%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ100^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:20:53 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 139 ( 8 ~; 0 |; 9 &; 94 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 4 con; 0-4 aty)
% ( 11 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 31 ( 22 ^; 8 !; 1 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
s: $i > $i ).
thf(func_def_1,type,
cCKB_E2: $i > $i > $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK1: $i > $o ).
thf(f1,axiom,
( cCKB_E2
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) )
& ( X2 @ X0 ) )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_E2_def) ).
thf(f2,conjecture,
! [X0: $i] : ( cCKB_E2 @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_L32000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] : ( cCKB_E2 @ X0 @ X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ! [X0: $i] : ( cCKB_E2 @ X0 @ X0 ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i] :
( ( cCKB_E2 @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( cCKB_E2
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) )
& ( X2 @ X0 ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i] :
( ( cCKB_E2 @ X0 @ X0 )
!= $true ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
( $true
!= ( cCKB_E2 @ sK0 @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( $true
!= ( cCKB_E2 @ sK0 @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK0 ) ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f15,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ sK0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
( ( ^ [Y0: $i > $o] :
( ( ( Y0 @ sK0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( $false
= ( ( ( sK1 @ sK0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK1 @ ( s @ ( s @ Y0 ) ) ) ) ) )
=> ( sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( $false
= ( sK1 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( $true
= ( ( sK1 @ sK0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK1 @ ( s @ ( s @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f17]) ).
thf(f21,plain,
( $true
= ( sK1 @ sK0 ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f25,plain,
$true = $false,
inference(forward_demodulation,[],[f18,f21]) ).
thf(f26,plain,
$false,
inference(trivial_inequality_removal,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ100^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n004.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 13:23:52 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.25 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
% 0.22/0.30 % (1266195)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (1266210)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3695802048:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (1266210) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1266195-1266210"...
% 0.22/0.30 % (1266210)...printing done.
% 0.22/0.30 % (1266210)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (1266210)------------------------------
% 0.22/0.30 % (1266210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1266210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1266210)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1266210)Termination reason: Refutation
% 0.22/0.30 % (1266210)Time elapsed: 0.001 s
% 0.22/0.30 % (1266210)Peak memory usage: 12 MB
% 0.22/0.30 % (1266210)Instructions burned: 2 (million)
% 0.22/0.30 % (1266195)Success in time 0.038 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------