%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU785^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:31:22 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 68 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 1103 ( 284 equ; 0 cnn)
% Maximal formula atoms : 14 ( 16 avg)
% Number of connectives : 1347 ( 168 ~; 167 |; 64 &; 882 @)
% ( 8 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 21 con; 0-2 aty)
% Number of variables : 181 ( 0 sgn 146 !; 35 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
breln1: $i > $i > $o ).
thf(func_def_4,type,
breln1unionIL: $o ).
thf(func_def_6,type,
breln1unionIR: $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
= breln1unionIL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIL) ).
thf(f2,axiom,
( breln1unionIR
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIR) ).
thf(f3,conjecture,
( breln1unionIL
=> ( breln1unionIR
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionI) ).
thf(f4,negated_conjecture,
~ ( breln1unionIL
=> ( breln1unionIR
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( breln1unionIR
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( ( breln1unionIR = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) )
= breln1unionIL ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ) )
<=> ( breln1unionIL = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( breln1unionIL
=> ( breln1unionIR
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( breln1unionIR = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( breln1 @ X0 @ X2 )
!= $true ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ( breln1unionIR = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
!= $true )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( breln1 @ X0 @ X2 )
!= $true ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) )
<=> ( breln1unionIL = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
( ( breln1unionIL = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true ) ) )
| ( ( breln1 @ X0 @ X2 )
!= $true ) ) ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( breln1unionIR = $true )
& ( breln1unionIL = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f16,plain,
( ( breln1unionIL = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( breln1unionIR = $true ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ( ( breln1unionIL = $true )
| ? [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true ) ) )
| ( ( breln1 @ X0 @ X2 )
!= $true ) ) )
| ( breln1unionIL != $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f18,plain,
( ( ( breln1unionIL = $true )
| ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) ) ) )
& ( ! [X5: $i,X6: $i] :
( ( ( breln1 @ X6 @ X5 )
!= $true )
| ! [X7: $i] :
( ! [X8: $i] :
( ( ( in @ X8 @ X6 )
!= $true )
| ! [X9: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X5 ) ) ) )
| ( ( breln1 @ X6 @ X7 )
!= $true ) ) )
| ( breln1unionIL != $true ) ) ),
inference(rectify,[],[f17]) ).
thf(f19,plain,
( ( ( breln1unionIL = $true )
| ( ( ( breln1 @ sK1 @ sK0 )
= $true )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( ( in @ sK4 @ sK1 )
= $true )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK0 ) )
& ( ( breln1 @ sK1 @ sK2 )
= $true ) ) )
& ( ! [X5: $i,X6: $i] :
( ( ( breln1 @ X6 @ X5 )
!= $true )
| ! [X7: $i] :
( ! [X8: $i] :
( ( ( in @ X8 @ X6 )
!= $true )
| ! [X9: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X5 ) ) ) )
| ( ( breln1 @ X6 @ X7 )
!= $true ) ) )
| ( breln1unionIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f18]) ).
thf(f20,plain,
( ( breln1unionIL = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( breln1unionIR = $true ) ),
inference(rectify,[],[f16]) ).
thf(f21,plain,
( ( breln1unionIL = $true )
& ( ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ sK7 ) )
| ( ( in @ ( kpair @ sK8 @ sK9 ) @ sK5 )
= $true ) )
& ( $true
!= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ sK7 ) ) )
& ( ( in @ sK9 @ sK6 )
= $true )
& ( ( in @ sK8 @ sK6 )
= $true )
& ( $true
= ( breln1 @ sK6 @ sK7 ) )
& ( ( breln1 @ sK6 @ sK5 )
= $true )
& ( breln1unionIR = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8),skolemize(X4,sK9)],[f20]) ).
thf(f22,plain,
( ( ( breln1unionIR = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
!= $true )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X4 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) )
| ( breln1unionIR != $true ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f23,plain,
( ( ( breln1unionIR = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X4 @ X1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) ) )
& ( ! [X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( breln1 @ X6 @ X7 )
!= $true )
| ! [X8: $i] :
( ! [X9: $i] :
( ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X7 )
!= $true ) )
| ( ( in @ X8 @ X6 )
!= $true ) ) )
| ( ( breln1 @ X6 @ X5 )
!= $true ) )
| ( breln1unionIR != $true ) ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
( ( ( breln1unionIR = $true )
| ( ( ( breln1 @ sK11 @ sK12 )
= $true )
& ( ( in @ ( kpair @ sK13 @ sK14 ) @ ( binunion @ sK10 @ sK12 ) )
!= $true )
& ( ( in @ sK14 @ sK11 )
= $true )
& ( $true
= ( in @ ( kpair @ sK13 @ sK14 ) @ sK12 ) )
& ( ( in @ sK13 @ sK11 )
= $true )
& ( ( breln1 @ sK11 @ sK10 )
= $true ) ) )
& ( ! [X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( breln1 @ X6 @ X7 )
!= $true )
| ! [X8: $i] :
( ! [X9: $i] :
( ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X7 )
!= $true ) )
| ( ( in @ X8 @ X6 )
!= $true ) ) )
| ( ( breln1 @ X6 @ X5 )
!= $true ) )
| ( breln1unionIR != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13),skolemize(X4,sK14)],[f23]) ).
thf(f25,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( breln1 @ X6 @ X5 )
!= $true )
| ( ( in @ X8 @ X6 )
!= $true )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X5 ) )
| ( ( breln1 @ X6 @ X7 )
!= $true )
| ( breln1unionIL != $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f32,plain,
breln1unionIR = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f33,plain,
( ( breln1 @ sK6 @ sK5 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f34,plain,
( $true
= ( breln1 @ sK6 @ sK7 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f35,plain,
( ( in @ sK8 @ sK6 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f36,plain,
( ( in @ sK9 @ sK6 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f37,plain,
( $true
!= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ sK7 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f38,plain,
( ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ sK7 ) )
| ( ( in @ ( kpair @ sK8 @ sK9 ) @ sK5 )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f39,plain,
breln1unionIL = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f40,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( breln1 @ X6 @ X7 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X7 )
!= $true )
| ( ( in @ X8 @ X6 )
!= $true )
| ( ( breln1 @ X6 @ X5 )
!= $true )
| ( breln1unionIR != $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f55,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( ( breln1 @ X6 @ X5 )
!= $true )
| ( ( in @ X8 @ X6 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X5 ) )
| ( $true != $true )
| ( ( breln1 @ X6 @ X7 )
!= $true ) ),
inference(definition_unfolding,[],[f25,f39]) ).
thf(f62,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( in @ ( kpair @ X8 @ X9 ) @ X7 )
!= $true )
| ( ( in @ X8 @ X6 )
!= $true )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true != $true )
| ( ( breln1 @ X6 @ X7 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( ( breln1 @ X6 @ X5 )
!= $true ) ),
inference(definition_unfolding,[],[f40,f32]) ).
thf(f63,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( in @ ( kpair @ X8 @ X9 ) @ X7 )
!= $true )
| ( ( breln1 @ X6 @ X5 )
!= $true )
| ( ( breln1 @ X6 @ X7 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ X8 @ X6 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f64,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ ( kpair @ X8 @ X9 ) @ X5 ) )
| ( ( in @ X8 @ X6 )
!= $true )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ ( kpair @ X8 @ X9 ) @ ( binunion @ X5 @ X7 ) )
= $true )
| ( ( breln1 @ X6 @ X7 )
!= $true )
| ( ( breln1 @ X6 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f66,definition,
( spl15_1
<=> ( ( in @ ( kpair @ sK8 @ sK9 ) @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
thf(f68,plain,
( ( ( in @ ( kpair @ sK8 @ sK9 ) @ sK5 )
= $true )
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f70,definition,
( spl15_2
<=> ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
thf(f72,plain,
( ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ sK7 ) )
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f38,f70,f66]) ).
thf(f74,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ sK7 ) )
| ( $true
!= ( in @ sK9 @ X0 ) )
| ( ( breln1 @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ sK8 @ X0 ) )
| ( ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ X1 @ sK7 ) )
= $true )
| ( $true != $true ) )
| ~ spl15_2 ),
inference(constrained_superposition,[],[f63,f72]) ).
thf(f75,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ sK7 ) )
| ( ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ X1 @ sK7 ) )
= $true )
| ( $true
!= ( in @ sK9 @ X0 ) )
| ( $true
!= ( in @ sK8 @ X0 ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) )
| ~ spl15_2 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( ! [X0: $i] :
( ( ( in @ sK8 @ sK6 )
!= $true )
| ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ X0 @ sK7 ) ) )
| ( $true
!= ( breln1 @ sK6 @ X0 ) )
| ( ( in @ sK9 @ sK6 )
!= $true )
| ( $true != $true ) )
| ~ spl15_2 ),
inference(constrained_superposition,[],[f75,f34]) ).
thf(f77,plain,
( ! [X0: $i] :
( ( ( in @ sK9 @ sK6 )
!= $true )
| ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ X0 @ sK7 ) ) )
| ( $true
!= ( breln1 @ sK6 @ X0 ) )
| ( ( in @ sK8 @ sK6 )
!= $true ) )
| ~ spl15_2 ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f78,plain,
( ! [X0: $i] :
( ( ( in @ sK8 @ sK6 )
!= $true )
| ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ X0 @ sK7 ) ) )
| ( $true
!= ( breln1 @ sK6 @ X0 ) ) )
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f77,f36]) ).
thf(f79,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ sK6 @ X0 ) )
| ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ X0 @ sK7 ) ) ) )
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f78,f35]) ).
thf(f80,plain,
( ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ sK7 ) ) )
| ( $true != $true )
| ~ spl15_2 ),
inference(constrained_superposition,[],[f79,f33]) ).
thf(f83,plain,
( ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ sK7 ) ) )
| ~ spl15_2 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f84,plain,
( $false
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f83,f37]) ).
thf(f85,plain,
~ spl15_2,
inference(avatar_contradiction_clause,[],[f84]) ).
thf(f100,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ sK5 ) )
| ( $true != $true )
| ( $true
!= ( in @ sK9 @ X0 ) )
| ( ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ X1 ) )
= $true )
| ( ( breln1 @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ sK8 @ X0 ) ) )
| ~ spl15_1 ),
inference(constrained_superposition,[],[f64,f68]) ).
thf(f104,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ sK5 ) )
| ( ( breln1 @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ sK9 @ X0 ) )
| ( ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ X1 ) )
= $true )
| ( $true
!= ( in @ sK8 @ X0 ) ) )
| ~ spl15_1 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f106,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ sK6 @ X0 ) )
| ( ( in @ sK8 @ sK6 )
!= $true )
| ( $true != $true )
| ( ( in @ sK9 @ sK6 )
!= $true )
| ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ X0 ) ) ) )
| ~ spl15_1 ),
inference(constrained_superposition,[],[f104,f33]) ).
thf(f107,plain,
( ! [X0: $i] :
( ( ( in @ sK8 @ sK6 )
!= $true )
| ( ( in @ sK9 @ sK6 )
!= $true )
| ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ X0 ) ) )
| ( $true
!= ( breln1 @ sK6 @ X0 ) ) )
| ~ spl15_1 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f108,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ X0 ) ) )
| ( ( in @ sK9 @ sK6 )
!= $true )
| ( $true
!= ( breln1 @ sK6 @ X0 ) ) )
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f107,f35]) ).
thf(f109,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ sK6 @ X0 ) )
| ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ X0 ) ) ) )
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f108,f36]) ).
thf(f111,plain,
( ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ sK7 ) ) )
| ( $true != $true )
| ~ spl15_1 ),
inference(constrained_superposition,[],[f109,f34]) ).
thf(f113,plain,
( ( $true
= ( in @ ( kpair @ sK8 @ sK9 ) @ ( binunion @ sK5 @ sK7 ) ) )
| ~ spl15_1 ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f114,plain,
( $false
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f113,f37]) ).
thf(f115,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[],[f114]) ).
cnf(s1,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f73]) ).
cnf(s2,plain,
~ spl15_2,
inference(sat_conversion,[],[f85]) ).
cnf(s3,plain,
~ spl15_1,
inference(sat_conversion,[],[f115]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f116,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU785^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n026.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:31:27 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 Running higher-order theorem proving
% 0.10/0.27 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
% 0.23/0.31 % (677024)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (677038)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2719211753:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (677038) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-677024-677038"...
% 0.23/0.31 % (677044)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (677044)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
% 0.23/0.31 % (677038)...printing done.
% 0.23/0.31 % (677038)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (677038)------------------------------
% 0.23/0.31 % (677038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (677038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (677038)CaDiCaL version: 2.1.3
% 0.23/0.31 % (677038)Termination reason: Refutation
% 0.23/0.31 % (677038)Time elapsed: 0.005 s
% 0.23/0.31 % (677038)Peak memory usage: 13 MB
% 0.23/0.31 % (677038)Instructions burned: 15 (million)
% 0.23/0.31 % (677024)Success in time 0.031 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------