%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN051^5 : 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 : 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 08:41:38 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 204 ( 58 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 129 ( 28 ~; 20 |; 24 &; 37 @)
% ( 0 <=>; 20 =>; 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 : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 6 !; 18 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
p: $o ).
thf(func_def_1,type,
cF: $i > $o ).
thf(f1,conjecture,
( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X0: $i] :
( p
=> ( cF @ X0 ) ) )
=> ? [X0: $i] :
( ( p
=> ( cF @ X0 ) )
& ( ( cF @ X0 )
=> p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL21) ).
thf(f2,negated_conjecture,
~ ( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X0: $i] :
( p
=> ( cF @ X0 ) ) )
=> ? [X0: $i] :
( ( p
=> ( cF @ X0 ) )
& ( ( cF @ X0 )
=> p ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ? [X0: $i] :
( ( cF @ X0 )
=> p )
& ? [X1: $i] :
( p
=> ( cF @ X1 ) ) )
=> ? [X2: $i] :
( ( p
=> ( cF @ X2 ) )
& ( ( cF @ X2 )
=> p ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ? [X0: $i] :
( ( ( cF @ X0 )
= $true )
=> ( p = $true ) )
& ? [X1: $i] :
( ( p = $true )
=> ( $true
= ( cF @ X1 ) ) ) )
=> ? [X2: $i] :
( ( ( p = $true )
=> ( $true
= ( cF @ X2 ) ) )
& ( ( $true
= ( cF @ X2 ) )
=> ( p = $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X2: $i] :
( ( ( $true
= ( cF @ X2 ) )
& ( p != $true ) )
| ( ( $true
!= ( cF @ X2 ) )
& ( p = $true ) ) )
& ? [X0: $i] :
( ( p = $true )
| ( ( cF @ X0 )
!= $true ) )
& ? [X1: $i] :
( ( $true
= ( cF @ X1 ) )
| ( p != $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X1: $i] :
( ( $true
= ( cF @ X1 ) )
| ( p != $true ) )
& ! [X2: $i] :
( ( ( $true
= ( cF @ X2 ) )
& ( p != $true ) )
| ( ( $true
!= ( cF @ X2 ) )
& ( p = $true ) ) )
& ? [X0: $i] :
( ( p = $true )
| ( ( cF @ X0 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i] :
( ( ( cF @ X0 )
= $true )
| ( p != $true ) )
& ! [X1: $i] :
( ( ( $true
= ( cF @ X1 ) )
& ( p != $true ) )
| ( ( $true
!= ( cF @ X1 ) )
& ( p = $true ) ) )
& ? [X2: $i] :
( ( p = $true )
| ( $true
!= ( cF @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( ( cF @ sK0 )
= $true )
| ( p != $true ) )
& ! [X1: $i] :
( ( ( $true
= ( cF @ X1 ) )
& ( p != $true ) )
| ( ( $true
!= ( cF @ X1 ) )
& ( p = $true ) ) )
& ( ( p = $true )
| ( ( cF @ sK1 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f7]) ).
thf(f9,plain,
( ( ( cF @ sK1 )
!= $true )
| ( p = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X1: $i] :
( ( $true
!= ( cF @ X1 ) )
| ( p != $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X1: $i] :
( ( $true
= ( cF @ X1 ) )
| ( p = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( ( cF @ sK0 )
= $true )
| ( p != $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( p = $true )
| ( p = $true )
| ( $true != $true ) ),
inference(superposition,[],[f9,f12]) ).
thf(f18,plain,
( ( $true != $true )
| ( p = $true ) ),
inference(duplicate_literal_removal,[],[f16]) ).
thf(f19,plain,
p = $true,
inference(trivial_inequality_removal,[],[f18]) ).
thf(f21,plain,
( ( cF @ sK0 )
= $true ),
inference(forward_subsumption_resolution,[],[f14,f12]) ).
thf(f22,plain,
( ( p != $true )
| ( $true != $true ) ),
inference(superposition,[],[f11,f21]) ).
thf(f23,plain,
p != $true,
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
$false,
inference(forward_subsumption_resolution,[],[f23,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN051^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:13:55 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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
% 0.21/0.28 % (922209)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (922218)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3831420098:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (922218) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-922209-922218"...
% 0.21/0.28 % (922218)...printing done.
% 0.21/0.28 % (922218)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (922218)------------------------------
% 0.21/0.28 % (922218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (922218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (922218)CaDiCaL version: 2.1.3
% 0.21/0.28 % (922218)Termination reason: Refutation
% 0.21/0.28 % (922218)Time elapsed: 0.001 s
% 0.21/0.28 % (922218)Peak memory usage: 12 MB
% 0.21/0.28 % (922218)Instructions burned: 1 (million)
% 0.21/0.28 % (922209)Success in time 0.03 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------