%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN056+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 12:26:59 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 31 unt; 3 def)
% Number of atoms : 223 ( 33 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 281 ( 131 ~; 103 |; 44 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 167 ( 0 sgn 138 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(f12,conjecture,
? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r1(X4)
& r2(X4,X3) ) ) ) )
& ? [X5] :
( ? [X6] :
( r3(X6,X5,X0)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) )
& ? [X8] :
( r2(X8,X5)
& ? [X9] :
( r1(X9)
& r2(X9,X8) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneplustwoeqthree) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r1(X4)
& r2(X4,X3) ) ) ) )
& ? [X5] :
( ? [X6] :
( r3(X6,X5,X0)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) )
& ? [X8] :
( r2(X8,X5)
& ? [X9] :
( r1(X9)
& r2(X9,X8) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( X0 != X1
| ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r2(X3,X2)
| ! [X4] :
( ~ r1(X4)
| ~ r2(X4,X3) ) ) ) )
| ! [X5] :
( ! [X6] :
( ~ r3(X6,X5,X0)
| ! [X7] :
( ~ r1(X7)
| ~ r2(X7,X6) ) )
| ! [X8] :
( ~ r2(X8,X5)
| ! [X9] :
( ~ r1(X9)
| ~ r2(X9,X8) ) ) ) ),
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(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(f25,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : sK4(X0,X1) = sK5(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
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(f63,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( X0 != X1
| ~ r2(X2,X1)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X6,X5,X0)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X8,X5)
| ~ r1(X9)
| ~ r2(X9,X8) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
! [X0,X1] : r2(sK7(X0,X1),sK5(X0,X1)),
inference(definition_unfolding,[],[f41,f42]) ).
fof(f67,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f69,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f77,plain,
! [X2,X3,X1,X8,X6,X9,X7,X4,X5] :
( ~ r3(X6,X5,X1)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r2(X2,X1)
| ~ r1(X7)
| ~ r2(X7,X6)
| ~ r2(X8,X5)
| ~ r1(X9)
| ~ r2(X9,X8) ),
inference(equality_resolution,[],[f63]) ).
fof(f82,definition,
( spl20_2
<=> ! [X4] : ~ r1(X4) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f83,plain,
( ! [X4] : ~ r1(X4)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f87,plain,
( $false
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f67,f83]) ).
fof(f88,plain,
~ spl20_2,
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f96,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f120,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f121,plain,
! [X0] : r3(X0,sK0,X0),
inference(forward_demodulation,[],[f120,f96]) ).
fof(f143,plain,
! [X0,X1] : sK1(X0) = sK6(X1,X0),
inference(resolution,[],[f30,f44]) ).
fof(f196,plain,
! [X0,X1] : r3(X0,sK1(X1),sK5(X0,X1)),
inference(forward_demodulation,[],[f43,f143]) ).
fof(f197,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r2(X1,sK5(X3,X4))
| ~ r1(X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1)
| ~ r1(X5)
| ~ r2(X5,X3)
| ~ r2(X6,sK1(X4))
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(resolution,[],[f196,f77]) ).
fof(f204,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r1(X0)
| ~ r2(X0,X1)
| ~ r2(X1,sK7(X2,X3))
| ~ r1(X4)
| ~ r2(X4,X2)
| ~ r2(X5,sK1(X3))
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(resolution,[],[f197,f64]) ).
fof(f224,plain,
! [X0,X1] : sK2(X0,X1) = sK7(X0,X1),
inference(resolution,[],[f34,f40]) ).
fof(f226,plain,
! [X0] : sK2(X0,sK0) = X0,
inference(resolution,[],[f34,f121]) ).
fof(f325,plain,
! [X0,X1] : r2(sK2(X0,X1),sK5(X0,X1)),
inference(superposition,[],[f64,f224]) ).
fof(f330,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r2(X1,sK2(X2,X3))
| ~ r1(X0)
| ~ r2(X0,X1)
| ~ r1(X4)
| ~ r2(X4,X2)
| ~ r2(X5,sK1(X3))
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(forward_demodulation,[],[f204,f224]) ).
fof(f348,plain,
! [X0] : r2(X0,sK5(X0,sK0)),
inference(superposition,[],[f325,f226]) ).
fof(f350,plain,
! [X0] : sK1(X0) = sK5(X0,sK0),
inference(resolution,[],[f348,f30]) ).
fof(f355,plain,
! [X0] : r3(X0,sK1(sK0),sK1(X0)),
inference(superposition,[],[f196,f350]) ).
fof(f361,plain,
! [X0] : sK1(X0) = sK2(X0,sK1(sK0)),
inference(resolution,[],[f355,f34]) ).
fof(f366,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X1,sK1(X0))
| ~ r1(X2)
| ~ r2(X2,X1)
| ~ r1(X3)
| ~ r2(X3,X0)
| ~ r2(X4,sK1(sK1(sK0)))
| ~ r1(X5)
| ~ r2(X5,X4) ),
inference(superposition,[],[f330,f361]) ).
fof(f373,definition,
( spl20_22
<=> ! [X4,X5] :
( ~ r2(X4,sK1(sK1(sK0)))
| ~ r1(X5)
| ~ r2(X5,X4) ) ),
introduced(definition,[new_symbols(definition,[spl20_22])],[avatar_definition]) ).
fof(f374,plain,
( ! [X4,X5] :
( ~ r2(X4,sK1(sK1(sK0)))
| ~ r1(X5)
| ~ r2(X5,X4) )
| ~ spl20_22 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f376,definition,
( spl20_23
<=> ! [X0,X3,X2,X1] :
( ~ r2(X1,sK1(X0))
| ~ r1(X3)
| ~ r2(X3,X0)
| ~ r1(X2)
| ~ r2(X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl20_23])],[avatar_definition]) ).
fof(f377,plain,
( ! [X2,X3,X0,X1] :
( ~ r2(X1,sK1(X0))
| ~ r1(X3)
| ~ r2(X3,X0)
| ~ r1(X2)
| ~ r2(X2,X1) )
| ~ spl20_23 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f378,plain,
( spl20_22
| spl20_23 ),
inference(avatar_split_clause,[],[f366,f376,f373]) ).
fof(f381,plain,
( ! [X0] :
( ~ r2(X0,sK1(sK0))
| ~ r1(X0) )
| ~ spl20_22 ),
inference(resolution,[],[f374,f69]) ).
fof(f382,plain,
( ~ r1(sK0)
| ~ spl20_22 ),
inference(resolution,[],[f381,f69]) ).
fof(f383,plain,
( $false
| ~ spl20_22 ),
inference(forward_subsumption_resolution,[],[f382,f67]) ).
fof(f384,plain,
~ spl20_22,
inference(avatar_contradiction_clause,[],[f383]) ).
fof(f385,plain,
( ! [X2,X0,X1] :
( ~ r2(X2,X1)
| ~ r2(X0,X1)
| ~ r1(X2)
| ~ r1(X0) )
| ~ spl20_23 ),
inference(resolution,[],[f377,f69]) ).
fof(f388,plain,
( ! [X0,X1] :
( ~ r2(X0,sK1(X1))
| ~ r1(X1)
| ~ r1(X0) )
| ~ spl20_23 ),
inference(resolution,[],[f385,f69]) ).
fof(f398,plain,
( ! [X0] :
( ~ r1(X0)
| ~ r1(X0) )
| ~ spl20_23 ),
inference(resolution,[],[f388,f69]) ).
fof(f400,plain,
( ! [X0] : ~ r1(X0)
| ~ spl20_23 ),
inference(duplicate_literal_removal,[],[f398]) ).
fof(f403,plain,
( spl20_2
| ~ spl20_23 ),
inference(avatar_split_clause,[],[f400,f376,f82]) ).
cnf(s37,plain,
~ spl20_2,
inference(sat_conversion,[],[f88]) ).
cnf(s241,plain,
( spl20_22
| spl20_23 ),
inference(sat_conversion,[],[f378]) ).
cnf(s249,plain,
~ spl20_22,
inference(sat_conversion,[],[f384]) ).
cnf(s266,plain,
( spl20_2
| ~ spl20_23 ),
inference(sat_conversion,[],[f403]) ).
cnf(s267,plain,
spl20_23,
inference(rat,[],[s241,s249]) ).
cnf(s268,plain,
spl20_2,
inference(rat,[],[s266,s267]) ).
cnf(s271,plain,
$false,
inference(rat,[],[s37,s268]) ).
fof(f404,plain,
$false,
inference(avatar_sat_refutation,[],[s271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN056+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n006.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 21:51:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.48 % (3356548)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3356556)dis+10_1_sil=32000:sp=arity:random_seed=6190446:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3356554)% WARNING: option uhcvi not known.
% 0.16/0.48 % (3356554)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3526952289:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (3356553)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1268529814_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (3356555)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=46287296:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3356557)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=407608184:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % TRYING [5]
% 0.16/0.48 % (3356555) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3356548-3356555"...
% 0.16/0.48 % (3356558)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=713292780:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (3356559)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=484640147:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (3356555)...printing done.
% 0.16/0.48 % (3356555)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3356555)------------------------------
% 0.16/0.48 % (3356555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3356555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3356555)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3356555)Termination reason: Refutation
% 0.16/0.48 % (3356555)Time elapsed: 0.011 s
% 0.16/0.48 % (3356555)Peak memory usage: 12 MB
% 0.16/0.48 % (3356555)Instructions burned: 14 (million)
% 0.16/0.48 % (3356548)Success in time 0.053 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------