%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO149^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:46:43 AM UTC 2026
% Result : Theorem 0.24s 0.35s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 36 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 128 ( 17 ~; 10 |; 17 &; 72 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP: $i > $o ).
thf(func_def_3,type,
cQ: $i > $o ).
thf(f1,conjecture,
( ( ! [X1: $i] :
( ( cQ @ X1 )
=> ( cP @ X1 ) )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) )
& ( cP @ a ) )
=> ( cP @ ( f @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSIMPLEPQ) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i] :
( ( cQ @ X1 )
=> ( cP @ X1 ) )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) )
& ( cP @ a ) )
=> ( cP @ ( f @ a ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( cQ @ X0 )
=> ( cP @ X0 ) )
& ! [X1: $i] :
( ( cP @ X1 )
=> ( cQ @ ( f @ X1 ) ) )
& ( cP @ a ) )
=> ( cP @ ( f @ a ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( $true
= ( cQ @ X0 ) )
=> ( ( cP @ X0 )
= $true ) )
& ( ( cP @ a )
= $true )
& ! [X1: $i] :
( ( ( cP @ X1 )
= $true )
=> ( $true
= ( cQ @ ( f @ X1 ) ) ) ) )
=> ( ( cP @ ( f @ a ) )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( cP @ ( f @ a ) )
!= $true )
& ! [X0: $i] :
( ( $true
!= ( cQ @ X0 ) )
| ( ( cP @ X0 )
= $true ) )
& ( ( cP @ a )
= $true )
& ! [X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( $true
= ( cQ @ ( f @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( cP @ ( f @ a ) )
!= $true )
& ! [X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( $true
= ( cQ @ ( f @ X1 ) ) ) )
& ! [X0: $i] :
( ( $true
!= ( cQ @ X0 ) )
| ( ( cP @ X0 )
= $true ) )
& ( ( cP @ a )
= $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ( cP @ ( f @ a ) )
!= $true )
& ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ ( f @ X0 ) )
= $true ) )
& ! [X1: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( ( cP @ X1 )
= $true ) )
& ( ( cP @ a )
= $true ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( cP @ a )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X1: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( ( cP @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ ( f @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( cP @ ( f @ a ) )
!= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( ( $true != $true )
| ( ( cQ @ ( f @ a ) )
= $true ) ),
inference(constrained_superposition,[],[f10,f8]) ).
thf(f15,plain,
( ( cQ @ ( f @ a ) )
= $true ),
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
( ( ( cP @ ( f @ a ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f9,f15]) ).
thf(f17,plain,
( ( cP @ ( f @ a ) )
= $true ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f18,plain,
$false,
inference(forward_subsumption_resolution,[],[f17,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO149^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n005.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 16:35:16 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.32 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
% 0.24/0.35 % (1885592)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.35 % (1885599)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1813251083:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.35 % (1885599) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1885592-1885599"...
% 0.24/0.35 % (1885599)...printing done.
% 0.24/0.35 % (1885599)Refutation found. Thanks to Tanya!
% 0.24/0.35 % SZS status Theorem for theBenchmark
% 0.24/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.36 % (1885599)------------------------------
% 0.24/0.36 % (1885599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (1885599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (1885599)CaDiCaL version: 2.1.3
% 0.24/0.36 % (1885599)Termination reason: Refutation
% 0.24/0.36 % (1885599)Time elapsed: 0.002 s
% 0.24/0.36 % (1885599)Peak memory usage: 12 MB
% 0.24/0.36 % (1885599)Instructions burned: 1 (million)
% 0.24/0.36 % (1885592)Success in time 0.027 s
% 0.24/0.36 % Vampire exiting
%------------------------------------------------------------------------------