%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU741^2 : 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 : n010.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 08:31:04 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 424 ( 119 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 479 ( 41 ~; 32 |; 40 &; 328 @)
% ( 4 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 15 con; 0-2 aty)
% Number of variables : 109 ( 0 ^; 82 !; 27 ?; 109 :)
% 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,
binunionIL: $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
binintersectER: $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(f2,axiom,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(f3,conjecture,
( binunionIL
=> ( binintersectER
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(f4,negated_conjecture,
~ ( binunionIL
=> ( binintersectER
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
<=> ( binintersectER = $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( binunionIL
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( binunionIL = $true )
=> ( ( binintersectER = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
=> ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
= binunionIL ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( binunionIL = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
<=> ( binintersectER = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) )
<=> ( binunionIL = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
!= $true )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) )
& ( $true
= ( in @ X4 @ X1 ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binintersectER = $true )
& ( binunionIL = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
!= $true )
& ( $true
= ( in @ X4 @ X1 ) )
& ( $true
= ( in @ X4 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionIL = $true )
& ( binintersectER = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
& ( $true
!= ( in @ X5 @ ( binunion @ X3 @ X4 ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
| ( binunionIL != $true ) )
& ( ( binunionIL = $true )
| ( ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
!= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
!= $true )
& ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionIL = $true )
& ( binintersectER = $true ) ),
inference(rectify,[],[f14]) ).
thf(f19,plain,
( ( $true
!= ( in @ sK7 @ ( binunion @ sK5 @ sK6 ) ) )
& ( $true
= ( in @ sK7 @ sK3 ) )
& ( $true
= ( in @ sK7 @ ( binintersect @ sK4 @ sK5 ) ) )
& ( $true
= ( in @ sK6 @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) )
& ( binunionIL = $true )
& ( binintersectER = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6),skolemize(X4,sK7)],[f18]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) )
& ( $true
!= ( in @ X5 @ X4 ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ( ( $true
= ( in @ sK10 @ ( binintersect @ sK8 @ sK9 ) ) )
& ( $true
!= ( in @ sK10 @ sK9 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X3,sK8),skolemize(X4,sK9),skolemize(X5,sK10)],[f21]) ).
thf(f25,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f26,plain,
binintersectER = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
binunionIL = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f31,plain,
( $true
= ( in @ sK7 @ ( binintersect @ sK4 @ sK5 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f33,plain,
( $true
!= ( in @ sK7 @ ( binunion @ sK5 @ sK6 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f36,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) ),
inference(definition_unfolding,[],[f25,f27]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f36,f26]) ).
thf(f45,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f46,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f47,plain,
( ( $true
= ( in @ sK7 @ sK5 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f45,f31]) ).
thf(f48,plain,
( $true
= ( in @ sK7 @ sK5 ) ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f54,plain,
! [X0: $i] :
( ( $true
= ( in @ sK7 @ ( binunion @ sK5 @ X0 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f46,f48]) ).
thf(f55,plain,
! [X0: $i] :
( $true
= ( in @ sK7 @ ( binunion @ sK5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f64,plain,
$true != $true,
inference(constrained_superposition,[],[f33,f55]) ).
thf(f65,plain,
$false,
inference(trivial_inequality_removal,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU741^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.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 14:19:49 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.28 % (2927968)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (2927973)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2026839062:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (2927973) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2927968-2927973"...
% 0.21/0.28 % (2927973)...printing done.
% 0.21/0.28 % (2927973)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (2927973)------------------------------
% 0.21/0.28 % (2927973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2927973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2927973)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2927973)Termination reason: Refutation
% 0.21/0.28 % (2927973)Time elapsed: 0.002 s
% 0.21/0.28 % (2927973)Peak memory usage: 12 MB
% 0.21/0.28 % (2927973)Instructions burned: 6 (million)
% 0.21/0.28 % (2927968)Success in time 0.032 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------