%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET143^5 : 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 : n015.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 08:23:14 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 8 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 87 ( 7 ~; 0 |; 32 &; 48 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 34 ( 16 ^; 12 !; 6 ?; 34 :)
% 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,
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 > $o ).
thf(f1,conjecture,
! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 )
& ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_67_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 )
& ( X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( X2 @ X4 )
& ( X1 @ X4 )
& ( X0 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 )
& ( X2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET143^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n015.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:40:18 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.23/0.30 % (3531274)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (3531281)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3748973222:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (3531281)Refutation not found, incomplete strategy
% 0.23/0.30 % (3531281)------------------------------
% 0.23/0.30 % (3531281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (3531281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (3531281)CaDiCaL version: 2.1.3
% 0.23/0.30 % (3531281)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (3531281)Time elapsed: 0.001 s
% 0.23/0.30 % (3531281)Peak memory usage: 12 MB
% 0.23/0.30 % (3531281)Instructions burned: 1 (million)
% 0.23/0.30 % (3531281)------------------------------
% 0.23/0.30 % (3531281)------------------------------
% 0.23/0.30 % (3531285)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (3531285)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
% 0.23/0.30 % (3531284)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1313556121:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (3531279)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2084341195:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (3531280)lrs+10_16_si=on:nwc=1.5:random_seed=1579619911:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (3531283)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1547291767:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (3531282)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=2853757940: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)
% 0.23/0.30 % (3531285)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=2661391144:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (3531285) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3531274-3531285"...
% 0.23/0.30 % (3531279) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3531274-3531279"...
% 0.23/0.30 % (3531283) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3531274-3531283"...
% 0.23/0.30 % (3531284) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3531274-3531284"...
% 0.23/0.30 % (3531280) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3531274-3531280"...
% 0.23/0.30 % (3531282) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3531274-3531282"...
% 0.23/0.30 % (3531285)...printing done.
% 0.23/0.30 % (3531279)...printing done.
% 0.23/0.30 % (3531285)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (3531285)------------------------------
% 0.23/0.30 % (3531285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (3531285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (3531285)CaDiCaL version: 2.1.3
% 0.23/0.30 % (3531285)Termination reason: Refutation
% 0.23/0.30 % (3531285)Time elapsed: 0.001 s
% 0.23/0.30 % (3531285)Peak memory usage: 12 MB
% 0.23/0.30 % (3531285)Instructions burned: 1 (million)
% 0.23/0.30 % (3531274)Success in time 0.048 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------