%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET591^5 : 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 : n003.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 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 74 ( 20 ~; 5 |; 9 &; 30 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 31 ( 10 ^; 19 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) )
=> ( ( ^ [X2: a] : $false )
= X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_50_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) )
=> ( ( ^ [X2: a] : $false )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) )
=> ( ( ^ [X3: a] : $false )
= X0 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
=> ( ( ^ [Y0: a] : $false )
= X0 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
=> ( ( ^ [Y0: a] : $false )
= X0 ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
& ( ( ^ [Y0: a] : $false )
!= X0 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X2: a] :
( ( $true
!= ( sK0 @ X2 ) )
| ( ( $true
!= ( sK0 @ X2 ) )
& ( $true
= ( sK1 @ X2 ) ) ) )
& ( ( ^ [Y0: a] : $false )
!= sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] : $false )
!= sK0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X2: a] :
( ( $true
!= ( sK0 @ X2 ) )
| ( $true
!= ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X2: a] :
( $true
!= ( sK0 @ X2 ) ),
inference(duplicate_literal_removal,[],[f10]) ).
thf(f14,plain,
( ( ^ [Y0: a] : $false
@ sK2 )
!= ( sK0 @ sK2 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f15,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f14]) ).
thf(f18,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f19,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f18]) ).
thf(f20,plain,
$false,
inference(forward_subsumption_resolution,[],[f19,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET591^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n003.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:40:13 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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
% 0.20/0.29 % (2509599)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (2509606)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2357493333:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (2509606)Refutation not found, incomplete strategy
% 0.20/0.29 % (2509606)------------------------------
% 0.20/0.29 % (2509606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2509606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2509606)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2509606)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (2509606)Time elapsed: 0.001 s
% 0.20/0.29 % (2509606)Peak memory usage: 12 MB
% 0.20/0.29 % (2509606)------------------------------
% 0.20/0.29 % (2509606)------------------------------
% 0.20/0.29 % (2509610)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 % (2509610)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 % (2509607)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=3666500251: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 % (2509604)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2220396977:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (2509605)lrs+10_16_si=on:nwc=1.5:random_seed=733304332:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (2509609)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1876762725:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (2509608)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4005931661:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (2509610)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=769707303:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (2509605) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2509599-2509605"...
% 0.20/0.29 % (2509604) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2509599-2509604"...
% 0.20/0.29 % (2509608) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2509599-2509608"...
% 0.20/0.29 % (2509609) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2509599-2509609"...
% 0.20/0.29 % (2509607) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2509599-2509607"...
% 0.20/0.29 % (2509605)...printing done.
% 0.20/0.29 % (2509604)...printing done.
% 0.20/0.29 % (2509610) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2509599-2509610"...
% 0.20/0.29 % (2509608)...printing done.
% 0.20/0.29 % (2509609)...printing done.
% 0.20/0.29 % (2509607)...printing done.
% 0.20/0.29 % (2509605)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 % (2509605)------------------------------
% 0.20/0.29 % (2509605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2509605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2509605)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2509605)Termination reason: Refutation
% 0.20/0.29 % (2509605)Time elapsed: 0.001 s
% 0.20/0.29 % (2509605)Peak memory usage: 12 MB
% 0.20/0.29 % (2509605)Instructions burned: 1 (million)
% 0.20/0.29 % (2509599)Success in time 0.04 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------