%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET626^5 : 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 : n012.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 08:23:24 AM UTC 2026
% Result : Theorem 0.07s 0.18s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 27 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 85 ( 14 ~; 5 |; 21 &; 41 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 0-2 aty)
% Number of variables : 26 ( 0 ^; 12 !; 14 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cZ: a > $o ).
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,
! [X1: a > $o,X0: a > $o] :
( ? [X2: a] :
( ( X0 @ X2 )
& ( cZ @ X2 )
& ( X1 @ X2 ) )
=> ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_102_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ? [X2: a] :
( ( X0 @ X2 )
& ( cZ @ X2 )
& ( X1 @ X2 ) )
=> ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
& ( cZ @ X2 )
& ( X0 @ X2 ) )
=> ? [X3: a] :
( ( X0 @ X3 )
& ( X1 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( cZ @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
=> ? [X3: a] :
( ( ( X1 @ X3 )
= $true )
& ( ( X0 @ X3 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ? [X2: a] :
( ( ( cZ @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) )
& ? [X3: a] :
( ( ( cZ @ X3 )
= $true )
& ( ( X1 @ X3 )
= $true )
& ( ( X0 @ X3 )
= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X2: a] :
( ( ( sK1 @ X2 )
!= $true )
| ( ( sK0 @ X2 )
!= $true ) )
& ( $true
= ( cZ @ sK2 ) )
& ( ( sK1 @ sK2 )
= $true )
& ( ( sK0 @ sK2 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[f6]) ).
thf(f8,plain,
( ( sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X2: a] :
( ( ( sK1 @ X2 )
!= $true )
| ( ( sK0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( ( $true != $true )
| ( ( sK0 @ sK2 )
!= $true ) ),
inference(constrained_superposition,[],[f11,f9]) ).
thf(f15,plain,
( ( sK0 @ sK2 )
!= $true ),
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
$false,
inference(forward_subsumption_resolution,[],[f15,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET626^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 13:39:33 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.13 Running higher-order theorem proving
% 0.07/0.14 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
% 0.07/0.18 % (113984)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.18 % (113992)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=3399793319: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)
% 0.07/0.18 % (113989)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2662109726:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.07/0.18 % (113990)lrs+10_16_si=on:nwc=1.5:random_seed=3799073178:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.07/0.18 % (113991)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=390218756:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.07/0.18 % (113990) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113984-113990"...
% 0.07/0.18 % (113989) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113984-113989"...
% 0.07/0.18 % (113991) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113984-113991"...
% 0.07/0.18 % (113992) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113984-113992"...
% 0.07/0.18 % (113989)...printing done.
% 0.07/0.18 % (113990)...printing done.
% 0.07/0.18 % (113992)...printing done.
% 0.07/0.18 % (113991)...printing done.
% 0.07/0.18 % (113990)Refutation found. Thanks to Tanya!
% 0.07/0.18 % SZS status Theorem for theBenchmark
% 0.07/0.18 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.18 % (113990)------------------------------
% 0.07/0.18 % (113990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.18 % (113990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.18 % (113990)CaDiCaL version: 2.1.3
% 0.07/0.18 % (113990)Termination reason: Refutation
% 0.07/0.18 % (113990)Time elapsed: 0.001 s
% 0.07/0.18 % (113990)Peak memory usage: 11 MB
% 0.07/0.18 % (113990)Instructions burned: 1 (million)
% 0.07/0.18 % (113984)Success in time 0.03 s
% 0.07/0.18 % Vampire exiting
%------------------------------------------------------------------------------