%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO096^5 : 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 : n014.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 08:46:36 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 47 equ; 0 cnn)
% Maximal formula atoms : 11 ( 10 avg)
% Number of connectives : 202 ( 25 ~; 16 |; 21 &; 128 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 44 !; 8 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_3,type,
cR: $i > $i > $o ).
thf(f1,conjecture,
( ( ! [X3: $i,X2: $i] :
( ( cQ @ X2 @ X3 )
=> ! [X4: $i] : ( cR @ X4 @ X3 ) )
& ( cR @ cA @ cB )
& ! [X0: $i] :
( ? [X1: $i] : ( cR @ X0 @ X1 )
=> ( cQ @ X0 @ X0 ) ) )
=> ? [X5: $i] :
( ( cQ @ X5 @ cA )
& ( cR @ cB @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cLX1) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: $i,X2: $i] :
( ( cQ @ X2 @ X3 )
=> ! [X4: $i] : ( cR @ X4 @ X3 ) )
& ( cR @ cA @ cB )
& ! [X0: $i] :
( ? [X1: $i] : ( cR @ X0 @ X1 )
=> ( cQ @ X0 @ X0 ) ) )
=> ? [X5: $i] :
( ( cQ @ X5 @ cA )
& ( cR @ cB @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cQ @ X1 @ X0 )
=> ! [X2: $i] : ( cR @ X2 @ X0 ) )
& ( cR @ cA @ cB )
& ! [X3: $i] :
( ? [X4: $i] : ( cR @ X3 @ X4 )
=> ( cQ @ X3 @ X3 ) ) )
=> ? [X5: $i] :
( ( cQ @ X5 @ cA )
& ( cR @ cB @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X3: $i] :
( ? [X4: $i] :
( ( cR @ X3 @ X4 )
= $true )
=> ( $true
= ( cQ @ X3 @ X3 ) ) )
& ( ( cR @ cA @ cB )
= $true )
& ! [X0: $i,X1: $i] :
( ( $true
= ( cQ @ X1 @ X0 ) )
=> ! [X2: $i] :
( ( cR @ X2 @ X0 )
= $true ) ) )
=> ? [X5: $i] :
( ( ( cQ @ X5 @ cA )
= $true )
& ( ( cR @ cB @ X5 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X5: $i] :
( ( ( cQ @ X5 @ cA )
!= $true )
| ( ( cR @ cB @ X5 )
!= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( cR @ X3 @ X4 )
!= $true )
| ( $true
= ( cQ @ X3 @ X3 ) ) )
& ( ( cR @ cA @ cB )
= $true )
& ! [X1: $i,X0: $i] :
( ( $true
!= ( cQ @ X1 @ X0 ) )
| ! [X2: $i] :
( ( cR @ X2 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X5: $i] :
( ( ( cQ @ X5 @ cA )
!= $true )
| ( ( cR @ cB @ X5 )
!= $true ) )
& ( ( cR @ cA @ cB )
= $true )
& ! [X1: $i,X0: $i] :
( ( $true
!= ( cQ @ X1 @ X0 ) )
| ! [X2: $i] :
( ( cR @ X2 @ X0 )
= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( cR @ X3 @ X4 )
!= $true )
| ( $true
= ( cQ @ X3 @ X3 ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 @ cA )
!= $true )
| ( ( cR @ cB @ X0 )
!= $true ) )
& ( ( cR @ cA @ cB )
= $true )
& ! [X1: $i,X2: $i] :
( ( ( cQ @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( cR @ X3 @ X2 )
= $true ) )
& ! [X4: $i] :
( ! [X5: $i] :
( $true
!= ( cR @ X4 @ X5 ) )
| ( ( cQ @ X4 @ X4 )
= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( cR @ X4 @ X5 ) )
| ( ( cQ @ X4 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( cQ @ X1 @ X2 )
!= $true )
| ( ( cR @ X3 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( cR @ cA @ cB )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X0: $i] :
( ( ( cR @ cB @ X0 )
!= $true )
| ( ( cQ @ X0 @ cA )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( ( ( cQ @ cA @ cA )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f8,f10]) ).
thf(f15,plain,
( ( cQ @ cA @ cA )
= $true ),
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
! [X0: $i] :
( ( $true
= ( cR @ X0 @ cA ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f9,f15]) ).
thf(f17,plain,
! [X0: $i] :
( $true
= ( cR @ X0 @ cA ) ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f18,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cQ @ X0 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f8,f17]) ).
thf(f19,plain,
! [X0: $i] :
( ( cQ @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f18]) ).
thf(f20,plain,
( ( $true != $true )
| ( ( cQ @ cA @ cA )
!= $true ) ),
inference(constrained_superposition,[],[f11,f17]) ).
thf(f21,plain,
( ( cQ @ cA @ cA )
!= $true ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
$false,
inference(forward_subsumption_resolution,[],[f21,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO096^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:33:30 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.09/0.26 % (2890085)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (2890095)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3808332974:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.26 % (2890095) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2890085-2890095"...
% 0.09/0.26 % (2890095)...printing done.
% 0.09/0.26 % (2890095)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (2890095)------------------------------
% 0.09/0.26 % (2890095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (2890095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (2890095)CaDiCaL version: 2.1.3
% 0.09/0.26 % (2890095)Termination reason: Refutation
% 0.09/0.26 % (2890095)Time elapsed: 0.001 s
% 0.09/0.26 % (2890095)Peak memory usage: 12 MB
% 0.09/0.26 % (2890095)Instructions burned: 2 (million)
% 0.09/0.26 % (2890085)Success in time 0.016 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------