%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN081+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 : n003.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 12:27:05 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 75 ( 11 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 80 ( 28 ~; 24 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% Number of variables : 84 ( 61 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r4(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
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/sandbox2/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(f20,plain,
! [X0,X1] :
( r2(X1,sK10(X0,X1))
& r4(X0,sK10(X0,X1),sK9(X0,X1))
& sK8(X0,X1) = sK9(X0,X1)
& r3(sK11(X0,X1),X0,sK8(X0,X1))
& r4(X0,X1,sK11(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f6]) ).
fof(f21,plain,
! [X0] :
( r1(sK13(X0))
& r3(X0,sK13(X0),sK12(X0))
& sK12(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f8]) ).
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(f49,plain,
! [X0,X1] : r2(X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f51,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f55,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f63,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(f77,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,[],[f63]) ).
fof(f86,plain,
! [X0,X1] : ~ r2(X1,sK10(X0,X1)),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f94,plain,
! [X3,X0,X1,X6,X4,X5] :
( r2(X6,X5)
| r2(X4,X3)
| r2(X5,X4)
| ~ r1(X6)
| ~ r3(X0,X1,X3) ),
inference(consistent_polarity_flipping,[],[f77]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4,X5] :
( r2(sK10(X2,X3),X0)
| r2(X0,X1)
| ~ r1(X3)
| ~ r3(X4,X5,X1) ),
inference(resolution,[],[f86,f94]) ).
fof(f134,plain,
! [X2,X3,X0,X1,X4,X5] :
( r2(sK10(X0,sK10(X1,X2)),X3)
| ~ r1(X2)
| ~ r3(X4,X5,X3) ),
inference(resolution,[],[f110,f86]) ).
fof(f143,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r3(X1,X2,sK10(X3,sK10(X4,sK10(X5,X0))))
| ~ r1(X0) ),
inference(resolution,[],[f134,f86]) ).
fof(f145,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(superposition,[],[f52,f51]) ).
fof(f172,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f145,f143]) ).
fof(f177,plain,
$false,
inference(resolution,[],[f172,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN081+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:00:11 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.11/0.45 % (954819)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (954830)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=387513986:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (954830) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-954819-954830"...
% 0.11/0.45 % (954825)% WARNING: option uhcvi not known.
% 0.11/0.45 % (954830)...printing done.
% 0.11/0.45 % (954830)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (954830)------------------------------
% 0.11/0.45 % (954830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (954830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (954830)CaDiCaL version: 2.1.3
% 0.11/0.45 % (954830)Termination reason: Refutation
% 0.11/0.45 % (954830)Time elapsed: 0.003 s
% 0.11/0.45 % (954830)Peak memory usage: 12 MB
% 0.11/0.45 % (954830)Instructions burned: 7 (million)
% 0.11/0.45 % (954819)Success in time 0.027 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------