%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO039^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:46:21 AM UTC 2026
% Result : Theorem 0.35s 0.44s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 20 unt; 0 typ; 8 def)
% Number of atoms : 164 ( 46 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 94 ( 36 ~; 24 |; 0 &; 31 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
h: $o > $i ).
thf(func_def_4,type,
vNOT: $o > $o ).
thf(func_def_5,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_6,type,
sF0: $o ).
thf(func_def_9,type,
sF3: $o ).
thf(f1,conjecture,
( ( h @ $false )
= ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',1) ).
thf(f2,negated_conjecture,
( ( h @ $false )
!= ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) )
!= ( h @ $false ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) )
!= ( h @ $false ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( h
@ ( ( h @ ~ $false )
= ( h @ $false ) ) )
!= ( h @ $false ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,definition,
( sF0 = ( ~ $false ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f10,definition,
( sF1
= ( h @ sF0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f11,definition,
( sF2
= ( h @ $false ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f12,definition,
( sF3
= ( sF1 = sF2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f13,definition,
( sF4
= ( h @ sF3 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f14,plain,
sF2 != sF4,
inference(definition_folding,[],[f6,f11,f13,f12,f11,f10,f9]) ).
thf(f15,plain,
( ( ( sF1 = sF2 )
= $false )
| ( sF3 = $true ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f16,plain,
( ( sF3 = $false )
| ( ( sF1 = sF2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f17,plain,
( ( sF3 = $false )
| ( sF2 = sF1 ) ),
inference(equality_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( sF3 = $true )
| ( sF2 != sF1 ) ),
inference(equality_proxy_clausification,[],[f15]) ).
thf(f19,plain,
( ( ( ~ $false ) = $false )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f22,plain,
( ( sF0 = $true )
| ( $true = $false ) ),
inference(not_proxy_clausification,[],[f19]) ).
thf(f23,plain,
sF0 = $true,
inference(trivial_inequality_removal,[],[f22]) ).
thf(f25,definition,
( spl5_1
<=> ( sF3 = $false ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f27,plain,
( ( sF3 = $false )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f29,definition,
( spl5_2
<=> ( sF2 = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f31,plain,
( ( sF2 = sF1 )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f32,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f17,f29,f25]) ).
thf(f34,definition,
( spl5_3
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f36,plain,
( ( sF3 = $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f37,plain,
( spl5_3
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f18,f29,f34]) ).
thf(f45,plain,
( sF1
= ( h @ $true ) ),
inference(forward_demodulation,[],[f10,f23]) ).
thf(f46,plain,
( ( sF2
= ( h @ $true ) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f45,f31]) ).
thf(f47,plain,
( ( sF4
= ( h @ $true ) )
| ~ spl5_3 ),
inference(forward_demodulation,[],[f13,f36]) ).
thf(f49,plain,
( ( sF2 = sF4 )
| ~ spl5_2
| ~ spl5_3 ),
inference(forward_demodulation,[],[f47,f46]) ).
thf(f50,plain,
( $false
| ~ spl5_2
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f49,f14]) ).
thf(f51,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f50]) ).
thf(f58,plain,
( ( ( h @ $false )
= sF4 )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f13,f27]) ).
thf(f59,plain,
( ( sF2 = sF4 )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f58,f11]) ).
thf(f60,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f59,f14]) ).
thf(f61,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
( ~ spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
~ spl5_1,
inference(sat_conversion,[],[f61]) ).
cnf(s6,plain,
spl5_2,
inference(rat,[],[s1,s5]) ).
cnf(s7,plain,
~ spl5_3,
inference(rat,[],[s3,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO039^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 % Computer : n002.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 16:26:23 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.35 Running higher-order theorem proving
% 0.29/0.36 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
% 0.35/0.44 % (1496582)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.44 % (1496592)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4077549710:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.35/0.44 % (1496590)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=2487835026: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)
% 0.35/0.44 % (1496588)lrs+10_16_si=on:nwc=1.5:random_seed=1042026294:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.35/0.44 % (1496587)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3052913185:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.44 % (1496589)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3418789939:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.35/0.44 % (1496591)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4094903551:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.35/0.44 % (1496591)Refutation not found, incomplete strategy
% 0.35/0.44 % (1496591)------------------------------
% 0.35/0.44 % (1496591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (1496589)Refutation not found, incomplete strategy
% 0.35/0.44 % (1496589)------------------------------
% 0.35/0.44 % (1496589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (1496587)Refutation not found, incomplete strategy
% 0.35/0.44 % (1496587)------------------------------
% 0.35/0.44 % (1496587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (1496588)Refutation not found, incomplete strategy
% 0.35/0.44 % (1496588)------------------------------
% 0.35/0.44 % (1496588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (1496591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (1496589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (1496587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (1496588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (1496591)CaDiCaL version: 2.1.3
% 0.35/0.44 % (1496591)Termination reason: Refutation not found, incomplete strategy
% 0.35/0.44 % (1496591)Time elapsed: 0.001 s
% 0.35/0.44 % (1496589)CaDiCaL version: 2.1.3
% 0.35/0.44 % (1496587)CaDiCaL version: 2.1.3
% 0.35/0.44 % (1496588)CaDiCaL version: 2.1.3
% 0.35/0.44 % (1496591)Peak memory usage: 11 MB
% 0.35/0.44 % (1496589)Termination reason: Refutation not found, incomplete strategy
% 0.35/0.44 % (1496589)Time elapsed: 0.001 s
% 0.35/0.44 % (1496587)Termination reason: Refutation not found, incomplete strategy
% 0.35/0.44 % (1496587)Time elapsed: 0.001 s
% 0.35/0.44 % (1496588)Termination reason: Refutation not found, incomplete strategy
% 0.35/0.44 % (1496588)Time elapsed: 0.001 s
% 0.35/0.44 % (1496589)Peak memory usage: 11 MB
% 0.35/0.44 % (1496587)Peak memory usage: 12 MB
% 0.35/0.44 % (1496588)Peak memory usage: 12 MB
% 0.35/0.44 % (1496590)Refutation not found, incomplete strategy
% 0.35/0.44 % (1496590)------------------------------
% 0.35/0.44 % (1496590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (1496590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (1496590)CaDiCaL version: 2.1.3
% 0.35/0.44 % (1496590)Termination reason: Refutation not found, incomplete strategy
% 0.35/0.44 % (1496590)Time elapsed: 0.002 s
% 0.35/0.44 % (1496590)Peak memory usage: 12 MB
% 0.35/0.44 % (1496592)Refutation not found, incomplete strategy
% 0.35/0.44 % (1496592)------------------------------
% 0.35/0.44 % (1496592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (1496592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (1496592)CaDiCaL version: 2.1.3
% 0.35/0.44 % (1496592)Termination reason: Refutation not found, incomplete strategy
% 0.35/0.44 % (1496592)Time elapsed: 0.002 s
% 0.35/0.44 % (1496592)Peak memory usage: 12 MB
% 0.35/0.44 % (1496592)Instructions burned: 1 (million)
% 0.35/0.44 % (1496588)------------------------------
% 0.35/0.44 % (1496588)------------------------------
% 0.35/0.44 % (1496591)------------------------------
% 0.35/0.44 % (1496591)------------------------------
% 0.35/0.44 % (1496589)------------------------------
% 0.35/0.44 % (1496589)------------------------------
% 0.35/0.44 % (1496587)------------------------------
% 0.35/0.44 % (1496587)------------------------------
% 0.35/0.44 % (1496590)------------------------------
% 0.35/0.44 % (1496590)------------------------------
% 0.35/0.44 % (1496592)------------------------------
% 0.35/0.44 % (1496592)------------------------------
% 0.35/0.44 % (1496593)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.35/0.44 % (1496593)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
% 0.35/0.44 % (1496593)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=4166560489:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.35/0.44 % (1496593) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1496582-1496593"...
% 0.35/0.44 % (1496593)...printing done.
% 0.35/0.44 % (1496593)Refutation found. Thanks to Tanya!
% 0.35/0.44 % SZS status Theorem for theBenchmark
% 0.35/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.44 % (1496593)------------------------------
% 0.35/0.44 % (1496593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (1496593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (1496593)CaDiCaL version: 2.1.3
% 0.35/0.44 % (1496593)Termination reason: Refutation
% 0.35/0.44 % (1496593)Time elapsed: 0.003 s
% 0.35/0.44 % (1496593)Peak memory usage: 13 MB
% 0.35/0.44 % (1496593)Instructions burned: 2 (million)
% 0.35/0.44 % (1496582)Success in time 0.064 s
% 0.35/0.44 % Vampire exiting
%------------------------------------------------------------------------------