%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO007^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:48:42 AM UTC 2026
% Result : Theorem 0.12s 0.23s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 72 ( 8 ~; 0 |; 2 &; 43 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 5 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 27 ( 15 ^; 10 !; 2 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
leibeq: $o > $o > $o ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: $o ).
thf(func_def_11,type,
sK1: $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
sK2: $o > $o ).
thf(f1,axiom,
( leibeq
= ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq1) ).
thf(f2,conjecture,
! [X0: $o,X1: $o] :
( ( X0
<=> X1 )
=> ( leibeq @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
~ ! [X0: $o,X1: $o] :
( ( X0
<=> X1 )
=> ( leibeq @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( leibeq
= ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $o,X1: $o] :
( ( X0
<=> X1 )
=> ( leibeq @ X0 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $o,X1: $o] :
( ( X0 = X1 )
=> ( ( leibeq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $o,X1: $o] :
( ( ( leibeq @ X0 @ X1 )
!= $true )
& ( X0 = X1 ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( leibeq @ sK0 @ sK1 ) )
& ( sK0 = sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
sK0 = sK1,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
!= ( leibeq @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK1 ) ),
inference(definition_unfolding,[],[f12,f10,f11]) ).
thf(f16,plain,
( $true
!= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( $false
= ( ^ [Y0: $o > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK1 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( $false
= ( ( sK2 @ sK1 )
=> ( sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( $false
= ( sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( $true
= ( sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f22,plain,
$true = $false,
inference(constrained_superposition,[],[f19,f20]) ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO007^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.16 % Computer : n019.cluster.edu
% 0.12/0.16 % Model : x86_64 x86_64
% 0.12/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.16 % Memory : 8046.5625MB
% 0.12/0.16 % OS : Linux 6.8.0-71-generic
% 0.12/0.16 % CPULimit : 300
% 0.12/0.16 % WCLimit : 300
% 0.12/0.16 % DateTime : Tue Sep 29 16:21:18 UTC 2026
% 0.12/0.16 % CPUTime :
% 0.12/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.19 Running first-order model finding
% 0.12/0.19 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
% 0.12/0.23 % (994157)Will run a generic schedule for satisfiability detection.
% 0.12/0.23 % (994167)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=578026883:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.23 % (994167) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-994157-994167"...
% 0.12/0.23 % (994167)...printing done.
% 0.12/0.23 % (994167)Refutation found. Thanks to Tanya!
% 0.12/0.23 % SZS status Theorem for theBenchmark
% 0.12/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.23 % (994167)------------------------------
% 0.12/0.23 % (994167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.23 % (994167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.23 % (994167)CaDiCaL version: 2.1.3
% 0.12/0.23 % (994167)Termination reason: Refutation
% 0.12/0.23 % (994167)Time elapsed: 0.001 s
% 0.12/0.23 % (994167)Peak memory usage: 12 MB
% 0.12/0.23 % (994167)Instructions burned: 1 (million)
% 0.12/0.23 % (994157)Success in time 0.033 s
% 0.12/0.23 % Vampire exiting
%------------------------------------------------------------------------------