%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM436+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:24:18 PM UTC 2026
% Result : Theorem 0.36s 0.47s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 88 ( 19 unt; 6 def)
% Number of atoms : 273 ( 51 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 309 ( 124 ~; 135 |; 36 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 46 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(f23,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
fof(f25,axiom,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1032) ).
fof(f26,axiom,
( sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb))
& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1071) ).
fof(f27,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xb,xp)
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xb,xp)
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f33,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f33]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(ennf_transformation,[],[f19]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f53]) ).
fof(f61,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& aInteger0(sK0(X0,X1))
& sdtasdt0(X1,sK0(X0,X1)) = X0 )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
& ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(nnf_transformation,[],[f54]) ).
fof(f71,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f93,plain,
! [X2,X0,X1] :
( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(cnf_transformation,[],[f66]) ).
fof(f99,plain,
sz00 != xq,
inference(cnf_transformation,[],[f23]) ).
fof(f100,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f23]) ).
fof(f101,plain,
sz00 != xp,
inference(cnf_transformation,[],[f23]) ).
fof(f102,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f23]) ).
fof(f103,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f23]) ).
fof(f104,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f23]) ).
fof(f107,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f108,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f26]) ).
fof(f109,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xp,sdtasdt0(xq,xm)),
inference(cnf_transformation,[],[f26]) ).
fof(f110,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ~ sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f93]) ).
fof(f114,definition,
( spl1_1
<=> sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f118,definition,
( spl1_2
<=> sdteqdtlpzmzozddtrp0(xa,xb,xp) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f120,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,xp)
| spl1_2 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f110,f118,f114]) ).
fof(f264,definition,
( spl1_5
<=> aInteger0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f266,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| spl1_5 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f281,definition,
( spl1_6
<=> aInteger0(sdtasdt0(xq,xm)) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f283,plain,
( ~ aInteger0(sdtasdt0(xq,xm))
| spl1_6 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f357,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2) ),
inference(forward_subsumption_resolution,[],[f111,f71]) ).
fof(f370,plain,
( aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(xp)
| sz00 = xp
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(superposition,[],[f357,f109]) ).
fof(f372,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(xq)
| sz00 = xq
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(superposition,[],[f357,f108]) ).
fof(f377,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sz00 = xq
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(forward_subsumption_resolution,[],[f372,f100]) ).
fof(f379,plain,
( aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sz00 = xp
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[],[f370,f102]) ).
fof(f391,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtasdt0(xp,xm)) ),
inference(forward_subsumption_resolution,[],[f377,f99]) ).
fof(f393,plain,
( aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[],[f379,f101]) ).
fof(f409,definition,
( spl1_13
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f411,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f412,plain,
( ~ spl1_5
| spl1_13 ),
inference(avatar_split_clause,[],[f391,f409,f264]) ).
fof(f415,definition,
( spl1_14
<=> aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f417,plain,
( aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f418,plain,
( ~ spl1_6
| spl1_14 ),
inference(avatar_split_clause,[],[f393,f415,f281]) ).
fof(f613,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xm)
| spl1_5 ),
inference(resolution,[],[f266,f71]) ).
fof(f614,plain,
( ~ aInteger0(xm)
| spl1_5 ),
inference(forward_subsumption_resolution,[],[f613,f102]) ).
fof(f615,plain,
( $false
| spl1_5 ),
inference(forward_subsumption_resolution,[],[f614,f107]) ).
fof(f616,plain,
spl1_5,
inference(avatar_contradiction_clause,[],[f615]) ).
fof(f641,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xm)
| spl1_6 ),
inference(resolution,[],[f283,f71]) ).
fof(f642,plain,
( ~ aInteger0(xm)
| spl1_6 ),
inference(forward_subsumption_resolution,[],[f641,f100]) ).
fof(f643,plain,
( $false
| spl1_6 ),
inference(forward_subsumption_resolution,[],[f642,f107]) ).
fof(f644,plain,
spl1_6,
inference(avatar_contradiction_clause,[],[f643]) ).
fof(f884,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| sz00 = xq
| ~ spl1_13 ),
inference(resolution,[],[f411,f95]) ).
fof(f894,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| sz00 = xq
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f884,f104]) ).
fof(f895,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aInteger0(xq)
| sz00 = xq
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f894,f103]) ).
fof(f896,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| sz00 = xq
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f895,f100]) ).
fof(f897,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f896,f99]) ).
fof(f898,plain,
( spl1_1
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f897,f409,f114]) ).
fof(f923,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xp)
| ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(xp)
| sz00 = xp
| ~ spl1_14 ),
inference(resolution,[],[f417,f95]) ).
fof(f927,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(xp)
| sz00 = xp
| spl1_2
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f923,f120]) ).
fof(f928,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xp)
| sz00 = xp
| spl1_2
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f927,f104]) ).
fof(f929,plain,
( ~ aInteger0(xp)
| sz00 = xp
| spl1_2
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f928,f103]) ).
fof(f930,plain,
( sz00 = xp
| spl1_2
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f929,f102]) ).
fof(f931,plain,
( $false
| spl1_2
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f930,f101]) ).
fof(f932,plain,
( spl1_2
| ~ spl1_14 ),
inference(avatar_contradiction_clause,[],[f931]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f121]) ).
cnf(s10,plain,
( ~ spl1_5
| spl1_13 ),
inference(sat_conversion,[],[f412]) ).
cnf(s11,plain,
( ~ spl1_6
| spl1_14 ),
inference(sat_conversion,[],[f418]) ).
cnf(s24,plain,
spl1_5,
inference(sat_conversion,[],[f616]) ).
cnf(s25,plain,
spl1_6,
inference(sat_conversion,[],[f644]) ).
cnf(s33,plain,
( spl1_1
| ~ spl1_13 ),
inference(sat_conversion,[],[f898]) ).
cnf(s34,plain,
( spl1_2
| ~ spl1_14 ),
inference(sat_conversion,[],[f932]) ).
cnf(s38,plain,
spl1_14,
inference(rat,[],[s11,s25]) ).
cnf(s39,plain,
spl1_2,
inference(rat,[],[s34,s38]) ).
cnf(s40,plain,
spl1_13,
inference(rat,[],[s10,s24]) ).
cnf(s41,plain,
spl1_1,
inference(rat,[],[s33,s40]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s1,s39,s41]) ).
fof(f933,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM436+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 19:54:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.36/0.47 % (129303)Will run a generic schedule for satisfiability detection.
% 0.36/0.47 % (129313)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2589870513:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.36/0.47 % (129309)% WARNING: option uhcvi not known.
% 0.36/0.47 % (129308)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2296853553_2999 on theBenchmark for (2999ds/0Mi)
% 0.36/0.47 % (129310)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1995984202:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.36/0.47 % (129312)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2524851776:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.36/0.47 % (129311)dis+10_1_sil=32000:sp=arity:random_seed=1362326557:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.36/0.47 % (129314)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1875481253:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.36/0.47 % (129309)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2479588303:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.36/0.47 % TRYING [1]
% 0.36/0.47 % TRYING [2]
% 0.36/0.47 % TRYING [3]
% 0.36/0.47 % TRYING [4]
% 0.36/0.47 % (129311) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-129303-129311"...
% 0.36/0.47 % (129311)...printing done.
% 0.36/0.47 % (129311)Refutation found. Thanks to Tanya!
% 0.36/0.47 % SZS status Theorem for theBenchmark
% 0.36/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.47 % (129311)------------------------------
% 0.36/0.47 % (129311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.47 % (129311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.47 % (129311)CaDiCaL version: 2.1.3
% 0.36/0.47 % (129311)Termination reason: Refutation
% 0.36/0.47 % (129311)Time elapsed: 0.020 s
% 0.36/0.47 % (129311)Peak memory usage: 13 MB
% 0.36/0.47 % (129311)Instructions burned: 29 (million)
% 0.36/0.47 % (129303)Success in time 0.057 s
% 0.36/0.47 % Vampire exiting
%------------------------------------------------------------------------------