%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET621^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:23:23 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 103 ( 19 unt; 0 typ; 6 def)
% Number of atoms : 851 ( 197 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1077 ( 194 ~; 274 |; 140 &; 463 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 12 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
vNOT: $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vOR: $o > $o > $o ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ~ ( X2 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ~ ( ( X2 @ X4 )
| ( X0 @ X4 ) ) )
| ( ( X0 @ X4 )
& ~ ( ( X1 @ X4 )
| ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_97_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
& ~ ( X2 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ~ ( ( X2 @ X4 )
| ( X0 @ X4 ) ) )
| ( ( X0 @ X4 )
& ~ ( ( X1 @ X4 )
| ( X2 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X2 @ X3 ) ) )
& ~ ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ~ ( ( X0 @ X4 )
| ( X2 @ X4 ) ) )
| ( ( X2 @ X4 )
& ~ ( ( X1 @ X4 )
| ( X0 @ X4 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) )
= ( ^ [Y0: a] :
( ( ~ ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( X2 @ Y0 ) )
| ( ~ ( ( X2 @ Y0 )
| ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( ( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( X2 @ Y0 ) )
| ( ~ ( ( X2 @ Y0 )
| ( X0 @ Y0 ) )
& ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X2 @ Y0 ) )
| ( ~ ( ( X2 @ Y0 )
| ( X1 @ Y0 ) )
& ( X0 @ Y0 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK2 @ Y0 ) )
| ( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK2 @ Y0 ) )
| ( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK2 @ Y0 ) )
| ( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK2 @ Y0 ) )
| ( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
@ sK3 )
= $true )
| ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( $false
= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ~ ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK2 @ Y0 ) )
| ( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $false )
| ( $false
= ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
| ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
| ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
| ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
| ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f15]) ).
thf(f18,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
| ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f27,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f28,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) ) )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f31]) ).
thf(f33,plain,
( ( $false
= ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
| ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f16]) ).
thf(f35,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $false )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f35]) ).
thf(f37,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $false
= ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f39,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f40]) ).
thf(f48,plain,
( ( ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
| ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f49,plain,
( ( ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f48]) ).
thf(f50,plain,
( ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f52,plain,
( ( $false
= ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f52]) ).
thf(f56,plain,
( ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $true )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f57,plain,
( ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $true )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f64,plain,
( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f57]) ).
thf(f65,plain,
( ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f64]) ).
thf(f67,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f75,plain,
( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f69]) ).
thf(f76,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f79,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f76]) ).
thf(f107,plain,
( ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $true )
| ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f108,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 )
& ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
= $true )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f107]) ).
thf(f110,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f108]) ).
thf(f111,plain,
( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f110]) ).
thf(f113,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f111]) ).
thf(f114,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f113]) ).
thf(f162,plain,
( ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f171,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f173,plain,
( ( ( ~ ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
& ( sK2 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f173]) ).
thf(f187,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f191,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f187]) ).
thf(f215,definition,
( spl4_1
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f217,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f219,definition,
( spl4_2
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f221,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f223,definition,
( spl4_3
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f225,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f226,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f32,f223,f219,f215]) ).
thf(f228,definition,
( spl4_4
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f230,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f232,definition,
( spl4_5
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f234,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f235,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f41,f232,f228,f223]) ).
thf(f237,definition,
( spl4_6
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f239,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f243,plain,
( spl4_2
| spl4_4 ),
inference(avatar_split_clause,[],[f79,f228,f219]) ).
thf(f244,plain,
spl4_6,
inference(avatar_split_clause,[],[f114,f237]) ).
thf(f254,plain,
( spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f191,f215,f232]) ).
thf(f255,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f221,f234]) ).
thf(f256,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f255]) ).
thf(f257,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f256]) ).
thf(f259,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_demodulation,[],[f217,f230]) ).
thf(f260,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f259]) ).
thf(f261,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f260]) ).
thf(f262,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f225,f239]) ).
thf(f263,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f264,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f263]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f226]) ).
cnf(s2,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f235]) ).
cnf(s6,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f243]) ).
cnf(s7,plain,
spl4_6,
inference(sat_conversion,[],[f244]) ).
cnf(s17,plain,
( spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f254]) ).
cnf(s18,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f257]) ).
cnf(s19,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f261]) ).
cnf(s20,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f264]) ).
cnf(s21,plain,
~ spl4_3,
inference(rat,[],[s20,s7]) ).
cnf(s22,plain,
( spl4_4
| spl4_5 ),
inference(rat,[],[s2,s21]) ).
cnf(s23,plain,
( spl4_1
| spl4_2 ),
inference(rat,[],[s1,s21]) ).
cnf(s24,plain,
spl4_1,
inference(rat,[],[s18,s23,s17]) ).
cnf(s25,plain,
~ spl4_4,
inference(rat,[],[s19,s24]) ).
cnf(s26,plain,
spl4_2,
inference(rat,[],[s6,s25]) ).
cnf(s27,plain,
spl4_5,
inference(rat,[],[s22,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s18,s27,s26]) ).
thf(f266,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET621^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:39:46 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (105637)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (105648)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4201864604:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (105648)Refutation not found, incomplete strategy
% 0.21/0.28 % (105648)------------------------------
% 0.21/0.28 % (105648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (105648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (105648)CaDiCaL version: 2.1.3
% 0.21/0.28 % (105648)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.28 % (105648)Time elapsed: 0.001 s
% 0.21/0.28 % (105648)Peak memory usage: 12 MB
% 0.21/0.28 % (105648)Instructions burned: 1 (million)
% 0.21/0.28 % (105648)------------------------------
% 0.21/0.28 % (105648)------------------------------
% 0.21/0.28 % (105652)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (105652)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
% 0.21/0.28 % (105645)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=645683554:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (105647)lrs+10_16_si=on:nwc=1.5:random_seed=3737716419:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (105651)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3106315518:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (105652)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=789248692:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (105649)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=1528927708: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)
% 0.21/0.28 % (105650)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3234697298:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (105647) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-105637-105647"...
% 0.21/0.28 % (105645) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-105637-105645"...
% 0.21/0.28 % (105651) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-105637-105651"...
% 0.21/0.28 % (105650) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-105637-105650"...
% 0.21/0.28 % (105649) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-105637-105649"...
% 0.21/0.28 % (105658)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2890644617:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.28 % (105652) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-105637-105652"...
% 0.21/0.28 % (105658)Instruction limit reached!
% 0.21/0.28 % (105658)------------------------------
% 0.21/0.28 % (105658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (105658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (105658)CaDiCaL version: 2.1.3
% 0.21/0.28 % (105658)Termination reason: Instruction limit
% 0.21/0.28 % (105658)Termination phase: Saturation
% 0.21/0.28 % (105658)Time elapsed: 0.001 s
% 0.21/0.28 % (105658)Peak memory usage: 12 MB
% 0.21/0.28 % (105658)Instructions burned: 3 (million)
% 0.21/0.28 % (105647)...printing done.
% 0.21/0.28 % (105645)...printing done.
% 0.21/0.28 % (105651)...printing done.
% 0.21/0.28 % (105650)...printing done.
% 0.21/0.28 % (105645)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 % (105645)------------------------------
% 0.21/0.28 % (105645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (105645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (105645)CaDiCaL version: 2.1.3
% 0.21/0.28 % (105645)Termination reason: Refutation
% 0.21/0.28 % (105645)Time elapsed: 0.006 s
% 0.21/0.28 % (105645)Peak memory usage: 13 MB
% 0.21/0.28 % (105645)Instructions burned: 9 (million)
% 0.21/0.28 % (105637)Success in time 0.045 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------