%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM667_8 : TPTP v9.3.1. Released v8.0.0.
% 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 12:25:16 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 106 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 99 ( 45 ~; 40 |; 3 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
y: nat ).
tff(func_def_2,type,
z: nat ).
tff(pred_def_1,type,
less: ( nat * nat ) > $o ).
tff(f1,axiom,
( ~ less(x,y)
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(f2,axiom,
( ~ less(y,z)
=> ( y = z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( ~ less(X0,X1)
=> ( X0 = X1 ) )
=> ( less(X1,X2)
=> less(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a) ).
tff(f6,conjecture,
( ~ less(x,z)
=> ( x = z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz17) ).
tff(f7,negated_conjecture,
~ ( ~ less(x,z)
=> ( x = z ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f10,plain,
( ( x = y )
| less(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f11,plain,
( ( y = z )
| less(y,z) ),
inference(ennf_transformation,[],[f2]) ).
tff(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X2)
| ~ less(X1,X2)
| ( ( X0 != X1 )
& ~ less(X0,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f14,plain,
! [X0: nat,X1: nat,X2: nat] :
( less(X0,X2)
| ~ less(X1,X2)
| ( ( X0 != X1 )
& ~ less(X0,X1) ) ),
inference(flattening,[],[f13]) ).
tff(f17,plain,
( ( x != z )
& ~ less(x,z) ),
inference(ennf_transformation,[],[f7]) ).
tff(f18,plain,
( less(x,y)
| ( x = y ) ),
inference(cnf_transformation,[],[f10]) ).
tff(f19,plain,
( less(y,z)
| ( y = z ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f20,plain,
! [X2: nat,X0: nat,X1: nat] :
( ~ less(X0,X1)
| ~ less(X1,X2)
| less(X0,X2) ),
inference(cnf_transformation,[],[f14]) ).
tff(f24,plain,
~ less(x,z),
inference(cnf_transformation,[],[f17]) ).
tff(f25,plain,
x != z,
inference(cnf_transformation,[],[f17]) ).
tff(f28,plain,
( ~ less(x,y)
| ( x = y ) ),
inference(consistent_polarity_flipping,[],[f18]) ).
tff(f29,plain,
( ~ less(y,z)
| ( y = z ) ),
inference(consistent_polarity_flipping,[],[f19]) ).
tff(f31,plain,
! [X2: nat,X0: nat,X1: nat] :
( ~ less(X0,X2)
| less(X1,X2)
| less(X0,X1) ),
inference(consistent_polarity_flipping,[],[f20]) ).
tff(f34,plain,
less(x,z),
inference(consistent_polarity_flipping,[],[f24]) ).
tff(f36,definition,
( spl0_1
<=> ( y = z ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f38,plain,
( ( y = z )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f40,definition,
( spl0_2
<=> less(y,z) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f42,plain,
( ~ less(y,z)
| spl0_2 ),
inference(avatar_component_clause,[],[f40]) ).
tff(f43,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f29,f40,f36]) ).
tff(f45,definition,
( spl0_3
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f47,plain,
( ( x = y )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f45]) ).
tff(f49,definition,
( spl0_4
<=> less(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f51,plain,
( ~ less(x,y)
| spl0_4 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f52,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f28,f49,f45]) ).
tff(f53,plain,
! [X0: nat] :
( less(X0,z)
| less(x,X0) ),
inference(resolution,[],[f31,f34]) ).
tff(f54,plain,
( less(x,y)
| spl0_2 ),
inference(resolution,[],[f53,f42]) ).
tff(f60,plain,
( less(x,y)
| ~ spl0_1 ),
inference(superposition,[],[f34,f38]) ).
tff(f61,plain,
( ( x != y )
| ~ spl0_1 ),
inference(superposition,[],[f25,f38]) ).
tff(f62,plain,
( ~ spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f61,f36,f45]) ).
tff(f63,plain,
( $false
| ~ spl0_1
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f60,f51]) ).
tff(f64,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f63]) ).
tff(f65,plain,
( spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f54,f40,f49]) ).
tff(f72,plain,
( ~ less(x,z)
| spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f42,f47]) ).
tff(f73,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f72,f34]) ).
tff(f74,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f73]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f62]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f64]) ).
cnf(s6,plain,
( spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s8,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f74]) ).
cnf(s9,plain,
spl0_2,
inference(rat,[],[s2,s6,s8]) ).
cnf(s10,plain,
spl0_1,
inference(rat,[],[s1,s9]) ).
cnf(s11,plain,
spl0_4,
inference(rat,[],[s5,s10]) ).
cnf(s12,plain,
~ spl0_3,
inference(rat,[],[s4,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s2,s11,s12]) ).
tff(f75,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM667_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:01:17 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.17/0.47 % (1156890)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1156896)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1156896)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=268959148:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1156896) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1156890-1156896"...
% 0.17/0.47 % (1156896)...printing done.
% 0.17/0.47 % (1156896)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1156896)------------------------------
% 0.17/0.47 % (1156896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1156896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1156896)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1156896)Termination reason: Refutation
% 0.17/0.47 % (1156896)Time elapsed: 0.002 s
% 0.17/0.47 % (1156896)Peak memory usage: 12 MB
% 0.17/0.47 % (1156896)Instructions burned: 2 (million)
% 0.17/0.47 % (1156890)Success in time 0.027 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------