%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN055^5 : 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 : n002.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 08:41:39 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 354 ( 102 equ; 0 cnn)
% Maximal formula atoms : 13 ( 15 avg)
% Number of connectives : 306 ( 49 ~; 36 |; 63 &; 138 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 40 !; 21 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $o ).
thf(func_def_1,type,
cQ: $i > $o ).
thf(func_def_2,type,
cR: $i > $o ).
thf(func_def_3,type,
cF: $i > $o ).
thf(func_def_4,type,
cG: $i > $o ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cF @ X0 )
=> ( ( cR @ X0 )
& ~ ( cG @ X0 ) ) )
& ? [X0: $i] : ( cP @ X0 )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( ( cG @ X0 )
& ( cF @ X0 ) ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ X0 ) )
| ? [X0: $i] :
( ( cR @ X0 )
& ( cP @ X0 ) ) ) )
=> ? [X0: $i] :
( ( cQ @ X0 )
& ( cP @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL25) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cF @ X0 )
=> ( ( cR @ X0 )
& ~ ( cG @ X0 ) ) )
& ? [X0: $i] : ( cP @ X0 )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( ( cG @ X0 )
& ( cF @ X0 ) ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ X0 ) )
| ? [X0: $i] :
( ( cR @ X0 )
& ( cP @ X0 ) ) ) )
=> ? [X0: $i] :
( ( cQ @ X0 )
& ( cP @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( cF @ X0 )
=> ( ( cR @ X0 )
& ~ ( cG @ X0 ) ) )
& ? [X1: $i] : ( cP @ X1 )
& ! [X2: $i] :
( ( cP @ X2 )
=> ( ( cG @ X2 )
& ( cF @ X2 ) ) )
& ( ! [X3: $i] :
( ( cP @ X3 )
=> ( cQ @ X3 ) )
| ? [X4: $i] :
( ( cR @ X4 )
& ( cP @ X4 ) ) ) )
=> ? [X5: $i] :
( ( cQ @ X5 )
& ( cP @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( ( cF @ X0 )
= $true )
=> ( ( ( cR @ X0 )
= $true )
& ( ( cG @ X0 )
!= $true ) ) )
& ? [X1: $i] :
( $true
= ( cP @ X1 ) )
& ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
=> ( ( ( cF @ X2 )
= $true )
& ( $true
= ( cG @ X2 ) ) ) )
& ( ! [X3: $i] :
( ( $true
= ( cP @ X3 ) )
=> ( $true
= ( cQ @ X3 ) ) )
| ? [X4: $i] :
( ( ( cR @ X4 )
= $true )
& ( ( cP @ X4 )
= $true ) ) ) )
=> ? [X5: $i] :
( ( $true
= ( cQ @ X5 ) )
& ( $true
= ( cP @ X5 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( ( cF @ X0 )
= $true )
=> ( ( ( cR @ X0 )
= $true )
& ( ( cG @ X0 )
!= $true ) ) )
& ( ! [X3: $i] :
( ( $true
= ( cP @ X3 ) )
=> ( $true
= ( cQ @ X3 ) ) )
| ? [X4: $i] :
( ( ( cR @ X4 )
= $true )
& ( ( cP @ X4 )
= $true ) ) )
& ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
=> ( ( ( cF @ X2 )
= $true )
& ( $true
= ( cG @ X2 ) ) ) )
& ? [X1: $i] :
( $true
= ( cP @ X1 ) ) )
=> ? [X5: $i] :
( ( $true
= ( cQ @ X5 ) )
& ( $true
= ( cP @ X5 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X5: $i] :
( ( $true
!= ( cQ @ X5 ) )
| ( $true
!= ( cP @ X5 ) ) )
& ! [X0: $i] :
( ( ( ( cR @ X0 )
= $true )
& ( ( cG @ X0 )
!= $true ) )
| ( ( cF @ X0 )
!= $true ) )
& ( ! [X3: $i] :
( ( $true
= ( cQ @ X3 ) )
| ( $true
!= ( cP @ X3 ) ) )
| ? [X4: $i] :
( ( ( cR @ X4 )
= $true )
& ( ( cP @ X4 )
= $true ) ) )
& ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( ( ( cF @ X2 )
= $true )
& ( $true
= ( cG @ X2 ) ) ) )
& ? [X1: $i] :
( $true
= ( cP @ X1 ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X5: $i] :
( ( $true
!= ( cQ @ X5 ) )
| ( $true
!= ( cP @ X5 ) ) )
& ( ! [X3: $i] :
( ( $true
= ( cQ @ X3 ) )
| ( $true
!= ( cP @ X3 ) ) )
| ? [X4: $i] :
( ( ( cR @ X4 )
= $true )
& ( ( cP @ X4 )
= $true ) ) )
& ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( ( ( cF @ X2 )
= $true )
& ( $true
= ( cG @ X2 ) ) ) )
& ? [X1: $i] :
( $true
= ( cP @ X1 ) )
& ! [X0: $i] :
( ( ( ( cR @ X0 )
= $true )
& ( ( cG @ X0 )
!= $true ) )
| ( ( cF @ X0 )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( ( $true
= ( cQ @ X1 ) )
| ( $true
!= ( cP @ X1 ) ) )
| ? [X2: $i] :
( ( $true
= ( cR @ X2 ) )
& ( $true
= ( cP @ X2 ) ) ) )
& ! [X3: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( ( ( cF @ X3 )
= $true )
& ( $true
= ( cG @ X3 ) ) ) )
& ? [X4: $i] :
( ( cP @ X4 )
= $true )
& ! [X5: $i] :
( ( ( $true
= ( cR @ X5 ) )
& ( ( cG @ X5 )
!= $true ) )
| ( $true
!= ( cF @ X5 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( ( $true
= ( cQ @ X1 ) )
| ( $true
!= ( cP @ X1 ) ) )
| ( ( $true
= ( cR @ sK0 ) )
& ( ( cP @ sK0 )
= $true ) ) )
& ! [X3: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( ( ( cF @ X3 )
= $true )
& ( $true
= ( cG @ X3 ) ) ) )
& ( $true
= ( cP @ sK1 ) )
& ! [X5: $i] :
( ( ( $true
= ( cR @ X5 ) )
& ( ( cG @ X5 )
!= $true ) )
| ( $true
!= ( cF @ X5 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X4,sK1)],[f8]) ).
thf(f10,plain,
! [X5: $i] :
( ( ( cG @ X5 )
!= $true )
| ( $true
!= ( cF @ X5 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
= ( cP @ sK1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X3: $i] :
( ( $true
= ( cG @ X3 ) )
| ( $true
!= ( cP @ X3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X3: $i] :
( ( ( cF @ X3 )
= $true )
| ( $true
!= ( cP @ X3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
! [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
| ( $true
= ( cQ @ X1 ) )
| ( ( cP @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cP @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cF @ X0 )
!= $true )
| ( ( cP @ X0 )
!= $true ) ),
inference(superposition,[],[f10,f13]) ).
thf(f20,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cF @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f19]) ).
thf(f21,plain,
! [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
| ( ( cP @ sK0 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f15,f17]) ).
thf(f22,plain,
( ( $true != $true )
| ( ( cP @ sK0 )
= $true ) ),
inference(superposition,[],[f21,f12]) ).
thf(f23,plain,
( ( cP @ sK0 )
= $true ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
! [X0: $i] :
( ( cP @ X0 )
!= $true ),
inference(forward_subsumption_resolution,[],[f20,f14]) ).
thf(f26,plain,
$true != $true,
inference(superposition,[],[f24,f23]) ).
thf(f27,plain,
$false,
inference(trivial_inequality_removal,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN055^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n002.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 16:16:52 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 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
% 0.10/0.26 % (1483173)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.26 % (1483182)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=366547745:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.10/0.26 % (1483182) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1483173-1483182"...
% 0.10/0.26 % (1483182)...printing done.
% 0.10/0.26 % (1483182)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (1483182)------------------------------
% 0.10/0.26 % (1483182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (1483182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (1483182)CaDiCaL version: 2.1.3
% 0.10/0.26 % (1483182)Termination reason: Refutation
% 0.10/0.26 % (1483182)Time elapsed: 0.001 s
% 0.10/0.26 % (1483182)Peak memory usage: 12 MB
% 0.10/0.26 % (1483182)Instructions burned: 3 (million)
% 0.10/0.26 % (1483173)Success in time 0.033 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------