%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:27:00 PM UTC 2026
% Result : Theorem 0.22s 0.51s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 22 unt; 2 def)
% Number of atoms : 101 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 23 |; 30 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 62 !; 24 ?)
% 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(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,X3] :
( ? [X4] :
( r4(X2,X2,X4)
& X3 = X4 )
& ? [X5] :
( r4(X1,X1,X5)
& ? [X6] :
( r4(X0,X0,X6)
& r3(X6,X5,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwo) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2,X3] :
( ? [X4] :
( r4(X2,X2,X4)
& X3 = X4 )
& ? [X5] :
( r4(X1,X1,X5)
& ? [X6] :
( r4(X0,X0,X6)
& r3(X6,X5,X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ~ r4(X2,X2,X4)
| X3 != X4 )
| ! [X5] :
( ~ r4(X1,X1,X5)
| ! [X6] :
( ~ r4(X0,X0,X6)
| ~ r3(X6,X5,X3) ) ) ),
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(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(f26,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0,X1] : r4(X0,X1,sK11(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(f53,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f21]) ).
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,X3,X0,X1,X6,X4,X5] :
( ~ r4(X2,X2,X4)
| X3 != X4
| ~ r4(X1,X1,X5)
| ~ r4(X0,X0,X6)
| ~ r3(X6,X5,X3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f66,plain,
! [X0] : r4(X0,sK15(X0),sK16(X0)),
inference(definition_unfolding,[],[f56,f54]) ).
fof(f77,plain,
! [X2,X0,X1,X6,X4,X5] :
( ~ r4(X2,X2,X4)
| ~ r4(X1,X1,X5)
| ~ r4(X0,X0,X6)
| ~ r3(X6,X5,X4) ),
inference(equality_resolution,[],[f63]) ).
fof(f99,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f100,plain,
! [X0] : sK0 = sK15(X0),
inference(resolution,[],[f26,f57]) ).
fof(f101,plain,
! [X0] : sK0 = sK16(X0),
inference(resolution,[],[f26,f55]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X4] :
( ~ r3(X3,X1,sK11(X4,X4))
| ~ r4(X2,X2,X3)
| ~ r4(X0,X0,X1) ),
inference(resolution,[],[f45,f77]) ).
fof(f125,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f126,plain,
! [X0] : r3(X0,sK0,X0),
inference(forward_demodulation,[],[f125,f99]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ r4(X0,X0,sK11(X1,X1))
| ~ r4(X2,X2,sK0) ),
inference(resolution,[],[f126,f120]) ).
fof(f131,definition,
( spl20_7
<=> ! [X2] : ~ r4(X2,X2,sK0) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
fof(f132,plain,
( ! [X2] : ~ r4(X2,X2,sK0)
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl20_8
<=> ! [X0,X1] : ~ r4(X0,X0,sK11(X1,X1)) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
fof(f135,plain,
( ! [X0,X1] : ~ r4(X0,X0,sK11(X1,X1))
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f136,plain,
( spl20_7
| spl20_8 ),
inference(avatar_split_clause,[],[f128,f134,f131]) ).
fof(f137,plain,
! [X0] : r4(X0,sK15(X0),sK0),
inference(forward_demodulation,[],[f66,f101]) ).
fof(f138,plain,
! [X0] : r4(X0,sK0,sK0),
inference(forward_demodulation,[],[f137,f100]) ).
fof(f139,plain,
( $false
| ~ spl20_7 ),
inference(resolution,[],[f138,f132]) ).
fof(f141,plain,
~ spl20_7,
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f142,plain,
( $false
| ~ spl20_8 ),
inference(resolution,[],[f135,f45]) ).
fof(f143,plain,
~ spl20_8,
inference(avatar_contradiction_clause,[],[f142]) ).
cnf(s85,plain,
( spl20_7
| spl20_8 ),
inference(sat_conversion,[],[f136]) ).
cnf(s90,plain,
~ spl20_7,
inference(sat_conversion,[],[f141]) ).
cnf(s94,plain,
~ spl20_8,
inference(sat_conversion,[],[f143]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s85,s94,s90]) ).
fof(f144,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.42 % Computer : n013.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 21:51:36 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.47 Running first-order model finding
% 0.16/0.47 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
% 0.22/0.51 % (591132)Will run a generic schedule for satisfiability detection.
% 0.22/0.51 % (591139)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2674486858:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.51 % (591139) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-591132-591139"...
% 0.22/0.51 % (591143)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3640461076:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.51 % (591139)...printing done.
% 0.22/0.51 % (591139)Refutation found. Thanks to Tanya!
% 0.22/0.51 % SZS status Theorem for theBenchmark
% 0.22/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.51 % (591139)------------------------------
% 0.22/0.51 % (591139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.51 % (591139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.51 % (591139)CaDiCaL version: 2.1.3
% 0.22/0.51 % (591139)Termination reason: Refutation
% 0.22/0.51 % (591139)Time elapsed: 0.004 s
% 0.22/0.51 % (591139)Peak memory usage: 12 MB
% 0.22/0.51 % (591139)Instructions burned: 4 (million)
% 0.22/0.51 % (591132)Success in time 0.026 s
% 0.22/0.51 % Vampire exiting
%------------------------------------------------------------------------------