%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO136^5 : 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 : n006.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 08:46:41 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 28 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 71 ( 13 ~; 4 |; 12 &; 26 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 5 !; 11 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_2,type,
cB: $o ).
thf(func_def_3,type,
cP: $i > $o ).
thf(f1,conjecture,
( ( ( ? [X0: $i] : ( cP @ X0 )
=> cB )
=> cB )
=> ( ( cQ @ x )
=> ? [X0: $i] : ( cQ @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cADDHYP3) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X0: $i] : ( cP @ X0 )
=> cB )
=> cB )
=> ( ( cQ @ x )
=> ? [X0: $i] : ( cQ @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ? [X0: $i] : ( cP @ X0 )
=> cB )
=> cB )
=> ( ( cQ @ x )
=> ? [X1: $i] : ( cQ @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
=> ( cB = $true ) )
=> ( cB = $true ) )
=> ( ( ( cQ @ x )
= $true )
=> ? [X1: $i] :
( $true
= ( cQ @ X1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X1: $i] :
( $true
!= ( cQ @ X1 ) )
& ( ( cQ @ x )
= $true )
& ( ( cB = $true )
| ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
& ( cB != $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X1: $i] :
( $true
!= ( cQ @ X1 ) )
& ( ( cQ @ x )
= $true )
& ( ( cB = $true )
| ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
& ( cB != $true ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( cQ @ X0 )
!= $true )
& ( ( cQ @ x )
= $true )
& ( ( cB = $true )
| ( ? [X1: $i] :
( $true
= ( cP @ X1 ) )
& ( cB != $true ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( cQ @ X0 )
!= $true )
& ( ( cQ @ x )
= $true )
& ( ( cB = $true )
| ( ( $true
= ( cP @ sK0 ) )
& ( cB != $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f7]) ).
thf(f11,plain,
( ( cQ @ x )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X0: $i] :
( ( cQ @ X0 )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f24,plain,
$true != $true,
inference(constrained_superposition,[],[f12,f11]) ).
thf(f25,plain,
$false,
inference(trivial_inequality_removal,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO136^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:34:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.28 % (952549)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (952554)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2371507076:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (952554) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-952549-952554"...
% 0.20/0.28 % (952554)...printing done.
% 0.20/0.28 % (952554)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (952554)------------------------------
% 0.20/0.28 % (952554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (952554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (952554)CaDiCaL version: 2.1.3
% 0.20/0.28 % (952554)Termination reason: Refutation
% 0.20/0.28 % (952554)Time elapsed: 0.001 s
% 0.20/0.28 % (952554)Peak memory usage: 12 MB
% 0.20/0.28 % (952554)Instructions burned: 1 (million)
% 0.20/0.28 % (952549)Success in time 0.038 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------