%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM742_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 12:25:33 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 37 ~; 33 |; 0 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
frac: $tType ).
tff(func_def_0,type,
x: frac ).
tff(func_def_1,type,
y: frac ).
tff(func_def_2,type,
z: frac ).
tff(pred_def_1,type,
lessf: ( frac * frac ) > $o ).
tff(pred_def_2,type,
eq: ( frac * frac ) > $o ).
tff(f1,axiom,
( ~ lessf(x,y)
=> eq(x,y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
tff(f2,axiom,
lessf(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
tff(f4,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( lessf(X0,X1)
=> ( eq(X0,X2)
=> ( eq(X1,X3)
=> lessf(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz45) ).
tff(f5,axiom,
! [X0: frac,X1: frac] :
( eq(X0,X1)
=> eq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).
tff(f6,axiom,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X1)
=> ( lessf(X1,X2)
=> lessf(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz50) ).
tff(f7,axiom,
! [X0: frac] : eq(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
tff(f8,conjecture,
lessf(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz51a) ).
tff(f9,negated_conjecture,
~ lessf(x,z),
inference(negated_conjecture,[status(cth)],[f8]) ).
tff(f13,plain,
~ lessf(x,z),
inference(flattening,[],[f9]) ).
tff(f14,plain,
( eq(x,y)
| lessf(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f16,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( lessf(X2,X3)
| ~ eq(X1,X3)
| ~ eq(X0,X2)
| ~ lessf(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f17,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( lessf(X2,X3)
| ~ eq(X1,X3)
| ~ eq(X0,X2)
| ~ lessf(X0,X1) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
! [X0: frac,X1: frac] :
( eq(X1,X0)
| ~ eq(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X2)
| ~ lessf(X1,X2)
| ~ lessf(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
tff(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X2)
| ~ lessf(X1,X2)
| ~ lessf(X0,X1) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
( eq(x,y)
| lessf(x,y) ),
inference(cnf_transformation,[],[f14]) ).
tff(f22,plain,
lessf(y,z),
inference(cnf_transformation,[],[f2]) ).
tff(f24,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ~ eq(X1,X3)
| lessf(X2,X3)
| ~ eq(X0,X2)
| ~ lessf(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f25,plain,
! [X0: frac,X1: frac] :
( ~ eq(X0,X1)
| eq(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f26,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ lessf(X1,X2)
| lessf(X0,X2)
| ~ lessf(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f27,plain,
! [X0: frac] : eq(X0,X0),
inference(cnf_transformation,[],[f7]) ).
tff(f28,plain,
~ lessf(x,z),
inference(cnf_transformation,[],[f13]) ).
tff(f32,definition,
( spl0_1
<=> lessf(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f34,plain,
( lessf(x,y)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f32]) ).
tff(f36,definition,
( spl0_2
<=> eq(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f38,plain,
( eq(x,y)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f39,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f21,f36,f32]) ).
tff(f41,plain,
( eq(y,x)
| ~ spl0_2 ),
inference(resolution,[],[f25,f38]) ).
tff(f46,plain,
! [X0: frac] :
( ~ lessf(X0,y)
| lessf(X0,z) ),
inference(resolution,[],[f26,f22]) ).
tff(f47,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ eq(X2,X0)
| lessf(X0,X1)
| ~ lessf(X2,X1) ),
inference(resolution,[],[f24,f27]) ).
tff(f82,plain,
( ! [X0: frac] :
( ~ lessf(y,X0)
| lessf(x,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f47,f41]) ).
tff(f100,plain,
( lessf(x,z)
| ~ spl0_2 ),
inference(resolution,[],[f82,f22]) ).
tff(f101,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f100,f28]) ).
tff(f102,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f101]) ).
tff(f103,plain,
( lessf(x,z)
| ~ spl0_1 ),
inference(resolution,[],[f34,f46]) ).
tff(f105,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f103,f28]) ).
tff(f106,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f105]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f102]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f106]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s5]) ).
tff(f107,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM742_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 21:19:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.44 % (2012887)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (2012897)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=763668162:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.44 % (2012897) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2012887-2012897"...
% 0.09/0.44 % (2012897)...printing done.
% 0.09/0.44 % (2012897)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (2012897)------------------------------
% 0.09/0.44 % (2012897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (2012897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (2012897)CaDiCaL version: 2.1.3
% 0.09/0.44 % (2012897)Termination reason: Refutation
% 0.09/0.44 % (2012897)Time elapsed: 0.002 s
% 0.09/0.44 % (2012897)Peak memory usage: 12 MB
% 0.09/0.44 % (2012897)Instructions burned: 3 (million)
% 0.09/0.44 % (2012887)Success in time 0.025 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------