%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET587^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:23:18 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 299 ( 81 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 311 ( 83 ~; 76 |; 30 &; 107 @)
% ( 9 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 80 ( 22 sgn 28 !; 8 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_11,type,
sK4: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_45_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X3: a] : $false ) )
<=> ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
<=> ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( $true
= ( X1 @ X4 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
<=> ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X1: a > $o,X0: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
<~> ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X1: a > $o,X0: a > $o] :
( ( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( ( ( sK1 @ sK2 )
= $true )
& ( ( sK0 @ sK2 )
!= $true ) )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
! [X3: a] :
( ( ( sK0 @ X3 )
= $true )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
| ( ( sK1 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( ( sK0 @ sK2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,definition,
( spl3_1
<=> ! [X3: a] :
( ( ( sK0 @ X3 )
= $true )
| ( ( sK1 @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f17,plain,
( ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
= $true ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,definition,
( spl3_2
<=> ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f20,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f21,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f10,f19,f16]) ).
thf(f24,definition,
( spl3_3
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f26,plain,
( ( ( sK0 @ sK2 )
!= $true )
| spl3_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
( ~ spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f11,f19,f24]) ).
thf(f29,definition,
( spl3_4
<=> ( ( sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f31,plain,
( ( ( sK1 @ sK2 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f32,plain,
( ~ spl3_2
| spl3_4 ),
inference(avatar_split_clause,[],[f12,f29,f19]) ).
thf(f33,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
@ X1 ) )
| ~ spl3_2 ),
inference(argument_congruence,[],[f21]) ).
thf(f34,plain,
( ! [X1: a] :
( ( $false
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: a] : $false
@ X1 )
= $true ) )
| ~ spl3_2 ),
inference(iff_proxy_clausification,[],[f33]) ).
thf(f40,plain,
( ! [X1: a] :
( ( ( ( sK1 @ X1 )
& ~ ( sK0 @ X1 ) )
= $false )
| ( $false = $true ) )
| ~ spl3_2 ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f41,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false = $true )
| ( $false
= ( ~ ( sK0 @ X1 ) ) ) )
| ~ spl3_2 ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) )
| ( $false = $true ) )
| ~ spl3_2 ),
inference(not_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f45,plain,
( ( ( sK0 @ sK2 )
= $true )
| ( $false = $true )
| ~ spl3_2
| ~ spl3_4 ),
inference(constrained_superposition,[],[f31,f43]) ).
thf(f47,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f50,plain,
( $false
| ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f47,f26]) ).
thf(f51,plain,
( ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f50]) ).
thf(f52,plain,
( ( ( ^ [Y0: a] : $false
@ sK4 )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
@ sK4 ) )
| spl3_2 ),
inference(negative_extensionality,[],[f20]) ).
thf(f53,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
@ sK4 )
= $true )
| ( ( ^ [Y0: a] : $false
@ sK4 )
= $true )
| spl3_2 ),
inference(xor_proxy_clausification,[],[f52]) ).
thf(f58,plain,
( ( $false = $true )
| ( ( ( sK1 @ sK4 )
& ~ ( sK0 @ sK4 ) )
= $true )
| spl3_2 ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f59,plain,
( ( ( ~ ( sK0 @ sK4 ) )
= $true )
| ( $false = $true )
| spl3_2 ),
inference(and_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $false = $true )
| spl3_2 ),
inference(and_proxy_clausification,[],[f58]) ).
thf(f61,plain,
( ( $true
= ( sK1 @ sK4 ) )
| spl3_2 ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f62,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK4 ) )
| spl3_2 ),
inference(not_proxy_clausification,[],[f59]) ).
thf(f63,plain,
( ( $false
= ( sK0 @ sK4 ) )
| spl3_2 ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f64,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $true != $true )
| ~ spl3_1
| spl3_2 ),
inference(constrained_superposition,[],[f17,f61]) ).
thf(f65,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl3_1
| spl3_2 ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
( ( $false = $true )
| ~ spl3_1
| spl3_2 ),
inference(forward_demodulation,[],[f65,f63]) ).
thf(f67,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f68,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f67]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( ~ spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
( ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f68]) ).
cnf(s7,plain,
~ spl3_2,
inference(rat,[],[s5,s2,s3]) ).
cnf(s8,plain,
~ spl3_1,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s7,s8]) ).
thf(f69,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET587^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n017.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 13:33:22 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running higher-order theorem proving
% 0.25/0.30 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
% 0.25/0.36 % (339666)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.36 % (339673)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2728004169:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.36 % (339673)Refutation not found, incomplete strategy
% 0.25/0.36 % (339673)------------------------------
% 0.25/0.36 % (339673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (339673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (339673)CaDiCaL version: 2.1.3
% 0.25/0.36 % (339673)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.36 % (339673)Time elapsed: 0.002 s
% 0.25/0.36 % (339673)Peak memory usage: 12 MB
% 0.25/0.36 % (339673)Instructions burned: 1 (million)
% 0.25/0.36 % (339673)------------------------------
% 0.25/0.36 % (339673)------------------------------
% 0.25/0.36 % (339677)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.36 % (339677)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
% 0.25/0.36 % (339671)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1100342179:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.36 % (339676)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=821953988:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.36 % (339672)lrs+10_16_si=on:nwc=1.5:random_seed=602398478:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.36 % (339677)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=2281162344:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.36 % (339671) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-339666-339671"...
% 0.25/0.36 % (339675)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2788158250:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.36 % (339674)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=238758840: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)
% 0.25/0.36 % (339671)...printing done.
% 0.25/0.36 % (339672) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-339666-339672"...
% 0.25/0.36 % (339676) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-339666-339676"...
% 0.25/0.36 % (339671)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.36 % (339671)------------------------------
% 0.25/0.36 % (339671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (339671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (339671)CaDiCaL version: 2.1.3
% 0.25/0.36 % (339671)Termination reason: Refutation
% 0.25/0.36 % (339671)Time elapsed: 0.006 s
% 0.25/0.36 % (339671)Peak memory usage: 13 MB
% 0.25/0.36 % (339671)Instructions burned: 4 (million)
% 0.25/0.36 % (339666)Success in time 0.041 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------