%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM505+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:24:35 PM UTC 2026
% Result : Theorem 0.22s 0.54s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 9 unt; 2 def)
% Number of atoms : 113 ( 26 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 130 ( 55 ~; 42 |; 26 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 17 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f50,conjecture,
( ~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xk,X0) = xp )
| sdtlseqdt0(xk,xp) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ( ~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xk,X0) = xp )
| sdtlseqdt0(xk,xp) ) ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f59,plain,
~ ( ~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtpldt0(xk,X1) )
| sdtlseqdt0(xk,xp) ) ) ),
inference(rectify,[],[f51]) ).
fof(f89,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f94,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f95,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f94]) ).
fof(f133,plain,
( ( xp = xk
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| xp != sdtpldt0(xk,X1) )
& ~ sdtlseqdt0(xk,xp) ) )
& ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xp,X0) != xk )
& ~ sdtlseqdt0(xp,xk) ),
inference(ennf_transformation,[],[f59]) ).
fof(f134,plain,
( ( xp = xk
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| xp != sdtpldt0(xk,X1) )
& ~ sdtlseqdt0(xk,xp) ) )
& ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xp,X0) != xk )
& ~ sdtlseqdt0(xp,xk) ),
inference(flattening,[],[f133]) ).
fof(f165,plain,
( ( xp = xk
| ( ! [X0] :
( ~ aNaturalNumber0(X0)
| xp != sdtpldt0(xk,X0) )
& ~ sdtlseqdt0(xk,xp) ) )
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xk != sdtpldt0(xp,X1) )
& ~ sdtlseqdt0(xp,xk) ),
inference(rectify,[],[f134]) ).
fof(f196,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f199,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f234,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f275,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f294,plain,
~ sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f165]) ).
fof(f296,plain,
( xp = xk
| ~ sdtlseqdt0(xk,xp) ),
inference(cnf_transformation,[],[f165]) ).
fof(f312,definition,
( spl16_1
<=> sdtlseqdt0(xk,xp) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f314,plain,
( ~ sdtlseqdt0(xk,xp)
| spl16_1 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f316,definition,
( spl16_2
<=> xp = xk ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f318,plain,
( xp = xk
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f319,plain,
( ~ spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f296,f316,f312]) ).
fof(f344,plain,
( ~ sdtlseqdt0(xp,xp)
| ~ spl16_2 ),
inference(superposition,[],[f294,f318]) ).
fof(f354,plain,
( ~ aNaturalNumber0(xp)
| ~ spl16_2 ),
inference(resolution,[],[f196,f344]) ).
fof(f355,plain,
( $false
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f354,f234]) ).
fof(f356,plain,
~ spl16_2,
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f482,plain,
( sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| spl16_1 ),
inference(resolution,[],[f199,f314]) ).
fof(f489,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f482,f294]) ).
fof(f491,plain,
( ~ aNaturalNumber0(xk)
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f489,f234]) ).
fof(f494,plain,
( $false
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f491,f275]) ).
fof(f495,plain,
spl16_1,
inference(avatar_contradiction_clause,[],[f494]) ).
cnf(s1,plain,
( ~ spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f319]) ).
cnf(s7,plain,
~ spl16_2,
inference(sat_conversion,[],[f356]) ).
cnf(s9,plain,
spl16_1,
inference(sat_conversion,[],[f495]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s7,s9]) ).
fof(f496,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM505+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.43 % Computer : n011.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 27 20:14:45 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.22/0.49 Running first-order model finding
% 0.22/0.49 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
% 0.22/0.54 % (2731877)Will run a generic schedule for satisfiability detection.
% 0.22/0.54 % (2731882)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2663252805_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.54 % (2731885)dis+10_1_sil=32000:sp=arity:random_seed=1185660401:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.54 % Detected minimum model sizes of [3]
% 0.22/0.54 % Detected maximum model sizes of [max]
% 0.22/0.54 % TRYING [3]
% 0.22/0.54 % (2731883)% WARNING: option uhcvi not known.
% 0.22/0.54 % (2731885) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2731877-2731885"...
% 0.22/0.54 % (2731885)...printing done.
% 0.22/0.54 % (2731885)Refutation found. Thanks to Tanya!
% 0.22/0.54 % SZS status Theorem for theBenchmark
% 0.22/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.54 % (2731885)------------------------------
% 0.22/0.54 % (2731885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.54 % (2731885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.54 % (2731885)CaDiCaL version: 2.1.3
% 0.22/0.54 % (2731885)Termination reason: Refutation
% 0.22/0.54 % (2731885)Time elapsed: 0.009 s
% 0.22/0.54 % (2731885)Peak memory usage: 13 MB
% 0.22/0.54 % (2731885)Instructions burned: 12 (million)
% 0.22/0.54 % (2731877)Success in time 0.039 s
% 0.22/0.54 % Vampire exiting
%------------------------------------------------------------------------------