%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO023^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:46:18 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 20 unt; 0 typ; 4 def)
% Number of atoms : 249 ( 69 equ; 3 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 188 ( 96 ~; 67 |; 12 &; 9 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 9 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 0 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
vNOT: $o > $o ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_9,type,
sK0: $o ).
thf(func_def_10,type,
sK1: $o ).
thf(f1,conjecture,
( ( ^ [X2: $o,X3: $o] :
~ ( ~ X2
| ~ X3 ) )
= ( ^ [X0: $o,X1: $o] :
( X1
& X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f2,negated_conjecture,
( ( ^ [X2: $o,X3: $o] :
~ ( ~ X2
| ~ X3 ) )
!= ( ^ [X0: $o,X1: $o] :
( X1
& X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: $o,X1: $o] :
~ ( ~ X0
| ~ X1 ) )
!= ( ^ [X2: $o,X3: $o] :
( X3
& X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) )
!= ( ^ [Y0: $o,Y1: $o] :
( Y0
& Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) )
!= ( ^ [Y0: $o,Y1: $o] :
( Y0
& Y1 ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) )
!= ( ^ [Y0: $o,Y1: $o] :
( Y0
& Y1 ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) )
!= (&) ),
inference(beta-eta_normalization,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 )
@ sK0 )
!= ( (&) @ sK0 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f11,plain,
( ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK0 ) )
!= ( (&) @ sK0 ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f12,plain,
( ( sK0
& sK1 )
!= ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK0 )
@ sK1 ) ),
inference(negative_extensionality,[],[f11]) ).
thf(f13,plain,
( ( ( sK0
& sK1 )
= $true )
| ( ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK0 )
@ sK1 )
= $true ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK0 )
@ sK1 )
= $false )
| ( ( sK0
& sK1 )
= $false ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f15,plain,
( ( sK0 = $false )
| ( sK1 = $false )
| ( ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK0 )
@ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( sK0 = $false )
| ( $false
= ( ~ ( ~ sK1
| ~ sK0 ) ) )
| ( sK1 = $false ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ( ( ~ sK1
| ~ sK0 )
= $true )
| ( sK0 = $false )
| ( sK1 = $false ) ),
inference(not_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( sK1 = $false )
| ( sK0 = $false )
| ( ( ~ sK1 ) = $true )
| ( $true = ( ~ sK0 ) ) ),
inference(or_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( sK1 = $false )
| ( sK1 = $false )
| ( $true = ( ~ sK0 ) )
| ( sK0 = $false ) ),
inference(not_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( sK0 = $false )
| ( sK1 = $false )
| ( sK0 = $false )
| ( sK1 = $false ) ),
inference(not_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( sK0 = $false )
| ( sK1 = $false ) ),
inference(duplicate_literal_removal,[],[f20]) ).
thf(f22,plain,
( ( sK1 = $true )
| ( ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK0 )
@ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f23,plain,
( ( sK0 = $true )
| ( ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK0 )
@ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f24,plain,
( ( ( ~ ( ~ sK1
| ~ sK0 ) )
= $true )
| ( sK0 = $true ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
( ( ( ~ sK1
| ~ sK0 )
= $false )
| ( sK0 = $true ) ),
inference(not_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( sK0 = $true )
| ( $false = ( ~ sK0 ) ) ),
inference(or_proxy_clausification,[],[f25]) ).
thf(f29,plain,
( ( sK0 = $true )
| ( sK0 = $true ) ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f30,plain,
sK0 = $true,
inference(duplicate_literal_removal,[],[f29]) ).
thf(f31,plain,
( ( ( ~ ( ~ sK1
| ~ sK0 ) )
= $true )
| ( sK1 = $true ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f32,plain,
( ( sK1 = $true )
| ( ( ~ sK1
| ~ sK0 )
= $false ) ),
inference(not_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( sK1 = $true )
| ( ( ~ sK1 ) = $false ) ),
inference(or_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ( sK1 = $true )
| ( sK1 = $true ) ),
inference(not_proxy_clausification,[],[f34]) ).
thf(f36,plain,
sK1 = $true,
inference(duplicate_literal_removal,[],[f35]) ).
thf(f39,definition,
( spl2_1
<=> ( sK1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f41,plain,
( ( sK1 = $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f43,definition,
( spl2_2
<=> ( sK0 = $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f45,plain,
( ( sK0 = $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f46,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f21,f43,f39]) ).
thf(f48,definition,
( spl2_3
<=> ( sK0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f50,plain,
( ( sK0 = $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f52,definition,
( spl2_4
<=> ( sK1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f54,plain,
( ( sK1 = $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f56,plain,
spl2_3,
inference(avatar_split_clause,[],[f30,f48]) ).
thf(f57,plain,
spl2_4,
inference(avatar_split_clause,[],[f36,f52]) ).
thf(f59,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f45,f50]) ).
thf(f60,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f61,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f60]) ).
thf(f62,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_4 ),
inference(forward_demodulation,[],[f41,f54]) ).
thf(f63,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f64,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f63]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s3,plain,
spl2_3,
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
spl2_4,
inference(sat_conversion,[],[f57]) ).
cnf(s6,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f61]) ).
cnf(s7,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f64]) ).
cnf(s8,plain,
~ spl2_1,
inference(rat,[],[s7,s4]) ).
cnf(s9,plain,
~ spl2_2,
inference(rat,[],[s6,s3]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s8]) ).
thf(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO023^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n010.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 16:23:41 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.29 % (3073943)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (3073954)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (3073954)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
% 0.20/0.29 % (3073949)lrs+10_16_si=on:nwc=1.5:random_seed=2803113859:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (3073948)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3649639372:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (3073950)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=54032969:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (3073951)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=2189950794: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)
% 0.20/0.29 % (3073952)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2150940867:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (3073950)Refutation not found, incomplete strategy
% 0.20/0.29 % (3073950)------------------------------
% 0.20/0.29 % (3073950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3073950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3073950)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3073950)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (3073950)Time elapsed: 0.001 s
% 0.20/0.29 % (3073950)Peak memory usage: 12 MB
% 0.20/0.29 % (3073954)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=55525526:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (3073948) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3073943-3073948"...
% 0.20/0.29 % (3073949) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3073943-3073949"...
% 0.20/0.29 % (3073952) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3073943-3073952"...
% 0.20/0.29 % (3073950)------------------------------
% 0.20/0.29 % (3073950)------------------------------
% 0.20/0.29 % (3073951) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3073943-3073951"...
% 0.20/0.29 % (3073954) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3073943-3073954"...
% 0.20/0.29 % (3073948)...printing done.
% 0.20/0.29 % (3073949)...printing done.
% 0.20/0.29 % (3073952)...printing done.
% 0.20/0.29 % (3073953)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1107944446:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (3073951)...printing done.
% 0.20/0.29 % (3073948)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 % (3073948)------------------------------
% 0.20/0.29 % (3073948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3073948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3073948)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3073948)Termination reason: Refutation
% 0.20/0.29 % (3073948)Time elapsed: 0.003 s
% 0.20/0.29 % (3073948)Peak memory usage: 12 MB
% 0.20/0.29 % (3073948)Instructions burned: 2 (million)
% 0.20/0.29 % (3073943)Success in time 0.045 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------