%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU584^2 : 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 : n004.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 08:30:11 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 361 ( 105 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 404 ( 43 ~; 33 |; 24 &; 282 @)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 13 con; 0-4 aty)
% Number of variables : 102 ( 10 ^; 73 !; 19 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
setunionI: $o ).
thf(func_def_6,type,
binunion: $i > $i > $i ).
thf(func_def_7,type,
upairset2IR: $o ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) )
= setunionI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(f2,axiom,
( binunion
= ( ^ [X0: $i,X1: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunion) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairset2IR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(f4,conjecture,
( setunionI
=> ( upairset2IR
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(f5,negated_conjecture,
~ ( setunionI
=> ( upairset2IR
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairset2IR ),
inference(rectify,[],[f3]) ).
thf(f8,plain,
( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
<=> ( upairset2IR = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X0 @ ( setunion @ X1 ) ) ) )
= setunionI ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( setunionI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( $true
= ( in @ X0 @ ( setunion @ X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( setunionI
=> ( upairset2IR
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
~ ( ( setunionI = $true )
=> ( ( upairset2IR = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
!= $true ) )
& ( upairset2IR = $true )
& ( setunionI = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ( upairset2IR = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
!= $true ) )
& ( setunionI = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( setunionI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f16,plain,
( ( setunionI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( $true
= ( in @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ( upairset2IR = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( setunionI = $true ) ),
inference(rectify,[],[f14]) ).
thf(f18,plain,
( ( upairset2IR = $true )
& ( $true
= ( in @ sK1 @ sK2 ) )
& ( $true
!= ( in @ sK1 @ ( binunion @ sK0 @ sK2 ) ) )
& ( setunionI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
thf(f19,plain,
( ( ( setunionI = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( $true
!= ( in @ X0 @ ( setunion @ X1 ) ) )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( $true
= ( in @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( setunionI != $true ) ) ),
inference(nnf_transformation,[],[f16]) ).
thf(f20,plain,
( ( ( setunionI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
!= ( in @ X2 @ ( setunion @ X1 ) ) )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( setunion @ X4 ) )
= $true )
| ( $true
!= ( in @ X3 @ X4 ) ) )
| ( setunionI != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( setunionI = $true )
| ( ( $true
= ( in @ sK5 @ sK3 ) )
& ( $true
!= ( in @ sK5 @ ( setunion @ sK4 ) ) )
& ( $true
= ( in @ sK3 @ sK4 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( setunion @ X4 ) )
= $true )
| ( $true
!= ( in @ X3 @ X4 ) ) )
| ( setunionI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f20]) ).
thf(f22,plain,
( ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( upairset2IR != $true ) )
& ( ( upairset2IR = $true )
| ? [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( upairset2IR != $true ) )
& ( ( upairset2IR = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( upairset2IR != $true ) )
& ( ( upairset2IR = $true )
| ( $true
!= ( in @ sK6 @ ( setadjoin @ sK7 @ ( setadjoin @ sK6 @ emptyset ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X2,sK6),skolemize(X3,sK7)],[f23]) ).
thf(f25,plain,
setunionI = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f26,plain,
( $true
!= ( in @ sK1 @ ( binunion @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f27,plain,
( $true
= ( in @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f28,plain,
upairset2IR = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f29,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( setunion @ X4 ) )
= $true )
| ( $true
!= ( in @ X3 @ X4 ) )
| ( setunionI != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f34,plain,
! [X0: $i,X1: $i] :
( ( upairset2IR != $true )
| ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f35,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f39,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(forward_subsumption_resolution,[],[f34,f28]) ).
thf(f40,plain,
! [X1: $i] :
( ( binunion @ X1 )
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f35]) ).
thf(f41,plain,
! [X1: $i] :
( ( binunion @ X1 )
= ( ^ [Y0: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( binunion @ X1 @ X2 )
= ( ^ [Y0: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 ) ),
inference(argument_congruence,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( binunion @ X1 @ X2 )
= ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X4 ) )
| ( ( in @ X5 @ ( setunion @ X4 ) )
= $true )
| ( $true
!= ( in @ X5 @ X3 ) ) ),
inference(forward_subsumption_resolution,[],[f29,f25]) ).
thf(f46,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
| ( ( in @ X2 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f44,f39]) ).
thf(f47,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f49,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(forward_demodulation,[],[f47,f43]) ).
thf(f52,plain,
( ( $true
!= ( in @ sK1 @ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[],[f26,f49]) ).
thf(f54,plain,
( $true
!= ( in @ sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f56,plain,
$false,
inference(forward_subsumption_resolution,[],[f54,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU584^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:52:23 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.28 % (1323114)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1323123)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2685915602:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (1323123) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1323114-1323123"...
% 0.22/0.28 % (1323123)...printing done.
% 0.22/0.28 % (1323123)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (1323123)------------------------------
% 0.22/0.28 % (1323123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1323123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1323123)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1323123)Termination reason: Refutation
% 0.22/0.28 % (1323123)Time elapsed: 0.002 s
% 0.22/0.28 % (1323123)Peak memory usage: 12 MB
% 0.22/0.28 % (1323123)Instructions burned: 5 (million)
% 0.22/0.28 % (1323114)Success in time 0.026 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------