%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU736^2 : 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 : n012.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 08:31:02 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 765 ( 212 equ; 0 cnn)
% Maximal formula atoms : 14 ( 15 avg)
% Number of connectives : 865 ( 106 ~; 83 |; 55 &; 557 @)
% ( 8 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 15 con; 0-2 aty)
% Number of variables : 123 ( 0 ^; 97 !; 26 ?; 123 :)
% 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,
subset: $i > $i > $o ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_4,type,
setminusI: $o ).
thf(func_def_6,type,
contrasubsetT: $o ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
( contrasubsetT
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT) ).
thf(f3,conjecture,
( setminusI
=> ( contrasubsetT
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( contrasubsetT
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( setminusI
=> ( contrasubsetT
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( setminusI = $true )
=> ( ( contrasubsetT = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) )
= setminusI ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( $true
!= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( contrasubsetT
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ( contrasubsetT = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( $true
!= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f8]) ).
thf(f12,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ) )
<=> ( contrasubsetT = $true ) ),
inference(flattening,[],[f10]) ).
thf(f13,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( contrasubsetT = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f16,plain,
( ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) )
& ( setminusI = $true )
& ( contrasubsetT = $true ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( contrasubsetT = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
<=> ( contrasubsetT = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( contrasubsetT != $true ) )
& ( ( contrasubsetT = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f18]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( contrasubsetT != $true ) )
& ( ( contrasubsetT = $true )
| ? [X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X6 ) )
& ( $true
= ( subset @ X4 @ ( setminus @ X5 @ X6 ) ) )
& ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X5 ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( contrasubsetT != $true ) )
& ( ( contrasubsetT = $true )
| ( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ( $true
= ( in @ sK3 @ sK2 ) )
& ( $true
= ( subset @ sK0 @ ( setminus @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f20]) ).
thf(f22,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) )
& ( $true
= ( in @ X5 @ X3 ) )
& ( $true
!= ( in @ X5 @ X4 ) ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( $true
!= ( in @ sK6 @ ( setminus @ sK4 @ sK5 ) ) )
& ( $true
= ( in @ sK6 @ sK4 ) )
& ( $true
!= ( in @ sK6 @ sK5 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f23]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) )
& ( setminusI = $true )
& ( contrasubsetT = $true ) ),
inference(rectify,[],[f16]) ).
thf(f26,plain,
( ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ( $true
= ( in @ sK10 @ sK7 ) )
& ( $true
!= ( in @ sK10 @ ( setminus @ sK7 @ sK8 ) ) )
& ( $true
= ( in @ sK10 @ sK9 ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) )
& ( $true
= ( subset @ sK8 @ ( setminus @ sK7 @ sK9 ) ) )
& ( setminusI = $true )
& ( contrasubsetT = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f25]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
!= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( contrasubsetT != $true )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f37,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( setminusI != $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f38,plain,
contrasubsetT = $true,
inference(cnf_transformation,[],[f26]) ).
thf(f39,plain,
setminusI = $true,
inference(cnf_transformation,[],[f26]) ).
thf(f40,plain,
( $true
= ( subset @ sK8 @ ( setminus @ sK7 @ sK9 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f41,plain,
( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f42,plain,
( $true
= ( in @ sK10 @ sK9 ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f43,plain,
( $true
!= ( in @ sK10 @ ( setminus @ sK7 @ sK8 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f44,plain,
( $true
= ( in @ sK10 @ sK7 ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f45,plain,
( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f49,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f37,f39]) ).
thf(f50,plain,
( ( $true
!= ( in @ sK10 @ sK7 ) )
| ( $true != $true )
| ( $true
= ( in @ sK10 @ sK8 ) ) ),
inference(superposition,[],[f43,f49]) ).
thf(f51,plain,
( ( $true
!= ( in @ sK10 @ sK7 ) )
| ( $true
= ( in @ sK10 @ sK8 ) ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f52,plain,
( $true
= ( in @ sK10 @ sK8 ) ),
inference(forward_subsumption_resolution,[],[f51,f44]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f33,f38]) ).
thf(f54,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK8 ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK7 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ sK9 @ ( powerset @ sK7 ) ) )
| ( $true
!= ( in @ X0 @ sK9 ) ) ),
inference(superposition,[],[f53,f40]) ).
thf(f55,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ X0 @ sK9 ) )
| ( $true
!= ( in @ X0 @ sK8 ) )
| ( $true
!= ( in @ sK8 @ ( powerset @ sK7 ) ) )
| ( $true
!= ( in @ sK9 @ ( powerset @ sK7 ) ) ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK9 ) )
| ( $true
!= ( in @ sK9 @ ( powerset @ sK7 ) ) )
| ( $true
!= ( in @ X0 @ sK8 ) )
| ( $true
!= ( in @ X0 @ sK7 ) ) ),
inference(forward_subsumption_resolution,[],[f55,f45]) ).
thf(f57,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK8 ) )
| ( $true
!= ( in @ X0 @ sK7 ) )
| ( $true
!= ( in @ X0 @ sK9 ) ) ),
inference(forward_subsumption_resolution,[],[f56,f41]) ).
thf(f58,plain,
( ( $true
!= ( in @ sK10 @ sK7 ) )
| ( $true
!= ( in @ sK10 @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[],[f57,f52]) ).
thf(f59,plain,
( ( $true
!= ( in @ sK10 @ sK9 ) )
| ( $true
!= ( in @ sK10 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f60,plain,
( $true
!= ( in @ sK10 @ sK7 ) ),
inference(forward_subsumption_resolution,[],[f59,f42]) ).
thf(f61,plain,
$false,
inference(forward_subsumption_resolution,[],[f60,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU736^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 14:18:04 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.13 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
% 0.08/0.17 % (171507)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.17 % (171518)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.17 % (171518)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
% 0.08/0.17 % (171512)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1510498904:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.17 % (171514)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4005215505:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.17 % (171513)lrs+10_16_si=on:nwc=1.5:random_seed=4275874819:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.17 % (171516)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3182107727:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.17 % (171515)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=2418903661: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)
% 0.08/0.17 % (171517)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=622506950:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.17 % (171518)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=729409484:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.17 % (171514)Refutation not found, incomplete strategy
% 0.08/0.17 % (171514)------------------------------
% 0.08/0.17 % (171514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (171514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (171514)CaDiCaL version: 2.1.3
% 0.08/0.17 % (171514)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.17 % (171514)Time elapsed: 0.001 s
% 0.08/0.17 % (171514)Peak memory usage: 12 MB
% 0.08/0.17 % (171514)Instructions burned: 3 (million)
% 0.08/0.17 % (171514)------------------------------
% 0.08/0.17 % (171514)------------------------------
% 0.08/0.17 % (171516) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-171507-171516"...
% 0.08/0.17 % (171515) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-171507-171515"...
% 0.08/0.17 % (171517) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-171507-171517"...
% 0.08/0.17 % (171513) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-171507-171513"...
% 0.08/0.17 % (171516)...printing done.
% 0.08/0.17 % (171512) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-171507-171512"...
% 0.08/0.17 % (171516)Refutation found. Thanks to Tanya!
% 0.08/0.17 % SZS status Theorem for theBenchmark
% 0.08/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.17 % (171516)------------------------------
% 0.08/0.17 % (171516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (171516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (171516)CaDiCaL version: 2.1.3
% 0.08/0.17 % (171516)Termination reason: Refutation
% 0.08/0.17 % (171516)Time elapsed: 0.002 s
% 0.08/0.17 % (171516)Peak memory usage: 12 MB
% 0.08/0.17 % (171516)Instructions burned: 8 (million)
% 0.08/0.17 % (171507)Success in time 0.029 s
% 0.08/0.17 % Vampire exiting
%------------------------------------------------------------------------------