%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM740^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Wed Sep 30 08:18:43 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 18 unt; 0 typ; 8 def)
% Number of atoms : 235 ( 57 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 239 ( 52 ~; 31 |; 1 &; 134 @)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 symbols : 17 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: frac ).
thf(func_def_1,type,
y: frac ).
thf(func_def_2,type,
moref: frac > frac > $o ).
thf(func_def_3,type,
eq: frac > frac > $o ).
thf(func_def_5,type,
lessf: frac > frac > $o ).
thf(func_def_8,type,
sF0: $o ).
thf(func_def_9,type,
sF1: $o ).
thf(f1,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
! [X1: frac,X0: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).
thf(f3,axiom,
! [X1: frac,X0: frac] :
( ( moref @ X0 @ X1 )
=> ( lessf @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz42) ).
thf(f4,conjecture,
( ~ ( lessf @ y @ x )
=> ( eq @ y @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz48) ).
thf(f5,negated_conjecture,
~ ( ~ ( lessf @ y @ x )
=> ( eq @ y @ x ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( ~ ( lessf @ y @ x )
=> ( eq @ y @ x ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
~ ( ( ( lessf @ y @ x )
!= $true )
=> ( ( eq @ y @ x )
= $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: frac,X1: frac] :
( ( eq @ X1 @ X0 )
=> ( eq @ X0 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: frac,X1: frac] :
( ( moref @ X1 @ X0 )
=> ( lessf @ X0 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
=> ( $true
= ( lessf @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[],[f7]) ).
thf(f15,plain,
~ ( ( ( lessf @ y @ x )
!= $true )
=> ( ( eq @ y @ x )
= $true ) ),
inference(flattening,[],[f9]) ).
thf(f16,plain,
( ( ( eq @ y @ x )
!= $true )
& ( ( lessf @ y @ x )
!= $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f17,plain,
! [X1: frac,X0: frac] :
( ( ( moref @ X1 @ X0 )
!= $true )
| ( $true
= ( lessf @ X0 @ X1 ) ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f18,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f19,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f20,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(rectify,[],[f18]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( lessf @ X1 @ X0 )
= $true ) ),
inference(rectify,[],[f17]) ).
thf(f22,plain,
( ( lessf @ y @ x )
!= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( ( eq @ y @ x )
!= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f25,plain,
( ( ( moref @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
! [X0: frac,X1: frac] :
( ( ( lessf @ X1 @ X0 )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f29,definition,
( sF0
= ( eq @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f30,plain,
( ( eq @ y @ x )
= sF0 ),
inference(reorient_equations,[],[f29]) ).
thf(f31,plain,
sF0 != $true,
inference(definition_folding,[],[f23,f30]) ).
thf(f32,definition,
( sF1
= ( lessf @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f33,plain,
( ( lessf @ y @ x )
= sF1 ),
inference(reorient_equations,[],[f32]) ).
thf(f34,plain,
$true != sF1,
inference(definition_folding,[],[f22,f33]) ).
thf(f36,plain,
( ( ( eq @ y @ x )
= $false )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f30]) ).
thf(f38,plain,
( ( $true = sF1 )
| ( ( lessf @ y @ x )
= $false ) ),
inference(iff_proxy_clausification,[],[f33]) ).
thf(f40,definition,
( spl2_1
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f44,definition,
( spl2_2
<=> ( ( eq @ y @ x )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f46,plain,
( ( ( eq @ y @ x )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f47,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f36,f44,f40]) ).
thf(f58,definition,
( spl2_5
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f62,definition,
( spl2_6
<=> ( ( lessf @ y @ x )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
thf(f64,plain,
( ( ( lessf @ y @ x )
= $false )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,plain,
( spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f38,f62,f58]) ).
thf(f75,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f31,f40]) ).
thf(f77,definition,
( spl2_9
<=> ( ( moref @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
thf(f79,plain,
( ( ( moref @ x @ y )
= $true )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f81,definition,
( spl2_10
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
thf(f84,plain,
( spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f25,f81,f77]) ).
thf(f85,plain,
~ spl2_5,
inference(avatar_split_clause,[],[f34,f58]) ).
thf(f113,plain,
( ( $false = $true )
| ( ( eq @ x @ y )
!= $true )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f24,f46]) ).
thf(f115,plain,
( ( ( eq @ x @ y )
!= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f117,plain,
( ~ spl2_10
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f115,f44,f81]) ).
thf(f132,plain,
( ( $false = $true )
| ( ( moref @ x @ y )
!= $true )
| ~ spl2_6 ),
inference(constrained_superposition,[],[f26,f64]) ).
thf(f135,plain,
( ( ( moref @ x @ y )
!= $true )
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f138,plain,
( $false
| ~ spl2_6
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f135,f79]) ).
thf(f139,plain,
( ~ spl2_6
| ~ spl2_9 ),
inference(avatar_contradiction_clause,[],[f138]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f65]) ).
cnf(s5,plain,
~ spl2_1,
inference(sat_conversion,[],[f75]) ).
cnf(s6,plain,
( spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f84]) ).
cnf(s7,plain,
~ spl2_5,
inference(sat_conversion,[],[f85]) ).
cnf(s11,plain,
( ~ spl2_2
| ~ spl2_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s14,plain,
( ~ spl2_6
| ~ spl2_9 ),
inference(sat_conversion,[],[f139]) ).
cnf(s17,plain,
spl2_6,
inference(rat,[],[s3,s7]) ).
cnf(s18,plain,
~ spl2_9,
inference(rat,[],[s14,s17]) ).
cnf(s19,plain,
spl2_10,
inference(rat,[],[s6,s18]) ).
cnf(s20,plain,
~ spl2_2,
inference(rat,[],[s11,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s20,s5]) ).
thf(f140,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM740^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:49:26 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.28 % (22217)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (22228)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (22228)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (22228)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=615727325:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.28 % (22228) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-22217-22228"...
% 0.22/0.28 % (22228)...printing done.
% 0.22/0.28 % (22228)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (22228)------------------------------
% 0.22/0.28 % (22228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (22228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (22228)CaDiCaL version: 2.1.3
% 0.22/0.28 % (22228)Termination reason: Refutation
% 0.22/0.28 % (22228)Time elapsed: 0.002 s
% 0.22/0.28 % (22228)Peak memory usage: 13 MB
% 0.22/0.28 % (22228)Instructions burned: 4 (million)
% 0.22/0.28 % (22217)Success in time 0.026 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------