%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM769^1 : 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 : 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 : Wed Sep 30 08:18:50 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 18 unt; 0 typ; 3 def)
% Number of atoms : 141 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 219 ( 29 ~; 21 |; 0 &; 160 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 13 ( 10 usr; 7 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_4,type,
eq: frac > frac > $o ).
thf(func_def_5,type,
pf: frac > frac > frac ).
thf(func_def_6,type,
mf: frac > frac > frac ).
thf(f1,axiom,
moref @ 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 )
=> ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz67c) ).
thf(f4,conjecture,
eq @ x @ ( pf @ y @ ( mf @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz67d) ).
thf(f5,negated_conjecture,
~ ( eq @ x @ ( pf @ y @ ( mf @ x @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ( eq @ x @ ( pf @ y @ ( mf @ x @ y ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( eq @ x @ ( pf @ y @ ( mf @ x @ y ) ) )
!= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: frac,X1: frac] :
( ( eq @ X1 @ X0 )
=> ( eq @ X0 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
moref @ x @ y,
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ( moref @ x @ y )
= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: frac,X1: frac] :
( ( moref @ X1 @ X0 )
=> ( eq @ ( pf @ X0 @ ( mf @ X1 @ X0 ) ) @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
=> ( ( eq @ ( pf @ X0 @ ( mf @ X1 @ X0 ) ) @ X1 )
= $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( eq @ x @ ( pf @ y @ ( mf @ x @ y ) ) )
!= $true ),
inference(flattening,[],[f7]) ).
thf(f15,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f16,plain,
! [X1: frac,X0: frac] :
( ( ( moref @ X1 @ X0 )
!= $true )
| ( ( eq @ ( pf @ X0 @ ( mf @ X1 @ X0 ) ) @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f17,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 )
= $true ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f15]) ).
thf(f19,plain,
( ( moref @ x @ y )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
( ( eq @ x @ ( pf @ y @ ( mf @ x @ y ) ) )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f25,definition,
( spl0_1
<=> ( ( moref @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f27,plain,
( ( ( moref @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f28,plain,
spl0_1,
inference(avatar_split_clause,[],[f19,f25]) ).
thf(f30,definition,
( spl0_2
<=> ( ( eq @ x @ ( pf @ y @ ( mf @ x @ y ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f32,plain,
( ( ( eq @ x @ ( pf @ y @ ( mf @ x @ y ) ) )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f20,f30]) ).
thf(f34,plain,
( ( $true != $true )
| ( ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x )
!= $true )
| spl0_2 ),
inference(superposition,[],[f32,f22]) ).
thf(f35,plain,
( ( ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x )
!= $true )
| spl0_2 ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f37,definition,
( spl0_3
<=> ( ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f39,plain,
( ( ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x )
!= $true )
| spl0_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f35,f30,f37]) ).
thf(f41,plain,
( ( ( moref @ x @ y )
!= $true )
| ( $true != $true )
| spl0_3 ),
inference(superposition,[],[f39,f21]) ).
thf(f44,plain,
( ( ( moref @ x @ y )
!= $true )
| spl0_3 ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f45,plain,
( $false
| ~ spl0_1
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f44,f27]) ).
thf(f46,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f45]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s5,plain,
~ spl0_3,
inference(rat,[],[s3,s2]) ).
cnf(s6,plain,
~ spl0_1,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6]) ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM769^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n011.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:54:46 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.23 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
% 0.19/0.27 % (45681)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (45689)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1944379381:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.27 % (45689) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-45681-45689"...
% 0.19/0.27 % (45689)...printing done.
% 0.19/0.27 % (45689)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (45689)------------------------------
% 0.19/0.27 % (45689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (45689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (45689)CaDiCaL version: 2.1.3
% 0.19/0.27 % (45689)Termination reason: Refutation
% 0.19/0.27 % (45689)Time elapsed: 0.002 s
% 0.19/0.27 % (45689)Peak memory usage: 13 MB
% 0.19/0.27 % (45689)Instructions burned: 3 (million)
% 0.19/0.27 % (45681)Success in time 0.025 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------