%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ083^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:20:51 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 119 ( 25 ~; 9 |; 0 &; 64 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 6 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 22 ( 8 ^; 14 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
says: $i > $o > $o ).
thf(func_def_3,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: $o ).
thf(func_def_11,type,
sK1: $o ).
thf(f1,axiom,
( says @ peter
@ ! [X0: $o] :
( ( says @ peter @ X0 )
=> ~ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f2,conjecture,
~ ! [X0: $o] :
( ( says @ peter @ X0 )
=> X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f3,negated_conjecture,
~ ~ ! [X0: $o] :
( ( says @ peter @ X0 )
=> X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( says @ peter
@ ! [X0: $o] :
( ( says @ peter @ X0 )
=> ~ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( $true
= ( says @ peter
@ ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ~ ! [X0: $o] :
( ( says @ peter @ X0 )
=> X0 ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ~ ! [X0: $o] :
( ( ( says @ peter @ X0 )
= $true )
=> ( $true = X0 ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: $o] :
( ( ( says @ peter @ X0 )
= $true )
=> ( $true = X0 ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
! [X0: $o] :
( ( ( says @ peter @ X0 )
!= $true )
| ( $true = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f10,plain,
! [X0: $o] :
( ( ( says @ peter @ X0 )
!= $true )
| ( $true = X0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( $true
= ( says @ peter
@ ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f14,plain,
( ( $true != $true )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) ) ) ),
inference(constrained_superposition,[],[f10,f11]) ).
thf(f15,plain,
! [X1: $o] :
( ( ( ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 )
@ X1 )
= $true )
| ( $true != $true ) ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X1: $o] :
( ( ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 )
@ X1 )
= $true ),
inference(trivial_inequality_removal,[],[f15]) ).
thf(f17,plain,
! [X1: $o] :
( $true
= ( ( says @ peter @ X1 )
=> ~ X1 ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X1: $o] :
( ( $false
= ( says @ peter @ X1 ) )
| ( $true = ( ~ X1 ) ) ),
inference(imp_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: $o] :
( ( $false
= ( says @ peter @ X1 ) )
| ( $false = X1 ) ),
inference(not_proxy_clausification,[],[f18]) ).
thf(f22,plain,
( ( ( !! @ $o
@ ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 ) )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f11,f19]) ).
thf(f23,plain,
( ( $false
= ( ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 )
@ sK0 ) )
| ( $true = $false ) ),
inference(sigma_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( $false
= ( ^ [Y0: $o] :
( ( says @ peter @ Y0 )
=> ~ Y0 )
@ sK0 ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
( $false
= ( ( says @ peter @ sK0 )
=> ~ sK0 ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
( $false = ( ~ sK0 ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( $true
= ( says @ peter @ sK0 ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f28,plain,
$true = sK0,
inference(not_proxy_clausification,[],[f26]) ).
thf(f37,plain,
( ( $true = $false )
| ( $false = sK0 ) ),
inference(constrained_superposition,[],[f19,f27]) ).
thf(f39,plain,
$false = sK0,
inference(trivial_inequality_removal,[],[f37]) ).
thf(f42,plain,
$true = $false,
inference(constrained_superposition,[],[f39,f28]) ).
thf(f45,plain,
$false,
inference(trivial_inequality_removal,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ083^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n015.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:25:18 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25 % (3504119)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.25 % (3504133)lrs+10_16_si=on:nwc=1.5:random_seed=2391733182:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.25 % (3504133) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3504119-3504133"...
% 0.08/0.25 % (3504133)...printing done.
% 0.08/0.25 % (3504133)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (3504133)------------------------------
% 0.08/0.25 % (3504133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (3504133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (3504133)CaDiCaL version: 2.1.3
% 0.08/0.25 % (3504133)Termination reason: Refutation
% 0.08/0.25 % (3504133)Time elapsed: 0.001 s
% 0.08/0.25 % (3504133)Peak memory usage: 12 MB
% 0.08/0.25 % (3504133)Instructions burned: 2 (million)
% 0.08/0.25 % (3504119)Success in time 0.03 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------