%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU504^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:32:13 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 111 ( 7 ~; 0 |; 12 &; 64 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 6 con; 0-4 aty)
% ( 6 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 43 ( 25 ^; 10 !; 8 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_2,type,
exuE1: $o ).
thf(func_def_3,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sK0: $i > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_17,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_18,type,
sK3: ( $i > $o ) > $i > $i ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(f3,conjecture,
( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(f4,negated_conjecture,
~ ( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] : ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f9,plain,
~ ( exuE1
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X2: $i] : ( X0 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( exuE1 = $true )
=> ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X2: $i] :
( ( X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( ( exuE1 = $true )
=> ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X1: $i] :
( ( X0 @ X1 )
= $true ) ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( exuE1 = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f13,plain,
( ! [X1: $i] :
( $true
!= ( sK0 @ X1 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( exuE1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f12]) ).
thf(f14,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
! [X1: $i] :
( $true
!= ( sK0 @ X1 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f22,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[],[f17,f14]) ).
thf(f23,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( $true
= ( ( sK0 @ sK1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK1 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f27,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f55,plain,
$false,
inference(forward_subsumption_resolution,[],[f27,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU504^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:47:03 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (788022)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (788028)% WARNING: option uhcvi not known.
% 0.21/0.28 % (788028)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3738456982:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (788030)dis+10_1_sil=32000:sp=arity:random_seed=622520779:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (788027)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1473378916_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (788028)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (788028)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.28 % Exception at run slice level
% 0.21/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.28 % (788030) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-788022-788030"...
% 0.21/0.28 % (788028) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-788022-788028"...
% 0.21/0.28 % (788030)...printing done.
% 0.21/0.28 % (788028)...printing done.
% 0.21/0.28 % (788030)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 % (788030)------------------------------
% 0.21/0.28 % (788030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (788030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (788030)CaDiCaL version: 2.1.3
% 0.21/0.28 % (788030)Termination reason: Refutation
% 0.21/0.28 % (788030)Time elapsed: 0.003 s
% 0.21/0.28 % (788030)Peak memory usage: 11 MB
% 0.21/0.28 % (788030)Instructions burned: 3 (million)
% 0.21/0.28 % (788022)Success in time 0.039 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------