%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ103^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:21:02 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of formulae : 50 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 314 ( 85 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 355 ( 15 ~; 36 |; 16 &; 232 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 5 con; 0-4 aty)
% ( 20 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 73 ( 46 ^; 26 !; 1 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_NUM: $i > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_15,type,
sK2: $i > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( cCKB6_NUM
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_NUM_def) ).
thf(f2,conjecture,
! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB6_L3000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( cCKB6_NUM
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i] :
( ( ( cCKB6_NUM @ X0 )
= $true )
=> ( ( cCKB6_NUM @ ( s @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i] :
( ( ( cCKB6_NUM @ ( s @ X0 ) )
!= $true )
& ( ( cCKB6_NUM @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( cCKB6_NUM @ ( s @ sK0 ) ) )
& ( $true
= ( cCKB6_NUM @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
( $true
= ( cCKB6_NUM @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
!= ( cCKB6_NUM @ ( s @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( s @ sK0 ) ) ),
inference(definition_unfolding,[],[f12,f10]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f11,f10]) ).
thf(f17,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: $i > $o] :
( $true
= ( ( ( X1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) ) )
=> ( X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) ) ) )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ c1 )
= $false ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) )
@ ( sK1 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ c1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ ( sK1 @ X1 ) )
=> ( X1 @ ( s @ ( sK1 @ X1 ) ) ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ c1 )
= $false ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ ( s @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ c1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ c1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ ( s @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f27,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ ( s @ sK0 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( $false
= ( ( ( sK2 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ Y0 ) ) ) ) )
=> ( sK2 @ ( s @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
( $false
= ( sK2 @ ( s @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( $true
= ( ( sK2 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( $true
= ( sK2 @ c1 ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( ( sK2 @ X1 )
=> ( sK2 @ ( s @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X1: $i] :
( ( $true
= ( sK2 @ ( s @ X1 ) ) )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f43,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK0 ) ) ),
inference(constrained_superposition,[],[f29,f35]) ).
thf(f44,plain,
( $false
= ( sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f233,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK2 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c1 ) )
| ( ( sK1 @ sK2 )
!= X0 ) ),
inference(constrained_superposition,[],[f35,f24]) ).
thf(f257,plain,
! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c1 ) )
| ( ( sK1 @ sK2 )
!= X0 ) ),
inference(trivial_inequality_removal,[],[f233]) ).
thf(f258,plain,
! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $true
= ( sK2 @ sK0 ) )
| ( $false
= ( sK2 @ c1 ) )
| ( ( sK1 @ sK2 )
!= X0 ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f286,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK2 @ c1 ) )
| ( ( sK1 @ sK2 )
!= X0 ) ),
inference(forward_demodulation,[],[f258,f44]) ).
thf(f287,plain,
! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK2 @ c1 ) )
| ( ( sK1 @ sK2 )
!= X0 ) ),
inference(trivial_inequality_removal,[],[f286]) ).
thf(f292,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK2 @ X0 ) )
| ( ( sK1 @ sK2 )
!= X0 ) ),
inference(forward_demodulation,[],[f287,f32]) ).
thf(f293,plain,
! [X0: $i] :
( ( ( sK1 @ sK2 )
!= X0 )
| ( $false
= ( sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f292]) ).
thf(f299,plain,
( $false
= ( sK2 @ ( sK1 @ sK2 ) ) ),
inference(equality_resolution,[],[f293]) ).
thf(f304,plain,
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c1 ) ) ),
inference(constrained_superposition,[],[f25,f299]) ).
thf(f308,plain,
( ( $true
= ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c1 ) ) ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f309,plain,
( ( $true
= ( sK2 @ sK0 ) )
| ( $false
= ( sK2 @ c1 ) ) ),
inference(beta-eta_normalization,[],[f308]) ).
thf(f314,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ c1 ) ) ),
inference(forward_demodulation,[],[f309,f44]) ).
thf(f315,plain,
( $false
= ( sK2 @ c1 ) ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f320,plain,
$true = $false,
inference(constrained_superposition,[],[f32,f315]) ).
thf(f324,plain,
$false,
inference(trivial_inequality_removal,[],[f320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ103^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n008.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 13:24:54 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.28 % (3139886)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (3139893)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=262664151:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (3139892)% WARNING: option uhcvi not known.
% 0.20/0.28 % (3139893) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3139886-3139893"...
% 0.20/0.28 % (3139892)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2568426449:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (3139891)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1499289067_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (3139894)dis+10_1_sil=32000:sp=arity:random_seed=4064019811:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (3139893)...printing done.
% 0.20/0.28 % (3139895)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2859077338:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (3139892)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (3139895)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (3139892)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 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 % (3139893)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 % (3139893)------------------------------
% 0.20/0.28 % (3139893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3139893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3139893)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3139893)Termination reason: Refutation
% 0.20/0.28 % (3139893)Time elapsed: 0.007 s
% 0.20/0.28 % (3139893)Peak memory usage: 12 MB
% 0.20/0.28 % (3139893)Instructions burned: 18 (million)
% 0.20/0.28 % (3139886)Success in time 0.038 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------