%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU647^2 : 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 : n020.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 08:30:30 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 357 ( 91 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 519 ( 32 ~; 24 |; 21 &; 424 @)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 86 ( 0 ^; 64 !; 22 ?; 86 :)
% 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,
setadjoinIL: $o ).
thf(func_def_5,type,
setukpairinjL1: $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
( setukpairinjL1
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(f3,conjecture,
( setadjoinIL
=> ( setukpairinjL1
=> ! [X1: $i,X2: $i,X0: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(f4,negated_conjecture,
~ ( setadjoinIL
=> ( setukpairinjL1
=> ! [X1: $i,X2: $i,X0: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setukpairinjL1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= $true )
=> ( X1 = X2 ) )
<=> ( setukpairinjL1 = $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( setadjoinIL
=> ( setukpairinjL1
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setukpairinjL1 = $true )
=> ! [X3: $i,X0: $i,X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X2 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( setukpairinjL1 = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( X1 = X2 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ? [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
& ( X1 != X2 ) )
& ( setukpairinjL1 = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
( ( setukpairinjL1 = $true )
& ? [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
& ( X1 != X2 ) )
& ( setadjoinIL = $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ( setukpairinjL1 = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
& ( X2 != X3 ) )
& ( setadjoinIL = $true ) ),
inference(rectify,[],[f13]) ).
thf(f15,plain,
( ( setukpairinjL1 = $true )
& ( ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
& ( sK2 != sK3 )
& ( setadjoinIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
!= $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( ( in @ sK4 @ ( setadjoin @ sK4 @ sK5 ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X2,sK4),skolemize(X3,sK5)],[f17]) ).
thf(f19,plain,
( ( ( setukpairinjL1 = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= $true )
& ( X1 != X2 ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( X1 = X2 ) )
| ( setukpairinjL1 != $true ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f20,plain,
( ( ( setukpairinjL1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( X3 = X4 ) )
| ( setukpairinjL1 != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( setukpairinjL1 = $true )
| ( ( $true
= ( in @ ( setadjoin @ sK7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK6 @ ( setadjoin @ sK8 @ emptyset ) ) @ emptyset ) ) ) )
& ( sK6 != sK7 ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( X3 = X4 ) )
| ( setukpairinjL1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f20]) ).
thf(f22,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
( ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f25,plain,
setukpairinjL1 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f28,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( X3 = X4 )
| ( setukpairinjL1 != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f27,f22]) ).
thf(f37,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( X3 = X4 )
| ( $true != $true )
| ( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) )
!= $true ) ),
inference(definition_unfolding,[],[f28,f25]) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f39,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( X3 = X4 ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f49,plain,
( ( in @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(constrained_superposition,[],[f38,f24]) ).
thf(f52,plain,
( ( $true != $true )
| ( sK2 = sK3 ) ),
inference(constrained_superposition,[],[f39,f49]) ).
thf(f53,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
$false,
inference(forward_subsumption_resolution,[],[f53,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU647^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n020.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 14:03:04 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.28 Running higher-order theorem proving
% 0.25/0.29 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
% 0.25/0.34 % (1102496)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.34 % (1102506)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1066013755:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.34 % (1102502)lrs+10_16_si=on:nwc=1.5:random_seed=3433257289:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.34 % (1102506) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1102496-1102506"...
% 0.25/0.34 % (1102502) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1102496-1102502"...
% 0.25/0.34 % (1102506)...printing done.
% 0.25/0.34 % (1102506)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status Theorem for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.34 % (1102506)------------------------------
% 0.25/0.34 % (1102506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (1102506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (1102506)CaDiCaL version: 2.1.3
% 0.25/0.34 % (1102506)Termination reason: Refutation
% 0.25/0.34 % (1102506)Time elapsed: 0.004 s
% 0.25/0.34 % (1102506)Peak memory usage: 12 MB
% 0.25/0.34 % (1102506)Instructions burned: 7 (million)
% 0.25/0.34 % (1102496)Success in time 0.033 s
% 0.25/0.34 % Vampire exiting
%------------------------------------------------------------------------------