%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 12 unt; 2 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 79 ( 36 ~; 27 |; 14 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 52 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(f6,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(f12,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( id(X3,X2)
& ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
fof(f18,axiom,
! [X0,X1] :
( ! [X2] :
( ~ id(X2,X1)
| ~ r1(X2) )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(f19,conjecture,
! [X0] :
? [X1,X2] :
( ! [X3] :
( ~ id(X2,X3)
| ~ r1(X3) )
& ? [X4] :
( id(X4,X1)
& r3(X0,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbersid) ).
fof(f20,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ! [X3] :
( ~ id(X2,X3)
| ~ r1(X3) )
& ? [X4] :
( id(X4,X1)
& r3(X0,X2,X4) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
! [X1,X2] :
( ? [X3] :
( id(X2,X3)
& r1(X3) )
| ! [X4] :
( ~ id(X4,X1)
| ~ r3(X0,X2,X4) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f26,plain,
! [X0,X1] :
( id(sK5(X0,X1),sK4(X0,X1))
& r2(X1,sK6(X0,X1))
& r3(X0,sK6(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))],[f12]) ).
fof(f31,plain,
! [X1,X2] :
( ( id(X2,sK21(X2))
& r1(sK21(X2)) )
| ! [X4] :
( ~ id(X4,X1)
| ~ r3(sK20,X2,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X0,sK20),skolemize(X3,sK21(X2))],[f21]) ).
fof(f48,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f67,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f70,plain,
! [X0,X1] : r2(X1,sK6(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f90,plain,
! [X2,X1,X4] :
( ~ r3(sK20,X2,X4)
| ~ id(X4,X1)
| r1(sK21(X2)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f91,plain,
! [X2,X1,X4] :
( ~ r3(sK20,X2,X4)
| ~ id(X4,X1)
| id(X2,sK21(X2)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ id(X0,sK6(X1,X2))
| ~ r1(X0) ),
inference(resolution,[],[f70,f89]) ).
fof(f189,definition,
( spl22_12
<=> ! [X2] : r1(sK21(X2)) ),
introduced(definition,[new_symbols(definition,[spl22_12])],[avatar_definition]) ).
fof(f190,plain,
( ! [X2] : r1(sK21(X2))
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f191,plain,
! [X0,X1] :
( ~ id(sK7(sK20,X0),X1)
| r1(sK21(X0)) ),
inference(resolution,[],[f90,f67]) ).
fof(f193,definition,
( spl22_13
<=> ! [X2] : id(X2,sK21(X2)) ),
introduced(definition,[new_symbols(definition,[spl22_13])],[avatar_definition]) ).
fof(f194,plain,
( ! [X2] : id(X2,sK21(X2))
| ~ spl22_13 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f195,plain,
! [X0,X1] :
( ~ id(sK7(sK20,X0),X1)
| id(X0,sK21(X0)) ),
inference(resolution,[],[f91,f67]) ).
fof(f196,plain,
( ! [X0] : id(sK21(X0),X0)
| ~ spl22_13 ),
inference(resolution,[],[f194,f49]) ).
fof(f199,plain,
( ! [X0,X1] : ~ r1(sK21(sK6(X0,X1)))
| ~ spl22_13 ),
inference(resolution,[],[f196,f125]) ).
fof(f203,plain,
( $false
| ~ spl22_12
| ~ spl22_13 ),
inference(forward_subsumption_resolution,[],[f199,f190]) ).
fof(f204,plain,
( ~ spl22_12
| ~ spl22_13 ),
inference(avatar_contradiction_clause,[],[f203]) ).
fof(f208,plain,
! [X0] : r1(sK21(X0)),
inference(resolution,[],[f191,f48]) ).
fof(f218,plain,
! [X0] : id(X0,sK21(X0)),
inference(resolution,[],[f195,f48]) ).
fof(f222,plain,
spl22_13,
inference(avatar_split_clause,[],[f218,f193]) ).
fof(f226,plain,
spl22_12,
inference(avatar_split_clause,[],[f208,f189]) ).
cnf(s150,plain,
( ~ spl22_12
| ~ spl22_13 ),
inference(sat_conversion,[],[f204]) ).
cnf(s177,plain,
spl22_13,
inference(sat_conversion,[],[f222]) ).
cnf(s186,plain,
spl22_12,
inference(sat_conversion,[],[f226]) ).
cnf(s187,plain,
$false,
inference(rat,[],[s150,s177,s186]) ).
fof(f227,plain,
$false,
inference(avatar_sat_refutation,[],[s187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 21:52:17 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.12/0.46 % (1210008)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (1210015)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2791809848:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.46 % (1210015) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1210008-1210015"...
% 0.12/0.46 % (1210014)% WARNING: option uhcvi not known.
% 0.12/0.46 % (1210015)...printing done.
% 0.12/0.46 % (1210015)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (1210015)------------------------------
% 0.12/0.46 % (1210015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.47 % (1210015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.47 % (1210015)CaDiCaL version: 2.1.3
% 0.12/0.47 % (1210015)Termination reason: Refutation
% 0.12/0.47 % (1210015)Time elapsed: 0.003 s
% 0.12/0.47 % (1210015)Peak memory usage: 12 MB
% 0.12/0.47 % (1210015)Instructions burned: 5 (million)
% 0.12/0.47 % (1210008)Success in time 0.036 s
% 0.12/0.47 % Vampire exiting
%------------------------------------------------------------------------------