%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO154^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:49:03 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% 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 : 139 ( 36 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 130 ( 17 ~; 10 |; 17 &; 74 @)
% ( 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 : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 20 !; 4 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_2,type,
cQ: $i > $o ).
thf(func_def_3,type,
f: $i > $i ).
thf(func_def_4,type,
cP: $i > $o ).
thf(f1,conjecture,
( ( ! [X1: $i] :
( ( cQ @ X1 )
=> ( cR @ ( g @ X1 ) ) )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) )
& ( cP @ a ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDEMO_TRIV1) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i] :
( ( cQ @ X1 )
=> ( cR @ ( g @ X1 ) ) )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) )
& ( cP @ a ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( cQ @ X0 )
=> ( cR @ ( g @ X0 ) ) )
& ! [X1: $i] :
( ( cP @ X1 )
=> ( cQ @ ( f @ X1 ) ) )
& ( cP @ a ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( ( cQ @ X0 )
= $true )
=> ( ( cR @ ( g @ X0 ) )
= $true ) )
& ! [X1: $i] :
( ( ( cP @ X1 )
= $true )
=> ( ( cQ @ ( f @ X1 ) )
= $true ) )
& ( ( cP @ a )
= $true ) )
=> ? [X2: $i] :
( ( cR @ X2 )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X2: $i] :
( ( cR @ X2 )
!= $true )
& ! [X0: $i] :
( ( ( cR @ ( g @ X0 ) )
= $true )
| ( ( cQ @ X0 )
!= $true ) )
& ! [X1: $i] :
( ( ( cQ @ ( f @ X1 ) )
= $true )
| ( ( cP @ X1 )
!= $true ) )
& ( ( cP @ a )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X2: $i] :
( ( cR @ X2 )
!= $true )
& ! [X0: $i] :
( ( ( cR @ ( g @ X0 ) )
= $true )
| ( ( cQ @ X0 )
!= $true ) )
& ! [X1: $i] :
( ( ( cQ @ ( f @ X1 ) )
= $true )
| ( ( cP @ X1 )
!= $true ) )
& ( ( cP @ a )
= $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( $true
!= ( cR @ X0 ) )
& ! [X1: $i] :
( ( ( cR @ ( g @ X1 ) )
= $true )
| ( ( cQ @ X1 )
!= $true ) )
& ! [X2: $i] :
( ( $true
= ( cQ @ ( f @ X2 ) ) )
| ( $true
!= ( cP @ X2 ) ) )
& ( ( cP @ a )
= $true ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( cP @ a )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cQ @ ( f @ X2 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X1: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( ( cR @ ( g @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X0: $i] :
( $true
!= ( cR @ X0 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( ( $true != $true )
| ( $true
= ( cQ @ ( f @ a ) ) ) ),
inference(constrained_superposition,[],[f9,f8]) ).
thf(f15,plain,
( $true
= ( cQ @ ( f @ a ) ) ),
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
( ( $true != $true )
| ( $true
= ( cR @ ( g @ ( f @ a ) ) ) ) ),
inference(constrained_superposition,[],[f10,f15]) ).
thf(f17,plain,
( $true
= ( cR @ ( g @ ( f @ a ) ) ) ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f18,plain,
$false,
inference(forward_subsumption_resolution,[],[f17,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO154^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 % Computer : n009.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 16:35:46 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.25 Running first-order model finding
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29 % (29568)Will run a generic schedule for satisfiability detection.
% 0.21/0.29 % (29582)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1762203631:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.21/0.29 % (29582) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-29568-29582"...
% 0.21/0.29 % (29582)...printing done.
% 0.21/0.29 % (29578)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2234040165:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.21/0.29 % (29582)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (29582)------------------------------
% 0.21/0.29 % (29582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (29582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (29582)CaDiCaL version: 2.1.3
% 0.21/0.29 % (29582)Termination reason: Refutation
% 0.21/0.29 % (29582)Time elapsed: 0.002 s
% 0.21/0.29 % (29582)Peak memory usage: 12 MB
% 0.21/0.29 % (29582)Instructions burned: 1 (million)
% 0.21/0.29 % (29568)Success in time 0.026 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------