%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n001.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 08:23:44 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 103 ( 18 unt; 0 typ; 6 def)
% Number of atoms : 879 ( 205 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1066 ( 182 ~; 284 |; 131 &; 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 : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 12 !; 3 ?; 35 :)
% 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,
vOR: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vNOT: $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,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X2 @ X3 )
& ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( ( X2 @ X4 )
| ( X0 @ X4 ) )
& ( X1 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_97_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X2 @ X3 )
& ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( ( X2 @ X4 )
| ( X0 @ X4 ) )
& ( X1 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X2 @ X3 )
& ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( ( X2 @ X4 )
| ( X0 @ X4 ) )
& ( X1 @ X4 ) )
| ( ~ ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( X0 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( ( X1 @ Y0 )
& ~ ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( ( sK1 @ Y0 )
& ~ ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f26]) ).
thf(f29,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f27]) ).
thf(f30,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f31]) ).
thf(f36,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f37,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f37]) ).
thf(f39,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f38]) ).
thf(f44,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f45,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f45]) ).
thf(f47,plain,
( ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f48,plain,
( ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f53,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f52]) ).
thf(f55,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f57,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f55]) ).
thf(f59,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f60,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f59]) ).
thf(f110,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f51]) ).
thf(f111,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f129,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f112]) ).
thf(f131,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f131]) ).
thf(f142,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f132]) ).
thf(f143,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f146,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f148,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f148]) ).
thf(f168,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f48]) ).
thf(f169,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f169]) ).
thf(f178,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f179,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f187,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f190,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f191,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f194,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f191]) ).
thf(f196,definition,
( spl4_1
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f198,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f200,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f202,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f204,definition,
( spl4_3
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f206,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f204]) ).
thf(f207,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f32,f204,f200,f196]) ).
thf(f209,definition,
( spl4_4
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f211,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f213,definition,
( spl4_5
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f215,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f216,plain,
( spl4_4
| spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f46,f204,f213,f209]) ).
thf(f217,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f60,f200,f213]) ).
thf(f219,definition,
( spl4_6
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f221,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f225,plain,
( spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f149,f196,f209]) ).
thf(f235,plain,
spl4_6,
inference(avatar_split_clause,[],[f194,f219]) ).
thf(f238,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4 ),
inference(constrained_superposition,[],[f202,f211]) ).
thf(f239,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f240,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f239]) ).
thf(f245,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5 ),
inference(forward_demodulation,[],[f215,f198]) ).
thf(f246,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f245]) ).
thf(f247,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f246]) ).
thf(f248,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f206,f221]) ).
thf(f249,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f250,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f249]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f207]) ).
cnf(s2,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f216]) ).
cnf(s3,plain,
( spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f217]) ).
cnf(s7,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f225]) ).
cnf(s17,plain,
spl4_6,
inference(sat_conversion,[],[f235]) ).
cnf(s18,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f240]) ).
cnf(s20,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f247]) ).
cnf(s21,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f250]) ).
cnf(s22,plain,
~ spl4_3,
inference(rat,[],[s21,s17]) ).
cnf(s23,plain,
( spl4_4
| spl4_5 ),
inference(rat,[],[s2,s22]) ).
cnf(s24,plain,
( spl4_1
| spl4_2 ),
inference(rat,[],[s1,s22]) ).
cnf(s25,plain,
spl4_1,
inference(rat,[],[s18,s24,s7]) ).
cnf(s26,plain,
~ spl4_5,
inference(rat,[],[s20,s25]) ).
cnf(s27,plain,
spl4_2,
inference(rat,[],[s3,s26]) ).
cnf(s28,plain,
spl4_4,
inference(rat,[],[s23,s26]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s18,s28,s27]) ).
thf(f252,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET621^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n001.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 13:45:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.27 % (1257502)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (1257522)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2683436261:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (1257522)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (1257522) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1257502-1257522"...
% 0.20/0.27 % (1257519)% WARNING: option uhcvi not known.
% 0.20/0.27 % (1257522)...printing done.
% 0.20/0.27 % (1257522)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (1257522)------------------------------
% 0.20/0.27 % (1257522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1257522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1257522)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1257522)Termination reason: Refutation
% 0.20/0.27 % (1257522)Time elapsed: 0.003 s
% 0.20/0.27 % (1257522)Peak memory usage: 12 MB
% 0.20/0.27 % (1257522)Instructions burned: 11 (million)
% 0.20/0.27 % (1257502)Success in time 0.036 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------