%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ113^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:20:55 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 4
% Syntax : Number of formulae : 72 ( 29 unt; 0 typ; 2 def)
% Number of atoms : 527 ( 106 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 892 ( 24 ~; 57 |; 43 &; 688 @)
% ( 2 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 8 con; 0-4 aty)
% ( 38 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 97 ( 0 sgn 37 !; 4 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_BLACK: $i > $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK2: $i > $i > $o ).
thf(func_def_17,type,
sK3: ( $i > $i > $o ) > $i ).
thf(func_def_18,type,
sK4: ( $i > $i > $o ) > $i ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ( ! [X4: $i,X3: $i] :
( ( X2 @ X3 @ X4 )
=> ( ( X2 @ ( s @ ( s @ X3 ) ) @ X4 )
& ( X2 @ ( s @ X3 ) @ ( s @ X4 ) ) ) )
& ( X2 @ c1 @ c1 ) )
=> ( X2 @ X0 @ X1 ) ) )
= cCKB6_BLACK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_BLACK_def) ).
thf(f2,conjecture,
! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_L11000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ( ! [X3: $i,X4: $i] :
( ( X2 @ X4 @ X3 )
=> ( ( X2 @ ( s @ ( s @ X4 ) ) @ X3 )
& ( X2 @ ( s @ X4 ) @ ( s @ X3 ) ) ) )
& ( X2 @ c1 @ c1 ) )
=> ( X2 @ X0 @ X1 ) ) )
= cCKB6_BLACK ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( cCKB6_BLACK
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
=> ( ( Y2 @ ( s @ Y3 ) @ ( s @ Y4 ) )
& ( Y2 @ ( s @ ( s @ Y3 ) ) @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i] :
( ( cCKB6_BLACK @ X0 @ X1 )
=> ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ X0 @ X1 )
= $true )
=> ( ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X1: $i,X0: $i] :
( ( ( cCKB6_BLACK @ ( s @ ( s @ X0 ) ) @ ( s @ ( s @ X1 ) ) )
!= $true )
& ( ( cCKB6_BLACK @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
? [X0: $i,X1: $i] :
( ( ( cCKB6_BLACK @ ( s @ ( s @ X1 ) ) @ ( s @ ( s @ X0 ) ) )
!= $true )
& ( ( cCKB6_BLACK @ X1 @ X0 )
= $true ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( ( cCKB6_BLACK @ ( s @ ( s @ sK1 ) ) @ ( s @ ( s @ sK0 ) ) )
!= $true )
& ( ( cCKB6_BLACK @ sK1 @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
thf(f11,plain,
( cCKB6_BLACK
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
=> ( ( Y2 @ ( s @ Y3 ) @ ( s @ Y4 ) )
& ( Y2 @ ( s @ ( s @ Y3 ) ) @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f12,plain,
( ( cCKB6_BLACK @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( ( cCKB6_BLACK @ ( s @ ( s @ sK1 ) ) @ ( s @ ( s @ sK0 ) ) )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
=> ( ( Y2 @ ( s @ Y3 ) @ ( s @ Y4 ) )
& ( Y2 @ ( s @ ( s @ Y3 ) ) @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( s @ ( s @ sK1 ) )
@ ( s @ ( s @ sK0 ) ) )
!= $true ),
inference(definition_unfolding,[],[f13,f11]) ).
thf(f17,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
=> ( ( Y2 @ ( s @ Y3 ) @ ( s @ Y4 ) )
& ( Y2 @ ( s @ ( s @ Y3 ) ) @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f12,f11]) ).
thf(f18,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( ( Y0 @ ( s @ Y1 ) @ ( s @ Y2 ) )
& ( Y0 @ ( s @ ( s @ Y1 ) ) @ Y2 ) ) ) ) ) )
=> ( Y0 @ ( s @ ( s @ sK1 ) ) @ ( s @ ( s @ sK0 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f19,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( ( Y0 @ ( s @ Y1 ) @ ( s @ Y2 ) )
& ( Y0 @ ( s @ ( s @ Y1 ) ) @ Y2 ) ) ) ) ) )
=> ( Y0 @ ( s @ ( s @ sK1 ) ) @ ( s @ ( s @ sK0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( $false
= ( ( ( sK2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ( sK2 @ ( s @ Y0 ) @ ( s @ Y1 ) )
& ( sK2 @ ( s @ ( s @ Y0 ) ) @ Y1 ) ) ) ) ) )
=> ( sK2 @ ( s @ ( s @ sK1 ) ) @ ( s @ ( s @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( $false
= ( sK2 @ ( s @ ( s @ sK1 ) ) @ ( s @ ( s @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( ( sK2 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ( sK2 @ ( s @ Y0 ) @ ( s @ Y1 ) )
& ( sK2 @ ( s @ ( s @ Y0 ) ) @ Y1 ) ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ( sK2 @ ( s @ Y0 ) @ ( s @ Y1 ) )
& ( sK2 @ ( s @ ( s @ Y0 ) ) @ Y1 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( sK2 @ c1 @ c1 )
= $true ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f25,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ( sK2 @ ( s @ Y0 ) @ ( s @ Y1 ) )
& ( sK2 @ ( s @ ( s @ Y0 ) ) @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f26,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ X1 @ Y0 )
=> ( ( sK2 @ ( s @ X1 ) @ ( s @ Y0 ) )
& ( sK2 @ ( s @ ( s @ X1 ) ) @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK2 @ X1 @ Y0 )
=> ( ( sK2 @ ( s @ X1 ) @ ( s @ Y0 ) )
& ( sK2 @ ( s @ ( s @ X1 ) ) @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X1 @ X2 )
=> ( ( sK2 @ ( s @ X1 ) @ ( s @ X2 ) )
& ( sK2 @ ( s @ ( s @ X1 ) ) @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK2 @ ( s @ X1 ) @ ( s @ X2 ) )
& ( sK2 @ ( s @ ( s @ X1 ) ) @ X2 ) )
= $true )
| ( ( sK2 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ ( s @ ( s @ X1 ) ) @ X2 )
= $true )
| ( ( sK2 @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ ( s @ X1 ) @ ( s @ X2 ) )
= $true )
| ( ( sK2 @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( ( Y0 @ ( s @ Y1 ) @ ( s @ Y2 ) )
& ( Y0 @ ( s @ ( s @ Y1 ) ) @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK1 @ sK0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f33,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( ( Y0 @ ( s @ Y1 ) @ ( s @ Y2 ) )
& ( Y0 @ ( s @ ( s @ Y1 ) ) @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK1 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X1: $i > $i > $o] :
( ( ( ( X1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( ( X1 @ ( s @ Y0 ) @ ( s @ Y1 ) )
& ( X1 @ ( s @ ( s @ Y0 ) ) @ Y1 ) ) ) ) ) )
=> ( X1 @ sK1 @ sK0 ) )
= $true ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK1 @ sK0 )
= $true )
| ( ( ( X1 @ c1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( ( X1 @ ( s @ Y0 ) @ ( s @ Y1 ) )
& ( X1 @ ( s @ ( s @ Y0 ) ) @ Y1 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK1 @ sK0 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( ( X1 @ ( s @ Y0 ) @ ( s @ Y1 ) )
& ( X1 @ ( s @ ( s @ Y0 ) ) @ Y1 ) ) ) ) ) )
| ( ( X1 @ c1 @ c1 )
= $false ) ),
inference(and_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK1 @ sK0 )
= $true )
| ( ( X1 @ c1 @ c1 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( ( X1 @ ( s @ Y0 ) @ ( s @ Y1 ) )
& ( X1 @ ( s @ ( s @ Y0 ) ) @ Y1 ) ) ) )
@ ( sK3 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ ( sK3 @ X1 ) @ Y0 )
=> ( ( X1 @ ( s @ ( sK3 @ X1 ) ) @ ( s @ Y0 ) )
& ( X1 @ ( s @ ( s @ ( sK3 @ X1 ) ) ) @ Y0 ) ) ) ) )
| ( ( X1 @ c1 @ c1 )
= $false )
| ( ( X1 @ sK1 @ sK0 )
= $true ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK1 @ sK0 )
= $true )
| ( ( X1 @ c1 @ c1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( X1 @ ( sK3 @ X1 ) @ Y0 )
=> ( ( X1 @ ( s @ ( sK3 @ X1 ) ) @ ( s @ Y0 ) )
& ( X1 @ ( s @ ( s @ ( sK3 @ X1 ) ) ) @ Y0 ) ) )
@ ( sK4 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK1 @ sK0 )
= $true )
| ( ( ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) )
=> ( ( X1 @ ( s @ ( sK3 @ X1 ) ) @ ( s @ ( sK4 @ X1 ) ) )
& ( X1 @ ( s @ ( s @ ( sK3 @ X1 ) ) ) @ ( sK4 @ X1 ) ) ) )
= $false )
| ( ( X1 @ c1 @ c1 )
= $false ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X1: $i > $i > $o] :
( ( ( ( X1 @ ( s @ ( sK3 @ X1 ) ) @ ( s @ ( sK4 @ X1 ) ) )
& ( X1 @ ( s @ ( s @ ( sK3 @ X1 ) ) ) @ ( sK4 @ X1 ) ) )
= $false )
| ( ( X1 @ c1 @ c1 )
= $false )
| ( ( X1 @ sK1 @ sK0 )
= $true ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) )
= $true )
| ( ( X1 @ sK1 @ sK0 )
= $true )
| ( ( X1 @ c1 @ c1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f43,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( s @ ( s @ ( sK3 @ X1 ) ) ) @ ( sK4 @ X1 ) ) )
| ( ( X1 @ sK1 @ sK0 )
= $true )
| ( ( X1 @ c1 @ c1 )
= $false )
| ( ( X1 @ ( s @ ( sK3 @ X1 ) ) @ ( s @ ( sK4 @ X1 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f49,plain,
( ( $false = $true )
| ( ( sK2 @ ( s @ sK1 ) @ ( s @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f21,f31]) ).
thf(f50,plain,
( ( sK2 @ ( s @ sK1 ) @ ( s @ sK0 ) )
= $false ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f52,plain,
( ( $false = $true )
| ( ( sK2 @ sK1 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f50,f31]) ).
thf(f54,plain,
( ( sK2 @ sK1 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f101,plain,
( ( ( sK2 @ c1 @ c1 )
= $false )
| ( ( sK2 @ sK1 @ sK0 )
= $true )
| ( ( sK2 @ ( s @ ( sK3 @ sK2 ) ) @ ( s @ ( sK4 @ sK2 ) ) )
= $false )
| ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f30,f43]) ).
thf(f122,plain,
( ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false )
| ( ( sK2 @ sK1 @ sK0 )
= $true )
| ( ( sK2 @ ( s @ ( sK3 @ sK2 ) ) @ ( s @ ( sK4 @ sK2 ) ) )
= $false )
| ( ( sK2 @ c1 @ c1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f136,plain,
( ( ( sK2 @ ( s @ ( sK3 @ sK2 ) ) @ ( s @ ( sK4 @ sK2 ) ) )
= $false )
| ( $false = $true )
| ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false )
| ( ( sK2 @ c1 @ c1 )
= $false ) ),
inference(forward_demodulation,[],[f122,f54]) ).
thf(f137,plain,
( ( ( sK2 @ ( s @ ( sK3 @ sK2 ) ) @ ( s @ ( sK4 @ sK2 ) ) )
= $false )
| ( ( sK2 @ c1 @ c1 )
= $false )
| ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f147,plain,
( ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false )
| ( ( sK2 @ ( s @ ( sK3 @ sK2 ) ) @ ( s @ ( sK4 @ sK2 ) ) )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f137,f24]) ).
thf(f148,plain,
( ( ( sK2 @ ( s @ ( sK3 @ sK2 ) ) @ ( s @ ( sK4 @ sK2 ) ) )
= $false )
| ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f150,definition,
( spl5_4
<=> ( ( sK2 @ ( s @ ( sK3 @ sK2 ) ) @ ( s @ ( sK4 @ sK2 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f152,plain,
( ( ( sK2 @ ( s @ ( sK3 @ sK2 ) ) @ ( s @ ( sK4 @ sK2 ) ) )
= $false )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f154,definition,
( spl5_5
<=> ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f156,plain,
( ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f154]) ).
thf(f159,plain,
( spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f148,f154,f150]) ).
thf(f161,plain,
( ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false )
| ( $false = $true )
| ~ spl5_4 ),
inference(constrained_superposition,[],[f31,f152]) ).
thf(f162,plain,
( ( ( sK2 @ ( sK3 @ sK2 ) @ ( sK4 @ sK2 ) )
= $false )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f164,plain,
( spl5_5
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f162,f150,f154]) ).
thf(f166,plain,
( ( ( sK2 @ c1 @ c1 )
= $false )
| ( $false = $true )
| ( ( sK2 @ sK1 @ sK0 )
= $true )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f42,f156]) ).
thf(f168,plain,
( ( ( sK2 @ c1 @ c1 )
= $false )
| ( ( sK2 @ sK1 @ sK0 )
= $true )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f171,plain,
( ( $false = $true )
| ( ( sK2 @ sK1 @ sK0 )
= $true )
| ~ spl5_5 ),
inference(forward_demodulation,[],[f168,f24]) ).
thf(f172,plain,
( ( ( sK2 @ sK1 @ sK0 )
= $true )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f171]) ).
thf(f176,plain,
( ( $false = $true )
| ~ spl5_5 ),
inference(forward_demodulation,[],[f172,f54]) ).
thf(f177,plain,
( $false
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f178,plain,
~ spl5_5,
inference(avatar_contradiction_clause,[],[f177]) ).
cnf(s5,plain,
( spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f159]) ).
cnf(s6,plain,
( ~ spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f164]) ).
cnf(s9,plain,
~ spl5_5,
inference(sat_conversion,[],[f178]) ).
cnf(s10,plain,
~ spl5_4,
inference(rat,[],[s6,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s5,s9,s10]) ).
thf(f179,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ113^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:24:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.29 % (3972544)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3972553)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=43067674:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (3972555)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (3972555)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.29 % (3972550)lrs+10_16_si=on:nwc=1.5:random_seed=1672976352:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (3972549)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=771943304:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (3972553)Instruction limit reached!
% 0.22/0.29 % (3972553)------------------------------
% 0.22/0.29 % (3972553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3972551)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3874131265:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (3972553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3972554)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1151257139:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (3972553)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3972553)Termination reason: Instruction limit
% 0.22/0.29 % (3972553)Termination phase: Saturation
% 0.22/0.29 % (3972553)Time elapsed: 0.007 s
% 0.22/0.29 % (3972553)Peak memory usage: 12 MB
% 0.22/0.29 % (3972553)Instructions burned: 26 (million)
% 0.22/0.29 % (3972552)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=656730513:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.29 % (3972555)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=273634573:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (3972551)Refutation not found, incomplete strategy
% 0.22/0.29 % (3972551)------------------------------
% 0.22/0.29 % (3972551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3972551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3972551)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3972551)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.29 % (3972551)Time elapsed: 0.002 s
% 0.22/0.29 % (3972551)Peak memory usage: 12 MB
% 0.22/0.29 % (3972551)Instructions burned: 2 (million)
% 0.22/0.29 % (3972551)------------------------------
% 0.22/0.29 % (3972551)------------------------------
% 0.22/0.29 % (3972549) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3972544-3972549"...
% 0.22/0.29 % (3972549)...printing done.
% 0.22/0.29 % (3972550)Instruction limit reached!
% 0.22/0.29 % (3972550)------------------------------
% 0.22/0.29 % (3972550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3972550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3972550)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3972550)Termination reason: Instruction limit
% 0.22/0.29 % (3972550)Termination phase: Saturation
% 0.22/0.29 % (3972550)Time elapsed: 0.010 s
% 0.22/0.29 % (3972550)Peak memory usage: 12 MB
% 0.22/0.29 % (3972550)Instructions burned: 19 (million)
% 0.22/0.29 % (3972562)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2583977962:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.29 % (3972549)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (3972549)------------------------------
% 0.22/0.30 % (3972549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3972549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3972549)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3972549)Termination reason: Refutation
% 0.22/0.30 % (3972549)Time elapsed: 0.008 s
% 0.22/0.30 % (3972549)Peak memory usage: 13 MB
% 0.22/0.30 % (3972549)Instructions burned: 14 (million)
% 0.22/0.30 % (3972544)Success in time 0.041 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------