%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU755^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 08:31:09 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 64 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 928 ( 258 equ; 0 cnn)
% Maximal formula atoms : 14 ( 14 avg)
% Number of connectives : 1055 ( 127 ~; 98 |; 65 &; 690 @)
% ( 11 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 19 con; 0-2 aty)
% Number of variables : 159 ( 0 ^; 127 !; 32 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_4,type,
setminusI: $o ).
thf(func_def_6,type,
setminusER: $o ).
thf(func_def_7,type,
binunionTEcontra: $o ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
( setminusER
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(f3,axiom,
( binunionTEcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTEcontra) ).
thf(f4,conjecture,
( setminusI
=> ( setminusER
=> ( binunionTEcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2) ).
thf(f5,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ( binunionTEcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ~ ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f7,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( setminusI
=> ( setminusER
=> ( binunionTEcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binunionTEcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
= setminusI ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( binunionTEcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( ( binunionTEcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X1 )
!= $true )
=> ( ( ( in @ X3 @ X2 )
!= $true )
=> ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
=> ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[],[f7]) ).
thf(f15,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f16,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X1 )
!= $true )
=> ( ( ( in @ X3 @ X2 )
!= $true )
=> ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true ) ) ) ) ) )
<=> ( binunionTEcontra = $true ) ),
inference(flattening,[],[f13]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( binunionTEcontra = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f18,plain,
( ( binunionTEcontra = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionTEcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f20,plain,
( ( binunionTEcontra = $true )
& ( setminusI = $true )
& ( setminusER = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f22,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f23,plain,
( ( setminusI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
( ( binunionTEcontra = $true )
& ( setminusI = $true )
& ( setminusER = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f25,plain,
( ( binunionTEcontra = $true )
& ( setminusI = $true )
& ( setminusER = $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK3 @ ( setminus @ sK1 @ sK2 ) ) )
& ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ sK2 ) ) )
!= $true )
& ( $true
= ( in @ sK3 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f24]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[],[f21]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
= $true )
& ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( ( in @ sK5 @ sK4 )
= $true )
& ( $true
= ( in @ sK5 @ ( setminus @ sK6 @ sK4 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f27]) ).
thf(f29,plain,
( ( ( setminusI = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[],[f23]) ).
thf(f30,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ X0 )
!= $true )
& ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[],[f29]) ).
thf(f31,plain,
( ( ( setminusI = $true )
| ( ( $true
= ( in @ sK8 @ sK9 ) )
& ( $true
!= ( in @ sK8 @ sK7 ) )
& ( $true
!= ( in @ sK8 @ ( setminus @ sK9 @ sK7 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f30]) ).
thf(f32,plain,
( ( ( binunionTEcontra = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X1 )
!= $true )
& ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( binunionTEcontra != $true ) ) ),
inference(nnf_transformation,[],[f18]) ).
thf(f33,plain,
( ( ( binunionTEcontra = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ X4 )
= $true )
| ( $true
!= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) ) )
| ( binunionTEcontra != $true ) ) ),
inference(rectify,[],[f32]) ).
thf(f34,plain,
( ( ( binunionTEcontra = $true )
| ( ( $true
= ( in @ sK10 @ ( powerset @ sK11 ) ) )
& ( ( in @ sK13 @ sK12 )
!= $true )
& ( $true
!= ( in @ sK13 @ sK10 ) )
& ( $true
= ( in @ sK13 @ ( binunion @ sK10 @ sK12 ) ) )
& ( $true
= ( in @ sK13 @ sK11 ) )
& ( ( in @ sK12 @ ( powerset @ sK11 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ X4 )
= $true )
| ( $true
!= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) ) )
| ( binunionTEcontra != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f33]) ).
thf(f35,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f36,plain,
( ( in @ sK3 @ ( setminus @ sK1 @ ( binunion @ sK0 @ sK2 ) ) )
!= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f37,plain,
( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f38,plain,
( $true
= ( in @ sK3 @ ( setminus @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f39,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f40,plain,
( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f41,plain,
setminusER = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f42,plain,
setminusI = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f43,plain,
binunionTEcontra = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f46,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
| ( setminusER != $true )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
| ( setminusI != $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f51,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ X4 )
= $true )
| ( $true
!= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( binunionTEcontra != $true )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( ( in @ X7 @ X6 )
= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f46,f41]) ).
thf(f63,plain,
( ( $true
!= ( in @ sK3 @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f62,f37]) ).
thf(f64,plain,
( ( $true != $true )
| ( ( in @ sK3 @ sK2 )
!= $true ) ),
inference(superposition,[],[f62,f38]) ).
thf(f65,plain,
( ( in @ sK3 @ sK2 )
!= $true ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
( $true
!= ( in @ sK3 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f67,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( $true
!= ( in @ X4 @ X5 ) ) ),
inference(forward_subsumption_resolution,[],[f47,f42]) ).
thf(f69,plain,
( ( $true
!= ( in @ sK3 @ sK1 ) )
| ( $true != $true )
| ( ( in @ sK3 @ ( binunion @ sK0 @ sK2 ) )
= $true ) ),
inference(superposition,[],[f36,f67]) ).
thf(f70,plain,
( ( ( in @ sK3 @ ( binunion @ sK0 @ sK2 ) )
= $true )
| ( $true
!= ( in @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f71,plain,
( ( in @ sK3 @ ( binunion @ sK0 @ sK2 ) )
= $true ),
inference(forward_subsumption_resolution,[],[f70,f35]) ).
thf(f72,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( ( in @ X7 @ X6 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f51,f43]) ).
thf(f73,plain,
! [X0: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ sK3 @ sK2 )
= $true )
| ( $true
= ( in @ sK3 @ sK0 ) )
| ( ( in @ sK3 @ X0 )
!= $true )
| ( ( in @ sK0 @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[],[f72,f71]) ).
thf(f74,plain,
! [X0: $i] :
( ( ( in @ sK3 @ sK2 )
= $true )
| ( ( in @ sK0 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( in @ sK3 @ sK0 ) )
| ( ( in @ sK3 @ X0 )
!= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f75,plain,
! [X0: $i] :
( ( $true
= ( in @ sK3 @ sK0 ) )
| ( ( in @ sK0 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK3 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f74,f65]) ).
thf(f76,plain,
! [X0: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK0 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK3 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f75,f66]) ).
thf(f77,plain,
( ( $true
!= ( in @ sK3 @ sK1 ) )
| ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f76,f39]) ).
thf(f78,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true )
| ( $true
!= ( in @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f79,plain,
( $true
!= ( in @ sK3 @ sK1 ) ),
inference(forward_subsumption_resolution,[],[f78,f40]) ).
thf(f80,plain,
$false,
inference(forward_subsumption_resolution,[],[f79,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU755^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n001.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:27:50 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.22 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
% 0.20/0.27 % (1320597)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1320604)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=237485648:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (1320604)Refutation not found, incomplete strategy
% 0.20/0.27 % (1320604)------------------------------
% 0.20/0.27 % (1320604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1320604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1320604)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1320604)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.27 % (1320604)Time elapsed: 0.002 s
% 0.20/0.27 % (1320604)Peak memory usage: 12 MB
% 0.20/0.27 % (1320604)Instructions burned: 4 (million)
% 0.20/0.27 % (1320604)------------------------------
% 0.20/0.27 % (1320604)------------------------------
% 0.20/0.27 % (1320602)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2354960714:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (1320603)lrs+10_16_si=on:nwc=1.5:random_seed=1099794911:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (1320606)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3296549974:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.27 % (1320605)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=2326114275: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)
% 0.20/0.27 % (1320608)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (1320608)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
% 0.20/0.27 % (1320606) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1320597-1320606"...
% 0.20/0.27 % (1320610)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2307294474:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.27 % (1320605) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1320597-1320605"...
% 0.20/0.27 % (1320603) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1320597-1320603"...
% 0.20/0.27 % (1320610)Instruction limit reached!
% 0.20/0.27 % (1320610)------------------------------
% 0.20/0.27 % (1320610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1320610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1320610)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1320610)Termination reason: Instruction limit
% 0.20/0.27 % (1320610)Termination phase: Saturation
% 0.20/0.27 % (1320610)Time elapsed: 0.001 s
% 0.20/0.27 % (1320610)Peak memory usage: 12 MB
% 0.20/0.27 % (1320610)Instructions burned: 3 (million)
% 0.20/0.27 % (1320608)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=316174793:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.27 % (1320606)...printing done.
% 0.20/0.27 % (1320606)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 % (1320606)------------------------------
% 0.20/0.27 % (1320606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1320606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1320606)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1320606)Termination reason: Refutation
% 0.20/0.27 % (1320606)Time elapsed: 0.006 s
% 0.20/0.27 % (1320606)Peak memory usage: 12 MB
% 0.20/0.27 % (1320606)Instructions burned: 11 (million)
% 0.20/0.27 % (1320597)Success in time 0.047 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------