%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV282^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:38:11 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 279 ( 33 ~; 0 |; 30 &; 162 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 125 ( 125 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 15 usr; 4 con; 0-4 aty)
% ( 13 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 83 ( 75 ^; 4 !; 4 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_1,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_4,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
sK0: ( ( $i > $o ) > $o ) > $o ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) )
= cZERO ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cZERO_def) ).
thf(f2,axiom,
( ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X0
@ ^ [X3: $i] :
( ( X3 != X2 )
& ( X1 @ X3 ) ) ) ) )
= cSUCC ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def) ).
thf(f3,axiom,
( ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1 @ cZERO )
& ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cNAT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cNAT_def) ).
thf(f4,conjecture,
cNAT @ cZERO,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTTTP6100) ).
thf(f5,negated_conjecture,
~ ( cNAT @ cZERO ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X0
@ ^ [X3: $i] :
( ( X3 != X2 )
& ( X1 @ X3 ) ) ) ) )
= cSUCC ),
inference(rectify,[],[f2]) ).
thf(f7,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1 @ cZERO )
& ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cNAT ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) )
= cZERO ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( cNAT @ cZERO ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
( ( cNAT @ cZERO )
!= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( cNAT @ cZERO )
!= $true ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,plain,
( ( cNAT @ cZERO )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y3
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 != Y6 ) ) )
& ( Y4 @ Y5 ) ) )
@ Y2 ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f16,f15,f17]) ).
thf(f22,plain,
( ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y3
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 != Y6 ) ) )
& ( Y4 @ Y5 ) ) )
@ Y2 ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
!= $true ),
inference(definition_unfolding,[],[f18,f21,f17]) ).
thf(f23,plain,
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( $false
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 != Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( $false
= ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( sK0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) )
& ( sK0
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
=> ( sK0
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
( $false
= ( sK0
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( sK0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) )
& ( sK0
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f28,plain,
( ( sK0
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $true ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f33,plain,
$false = $true,
inference(forward_demodulation,[],[f26,f28]) ).
thf(f34,plain,
$false,
inference(trivial_inequality_removal,[],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV282^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n006.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 15:30:55 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.24 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
% 0.22/0.28 % (867726)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (867737)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2569621980:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.28 % (867737) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-867726-867737"...
% 0.22/0.28 % (867737)...printing done.
% 0.22/0.28 % (867737)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (867737)------------------------------
% 0.22/0.28 % (867737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (867737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (867737)CaDiCaL version: 2.1.3
% 0.22/0.28 % (867737)Termination reason: Refutation
% 0.22/0.28 % (867737)Time elapsed: 0.002 s
% 0.22/0.28 % (867737)Peak memory usage: 12 MB
% 0.22/0.28 % (867737)Instructions burned: 4 (million)
% 0.22/0.28 % (867726)Success in time 0.028 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------