%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n015.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 08:39:15 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% 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,
vNOT: $o > $o ).
thf(func_def_5,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
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,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cZERO_def) ).
thf(f2,axiom,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X1 @ X3 )
& ( X3 != X2 ) ) )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def) ).
thf(f3,axiom,
( cNAT
= ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) )
& ( X1 @ cZERO ) )
=> ( X1 @ X0 ) ) ) ),
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,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X1 @ X3 )
& ( X3 != X2 ) ) )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( cNAT
= ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) )
& ( X1 @ cZERO ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1 @ cZERO )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
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,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1 @ cZERO )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
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] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y5 != Y6 )
& ( Y4 @ Y6 ) ) ) ) )
@ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f17,f15,f16]) ).
thf(f22,plain,
( $true
!= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
& ( Y3
@ ^ [Y6: $i] :
( ( Y5 != Y6 )
& ( Y4 @ Y6 ) ) ) ) )
@ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f18,f21,f15]) ).
thf(f23,plain,
( $true
!= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( $false
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( $false
= ( ( ( sK0
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( sK0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
=> ( 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,
( $true
= ( ( sK0
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
& ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( sK0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f29,plain,
( $true
= ( sK0
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f33,plain,
$true = $false,
inference(forward_demodulation,[],[f29,f26]) ).
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 SAT
% 0.10/0.20 % Computer : n015.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 15:34:33 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.28 % (3665086)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (3665094)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3732480119_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (3665095)% WARNING: option uhcvi not known.
% 0.20/0.28 % (3665095)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3912310485:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (3665096)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4052172096:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (3665098)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2445971580:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (3665097)dis+10_1_sil=32000:sp=arity:random_seed=255506865:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (3665095)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (3665099)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3983176624:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (3665095)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (3665098)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (3665100)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3250613646:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (3665095) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3665086-3665095"...
% 0.20/0.28 % (3665096) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3665086-3665096"...
% 0.20/0.28 % (3665098) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3665086-3665098"...
% 0.20/0.28 % (3665097) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3665086-3665097"...
% 0.20/0.28 % (3665099) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3665086-3665099"...
% 0.20/0.28 % (3665100) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3665086-3665100"...
% 0.20/0.28 % (3665095)...printing done.
% 0.20/0.28 % (3665096)...printing done.
% 0.20/0.28 % (3665098)...printing done.
% 0.20/0.28 % (3665097)...printing done.
% 0.20/0.28 % (3665106)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1089605443:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.28 % (3665095)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3665095)------------------------------
% 0.20/0.28 % (3665095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3665095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3665095)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3665095)Termination reason: Refutation
% 0.20/0.28 % (3665095)Time elapsed: 0.003 s
% 0.20/0.28 % (3665095)Peak memory usage: 12 MB
% 0.20/0.28 % (3665095)Instructions burned: 4 (million)
% 0.20/0.28 % (3665086)Success in time 0.036 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------