%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM746^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:19:26 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 87 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 461 ( 117 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 554 ( 124 ~; 88 |; 5 &; 290 @)
% ( 4 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 71 !; 0 ?; 71 :)
% 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,
z: frac ).
thf(func_def_3,type,
lessf: frac > frac > $o ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(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) ).
thf(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) ).
thf(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) ).
thf(f7,conjecture,
( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz52) ).
thf(f8,negated_conjecture,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( ( ( lessf @ y @ z )
!= $true )
=> ( ( eq @ y @ z )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X1 @ X2 )
= $true )
=> ( ( eq @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X0 @ X1 )
=> ( ( ~ ( lessf @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( lessf @ X0 @ X2 ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( ( ( lessf @ X1 @ X2 )
!= $true )
=> ( ( eq @ X1 @ X2 )
= $true ) )
=> ( ( lessf @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ~ ( lessf @ X0 @ X1 )
=> ( eq @ X0 @ X1 ) )
=> ( ( lessf @ X1 @ X2 )
=> ( lessf @ X0 @ X2 ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( ( lessf @ X0 @ X1 )
!= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) )
=> ( ( ( lessf @ X1 @ X2 )
= $true )
=> ( ( lessf @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
~ ( ( ( lessf @ x @ z )
!= $true )
=> ( ( eq @ x @ z )
= $true ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[],[f10]) ).
thf(f24,plain,
( ( ( lessf @ y @ z )
!= $true )
=> ( ( eq @ y @ z )
= $true ) ),
inference(flattening,[],[f12]) ).
thf(f26,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( ( ( lessf @ X1 @ X2 )
!= $true )
=> ( ( eq @ X1 @ X2 )
= $true ) )
=> ( ( lessf @ X0 @ X2 )
= $true ) ) ),
inference(flattening,[],[f18]) ).
thf(f27,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( ( lessf @ X0 @ X1 )
!= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) )
=> ( ( ( lessf @ X1 @ X2 )
= $true )
=> ( ( lessf @ X0 @ X2 )
= $true ) ) ),
inference(flattening,[],[f20]) ).
thf(f28,plain,
~ ( ( ( lessf @ x @ z )
!= $true )
=> ( ( eq @ x @ z )
= $true ) ),
inference(flattening,[],[f22]) ).
thf(f29,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( lessf @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f30,plain,
( ( ( eq @ y @ z )
= $true )
| ( ( lessf @ y @ z )
= $true ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f32,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f33,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f32]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X2 )
= $true )
| ( ( ( eq @ X1 @ X2 )
!= $true )
& ( ( lessf @ X1 @ X2 )
!= $true ) )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X2 )
= $true )
| ( ( ( eq @ X1 @ X2 )
!= $true )
& ( ( lessf @ X1 @ X2 )
!= $true ) )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f34]) ).
thf(f36,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X2 )
= $true )
| ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( ( eq @ X0 @ X1 )
!= $true )
& ( ( lessf @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f27]) ).
thf(f37,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X2 )
= $true )
| ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( ( eq @ X0 @ X1 )
!= $true )
& ( ( lessf @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f36]) ).
thf(f38,plain,
( ( ( eq @ x @ z )
!= $true )
& ( ( lessf @ x @ z )
!= $true ) ),
inference(ennf_transformation,[],[f28]) ).
thf(f39,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( lessf @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f40,plain,
( ( ( eq @ y @ z )
= $true )
| ( ( lessf @ y @ z )
= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f42,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f43,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X2 )
= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f44,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X2 )
= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f46,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f47,plain,
( ( lessf @ x @ z )
!= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f48,plain,
( ( eq @ x @ z )
!= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f110,definition,
( spl0_3
<=> ( ( lessf @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f112,plain,
( ( ( lessf @ x @ y )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f114,definition,
( spl0_4
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f116,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f117,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f39,f114,f110]) ).
thf(f119,definition,
( spl0_5
<=> ( ( lessf @ y @ z )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f121,plain,
( ( ( lessf @ y @ z )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f123,definition,
( spl0_6
<=> ( ( eq @ y @ z )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f125,plain,
( ( ( eq @ y @ z )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f126,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f40,f123,f119]) ).
thf(f174,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( $true
= ( eq @ X0 @ z ) )
| ( $true
!= ( eq @ X0 @ y ) ) )
| ~ spl0_6 ),
inference(constrained_superposition,[],[f42,f125]) ).
thf(f175,plain,
( ! [X0: frac] :
( ( $true
!= ( eq @ X0 @ y ) )
| ( $true
= ( eq @ X0 @ z ) ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f243,plain,
( ( $true != $true )
| ( ( eq @ x @ z )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(constrained_superposition,[],[f175,f116]) ).
thf(f244,plain,
( ( ( eq @ x @ z )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f246,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f244,f48]) ).
thf(f247,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f246]) ).
thf(f297,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( $true
= ( lessf @ X0 @ z ) )
| ( $true
!= ( lessf @ X0 @ y ) ) )
| ~ spl0_6 ),
inference(constrained_superposition,[],[f44,f125]) ).
thf(f300,plain,
( ! [X0: frac] :
( ( $true
!= ( lessf @ X0 @ y ) )
| ( $true
= ( lessf @ X0 @ z ) ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f330,plain,
( ( $true != $true )
| ( ( lessf @ x @ z )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(constrained_superposition,[],[f300,f112]) ).
thf(f331,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f333,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f331,f47]) ).
thf(f334,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f333]) ).
thf(f345,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( $true
= ( lessf @ X0 @ z ) )
| ( $true
!= ( lessf @ X0 @ y ) ) )
| ~ spl0_5 ),
inference(constrained_superposition,[],[f43,f121]) ).
thf(f346,plain,
( ! [X0: frac] :
( ( $true
!= ( lessf @ X0 @ y ) )
| ( $true
= ( lessf @ X0 @ z ) ) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f345]) ).
thf(f369,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( $true
!= ( lessf @ y @ X0 ) )
| ( $true
= ( lessf @ x @ X0 ) ) )
| ~ spl0_4 ),
inference(constrained_superposition,[],[f46,f116]) ).
thf(f372,plain,
( ! [X0: frac] :
( ( $true
!= ( lessf @ y @ X0 ) )
| ( $true
= ( lessf @ x @ X0 ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f383,plain,
( ( $true != $true )
| ( ( lessf @ x @ z )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(constrained_superposition,[],[f372,f121]) ).
thf(f384,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f383]) ).
thf(f386,plain,
( $false
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f384,f47]) ).
thf(f387,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f386]) ).
thf(f443,plain,
( ( $true != $true )
| ( ( lessf @ x @ z )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(constrained_superposition,[],[f346,f112]) ).
thf(f444,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f446,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f444,f47]) ).
thf(f447,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f446]) ).
cnf(s31,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f117]) ).
cnf(s35,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f126]) ).
cnf(s95,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f247]) ).
cnf(s133,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f334]) ).
cnf(s157,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f387]) ).
cnf(s184,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f447]) ).
cnf(s186,plain,
~ spl0_4,
inference(rat,[],[s35,s95,s157]) ).
cnf(s187,plain,
spl0_3,
inference(rat,[],[s31,s186]) ).
cnf(s188,plain,
~ spl0_5,
inference(rat,[],[s184,s187]) ).
cnf(s190,plain,
~ spl0_6,
inference(rat,[],[s133,s187]) ).
cnf(s192,plain,
$false,
inference(rat,[],[s35,s190,s188]) ).
thf(f448,plain,
$false,
inference(avatar_sat_refutation,[],[s192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM746^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:50:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.29 % (23475)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (23488)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4282296218:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (23487)% WARNING: option uhcvi not known.
% 0.20/0.29 % (23489)dis+10_1_sil=32000:sp=arity:random_seed=3980693431:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (23486)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2590402492_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (23488) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-23475-23488"...
% 0.20/0.29 % (23487)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2876405377:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (23490)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=20167878:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (23487)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (23491)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2136086530:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (23490)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (23487)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (23488)...printing done.
% 0.20/0.29 % (23492)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3893515797:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (23488)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (23488)------------------------------
% 0.20/0.29 % (23488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (23488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (23488)CaDiCaL version: 2.1.3
% 0.20/0.29 % (23488)Termination reason: Refutation
% 0.20/0.29 % (23488)Time elapsed: 0.014 s
% 0.20/0.29 % (23488)Peak memory usage: 13 MB
% 0.20/0.29 % (23488)Instructions burned: 22 (million)
% 0.20/0.29 % (23475)Success in time 0.058 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------