%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM746_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 : n009.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 12:25:34 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 167 ( 82 ~; 64 |; 5 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 43 :)
% 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/sandbox/benchmark/theBenchmark.p',l) ).
tff(f2,axiom,
( ~ lessf(y,z)
=> eq(y,z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
tff(f4,axiom,
! [X0: frac,X1: frac,X2: frac] :
( eq(X0,X1)
=> ( eq(X1,X2)
=> eq(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
tff(f5,axiom,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X1)
=> ( ( ~ lessf(X1,X2)
=> eq(X1,X2) )
=> lessf(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51b) ).
tff(f6,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( ~ lessf(X0,X1)
=> eq(X0,X1) )
=> ( lessf(X1,X2)
=> lessf(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51a) ).
tff(f7,conjecture,
( ~ lessf(x,z)
=> eq(x,z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz52) ).
tff(f8,negated_conjecture,
~ ( ~ lessf(x,z)
=> eq(x,z) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f12,plain,
( eq(x,y)
| lessf(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f13,plain,
( eq(y,z)
| lessf(y,z) ),
inference(ennf_transformation,[],[f2]) ).
tff(f15,plain,
! [X0: frac,X1: frac,X2: frac] :
( eq(X0,X2)
| ~ eq(X1,X2)
| ~ eq(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f16,plain,
! [X0: frac,X1: frac,X2: frac] :
( eq(X0,X2)
| ~ eq(X1,X2)
| ~ eq(X0,X1) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X2)
| ( ~ eq(X1,X2)
& ~ lessf(X1,X2) )
| ~ lessf(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f18,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X2)
| ( ~ eq(X1,X2)
& ~ lessf(X1,X2) )
| ~ lessf(X0,X1) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X2)
| ~ lessf(X1,X2)
| ( ~ eq(X0,X1)
& ~ lessf(X0,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
tff(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X2)
| ~ lessf(X1,X2)
| ( ~ eq(X0,X1)
& ~ lessf(X0,X1) ) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
( ~ eq(x,z)
& ~ lessf(x,z) ),
inference(ennf_transformation,[],[f8]) ).
tff(f22,plain,
( eq(x,y)
| lessf(x,y) ),
inference(cnf_transformation,[],[f12]) ).
tff(f23,plain,
( eq(y,z)
| lessf(y,z) ),
inference(cnf_transformation,[],[f13]) ).
tff(f25,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ eq(X1,X2)
| eq(X0,X2)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f27,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ eq(X1,X2)
| lessf(X0,X2)
| ~ lessf(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f28,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ lessf(X1,X2)
| lessf(X0,X2)
| ~ lessf(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f29,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ eq(X0,X1)
| ~ lessf(X1,X2)
| lessf(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
tff(f30,plain,
~ lessf(x,z),
inference(cnf_transformation,[],[f21]) ).
tff(f31,plain,
~ eq(x,z),
inference(cnf_transformation,[],[f21]) ).
tff(f35,definition,
( spl0_1
<=> lessf(y,z) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f37,plain,
( lessf(y,z)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f39,definition,
( spl0_2
<=> eq(y,z) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f41,plain,
( eq(y,z)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f23,f39,f35]) ).
tff(f44,definition,
( spl0_3
<=> lessf(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f46,plain,
( lessf(x,y)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f48,definition,
( spl0_4
<=> eq(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f50,plain,
( eq(x,y)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f51,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f22,f48,f44]) ).
tff(f56,plain,
( ! [X0: frac] :
( ~ lessf(X0,y)
| lessf(X0,z) )
| ~ spl0_2 ),
inference(resolution,[],[f27,f41]) ).
tff(f58,plain,
( lessf(x,z)
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f56,f46]) ).
tff(f59,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f58,f30]) ).
tff(f60,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f59]) ).
tff(f61,plain,
( ! [X0: frac] :
( ~ lessf(X0,y)
| lessf(X0,z) )
| ~ spl0_1 ),
inference(resolution,[],[f37,f28]) ).
tff(f62,plain,
( lessf(x,z)
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f61,f46]) ).
tff(f63,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f62,f30]) ).
tff(f64,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f63]) ).
tff(f67,plain,
( ! [X0: frac] :
( ~ eq(X0,y)
| eq(X0,z) )
| ~ spl0_2 ),
inference(resolution,[],[f41,f25]) ).
tff(f68,plain,
( ! [X0: frac] :
( ~ lessf(y,X0)
| lessf(x,X0) )
| ~ spl0_4 ),
inference(resolution,[],[f50,f29]) ).
tff(f71,plain,
( eq(x,z)
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f67,f50]) ).
tff(f72,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f71,f31]) ).
tff(f73,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f72]) ).
tff(f75,plain,
( lessf(x,z)
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f68,f37]) ).
tff(f76,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f75,f30]) ).
tff(f77,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f76]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f77]) ).
cnf(s7,plain,
~ spl0_2,
inference(rat,[],[s2,s3,s5]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s1,s7]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s4,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s9,s10]) ).
tff(f78,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM746_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n009.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
% 0.11/0.39 % DateTime : Sun Sep 27 21:15:30 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.15/0.47 % (2399090)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (2399100)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=516024529:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (2399100) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2399090-2399100"...
% 0.15/0.47 % (2399100)...printing done.
% 0.15/0.47 % (2399100)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (2399100)------------------------------
% 0.15/0.47 % (2399100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (2399100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (2399100)CaDiCaL version: 2.1.3
% 0.15/0.47 % (2399100)Termination reason: Refutation
% 0.15/0.47 % (2399100)Time elapsed: 0.002 s
% 0.15/0.47 % (2399100)Peak memory usage: 12 MB
% 0.15/0.47 % (2399100)Instructions burned: 2 (million)
% 0.15/0.47 % (2399090)Success in time 0.037 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------