%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV450^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:38:39 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 132 ( 8 ~; 8 |; 0 &; 116 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 48 ( 0 ^; 46 !; 2 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vOR: $o > $o > $o ).
thf(func_def_8,type,
sK1: sK0 > $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_12,type,
sK2: sK0 ).
thf(f1,axiom,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f2,axiom,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/UNION_IDEMPOT_') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
= X1 ),
inference(fool_elimination,[],[f5]) ).
thf(f8,plain,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( X2 @ X1 )
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( X2 @ X1 )
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
| ( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X1 ) )
= ( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
| ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
? [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
!= X1 ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
!= sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( X2 @ X1 )
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
!= sK1 ),
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X1 ) )
= ( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
| ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X1 ) )
= ( ( X3 @ X2 )
| ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
inference(forward_demodulation,[],[f17,f14]) ).
thf(f21,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0 > $o] :
( ( ( X3 @ X2 )
| ( X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X1 ) ) ),
inference(forward_demodulation,[],[f20,f14]) ).
thf(f22,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0 > $o] :
( ( ( X3 @ X2 )
| ( X1 @ X2 ) )
= ( 'const/sets/UNION' @ X0 @ X3 @ X1 @ X2 ) ),
inference(forward_demodulation,[],[f21,f14]) ).
thf(f23,plain,
( ( sK1 @ sK2 )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK2 ) ),
inference(negative_extensionality,[],[f15]) ).
thf(f24,plain,
( ( ( sK1 @ sK2 )
| ( sK1 @ sK2 ) )
!= ( sK1 @ sK2 ) ),
inference(forward_demodulation,[],[f23,f22]) ).
thf(f25,plain,
( ( sK1 @ sK2 )
!= ( sK1 @ sK2 ) ),
inference(boolean_simplification,[],[f24]) ).
thf(f26,plain,
$false,
inference(trivial_inequality_removal,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV450^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n019.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 15:48:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.21/0.29 % (950777)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (950791)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2368372684:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (950792)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (950792)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
% 0.21/0.29 % (950786)lrs+10_16_si=on:nwc=1.5:random_seed=4121568714:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (950789)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=3698465651: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)
% 0.21/0.29 % (950787)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=750981166:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (950785)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4034256039:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (950790)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2190826533:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (950792)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=2114253417:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (950787) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-950777-950787"...
% 0.21/0.29 % (950791) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-950777-950791"...
% 0.21/0.29 % (950787)...printing done.
% 0.21/0.29 % (950787)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (950787)------------------------------
% 0.21/0.29 % (950787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (950787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (950787)CaDiCaL version: 2.1.3
% 0.21/0.29 % (950787)Termination reason: Refutation
% 0.21/0.29 % (950787)Time elapsed: 0.002 s
% 0.21/0.29 % (950787)Peak memory usage: 12 MB
% 0.21/0.29 % (950787)Instructions burned: 2 (million)
% 0.21/0.29 % (950777)Success in time 0.027 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------