%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU746^2 : 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 : n005.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 08:31:06 AM UTC 2026
% Result : Theorem 0.12s 0.29s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 436 ( 117 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 446 ( 47 ~; 51 |; 37 &; 266 @)
% ( 6 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 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 : 20 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 53 !; 21 ?; 74 :)
% 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,
binunionE: $o ).
thf(func_def_13,type,
sK6: $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) )
= binunionE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f2,conjecture,
( binunionE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $o,X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
=> ( ( ( in @ X4 @ X1 )
=> X3 )
=> ( ( ( in @ X4 @ X2 )
=> X3 )
=> X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTE) ).
thf(f3,negated_conjecture,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $o,X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
=> ( ( ( in @ X4 @ X1 )
=> X3 )
=> ( ( ( in @ X4 @ X2 )
=> X3 )
=> X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
=> ( ( in @ X1 @ X0 )
| ( in @ X1 @ X2 ) ) )
= binunionE ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true )
=> ( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ X2 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $o,X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
=> ( ( ( in @ X4 @ X1 )
=> X3 )
=> ( ( ( in @ X4 @ X2 )
=> X3 )
=> X3 ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( binunionE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $o,X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
= $true )
=> ( ( ( ( in @ X4 @ X1 )
= $true )
=> ( $true = X3 ) )
=> ( ( ( ( in @ X4 @ X2 )
= $true )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $o,X4: $i] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X4 @ X2 )
!= $true ) )
& ( ( $true = X3 )
| ( ( in @ X4 @ X1 )
!= $true ) )
& ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $o,X4: $i] :
( ( ( $true = X3 )
| ( ( in @ X4 @ X1 )
!= $true ) )
& ( ( $true = X3 )
| ( ( in @ X4 @ X2 )
!= $true ) )
& ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true )
& ( $true != X3 ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionE = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f11,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ X2 ) ) )
<=> ( binunionE = $true ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ X2 ) ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( binunion @ X0 @ X2 ) )
= $true )
& ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ X2 ) ) ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f13,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true
= ( in @ X0 @ X1 ) ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binunion @ X5 @ X4 ) )
= $true )
& ( $true
!= ( in @ X3 @ X5 ) )
& ( $true
!= ( in @ X3 @ X4 ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true
= ( in @ X0 @ X1 ) ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ( ( $true
= ( in @ sK0 @ ( binunion @ sK2 @ sK1 ) ) )
& ( ( in @ sK0 @ sK2 )
!= $true )
& ( ( in @ sK0 @ sK1 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $o,X4: $i] :
( ( ( $true = X3 )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( ( $true = X3 )
| ( ( in @ X4 @ X2 )
!= $true ) )
& ( ( in @ X4 @ ( binunion @ X0 @ X2 ) )
= $true )
& ( ( in @ X4 @ X1 )
= $true )
& ( $true != X3 ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binunionE = $true ) ),
inference(rectify,[],[f9]) ).
thf(f16,plain,
( ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ( ( $true = sK6 )
| ( $true
!= ( in @ sK7 @ sK3 ) ) )
& ( ( $true = sK6 )
| ( $true
!= ( in @ sK7 @ sK5 ) ) )
& ( $true
= ( in @ sK7 @ ( binunion @ sK3 @ sK5 ) ) )
& ( ( in @ sK7 @ sK4 )
= $true )
& ( $true != sK6 )
& ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ( binunionE = $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)],[f15]) ).
thf(f20,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true
= ( in @ X0 @ X1 ) )
| ( binunionE != $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
binunionE = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
$true != sK6,
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( $true
= ( in @ sK7 @ ( binunion @ sK3 @ sK5 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
( ( $true = sK6 )
| ( $true
!= ( in @ sK7 @ sK5 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( ( $true = sK6 )
| ( $true
!= ( in @ sK7 @ sK3 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f20,f21]) ).
thf(f35,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f37,definition,
( spl8_1
<=> ( $true = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f41,definition,
( spl8_2
<=> ( $true
= ( in @ sK7 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f43,plain,
( ( $true
!= ( in @ sK7 @ sK3 ) )
| spl8_2 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f27,f41,f37]) ).
thf(f45,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f23,f37]) ).
thf(f47,definition,
( spl8_3
<=> ( $true
= ( in @ sK7 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f49,plain,
( ( $true
!= ( in @ sK7 @ sK5 ) )
| spl8_3 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f50,plain,
( ~ spl8_3
| spl8_1 ),
inference(avatar_split_clause,[],[f26,f37,f47]) ).
thf(f51,plain,
( ( $true != $true )
| ( $true
= ( in @ sK7 @ sK5 ) )
| ( $true
= ( in @ sK7 @ sK3 ) ) ),
inference(constrained_superposition,[],[f35,f25]) ).
thf(f52,plain,
( ( $true
= ( in @ sK7 @ sK3 ) )
| ( $true
= ( in @ sK7 @ sK5 ) ) ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f53,plain,
( ( $true
= ( in @ sK7 @ sK5 ) )
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f52,f43]) ).
thf(f54,plain,
( $false
| spl8_2
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f53,f49]) ).
thf(f55,plain,
( spl8_2
| spl8_3 ),
inference(avatar_contradiction_clause,[],[f54]) ).
cnf(s1,plain,
( spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
~ spl8_1,
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
( spl8_1
| ~ spl8_3 ),
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
( spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
~ spl8_3,
inference(rat,[],[s3,s2]) ).
cnf(s6,plain,
spl8_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s2]) ).
thf(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU746^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n005.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 14:20:02 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.24 Running higher-order theorem proving
% 0.12/0.25 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
% 0.12/0.29 % (1734971)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.12/0.29 % (1734976)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3733881972:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.12/0.29 % (1734976) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1734971-1734976"...
% 0.12/0.29 % (1734977)lrs+10_16_si=on:nwc=1.5:random_seed=1220202349:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.12/0.29 % (1734976)...printing done.
% 0.12/0.29 % (1734976)Refutation found. Thanks to Tanya!
% 0.12/0.29 % SZS status Theorem for theBenchmark
% 0.12/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.29 % (1734976)------------------------------
% 0.12/0.29 % (1734976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.29 % (1734976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.29 % (1734976)CaDiCaL version: 2.1.3
% 0.12/0.29 % (1734976)Termination reason: Refutation
% 0.12/0.29 % (1734976)Time elapsed: 0.003 s
% 0.12/0.29 % (1734976)Peak memory usage: 13 MB
% 0.12/0.29 % (1734976)Instructions burned: 5 (million)
% 0.12/0.29 % (1734971)Success in time 0.025 s
% 0.12/0.29 % Vampire exiting
%------------------------------------------------------------------------------