 % (2792716)Refutation found. Thanks to Tanya!
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.36 % (2792716)------------------------------
% 0.07/0.36 % (2792716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.36 % (2792716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.36 % (2792716)CaDiCaL version: 2.1.3
% 0.07/0.36 % (2792716)Termination reason: Refutation
% 0.07/0.36 % (2792716)Time elapsed: 0.003 s
% 0.07/0.36 % (2792716)Peak memory usage: 12 MB
% 0.07/0.36 % (2792716)Instructions burned: 7 (million)
% 0.07/0.36 % (2792709)Success in time 0.032 s
% 0.07/0.36 % Vampire exiting
%------------------------------------------------------------------------------