%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU886^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:31:52 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 56 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 149 ( 31 ~; 19 |; 29 &; 66 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 15 !; 16 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: b > a ).
thf(func_def_1,type,
y: b > $o ).
thf(func_def_2,type,
x: b > $o ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: b ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 ) )
& ? [X1: b] :
( ( x @ X1 )
& ( X0
= ( f @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5203_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 ) )
& ? [X1: b] :
( ( x @ X1 )
& ( X0
= ( f @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X2: b] :
( ( ( f @ X2 )
= X0 )
& ( y @ X2 ) )
& ? [X3: b] :
( ( x @ X3 )
& ( ( f @ X3 )
= X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( y @ X1 )
= $true )
& ( ( f @ X1 )
= X0 )
& ( ( x @ X1 )
= $true ) )
=> ( ? [X2: b] :
( ( ( f @ X2 )
= X0 )
& ( $true
= ( y @ X2 ) ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ( $true
= ( x @ X3 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a] :
( ? [X1: b] :
( ( ( y @ X1 )
= $true )
& ( ( f @ X1 )
= X0 )
& ( ( x @ X1 )
= $true ) )
& ( ! [X3: b] :
( ( ( f @ X3 )
!= X0 )
| ( $true
!= ( x @ X3 ) ) )
| ! [X2: b] :
( ( $true
!= ( y @ X2 ) )
| ( ( f @ X2 )
!= X0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a] :
( ? [X1: b] :
( ( ( y @ X1 )
= $true )
& ( ( f @ X1 )
= X0 )
& ( ( x @ X1 )
= $true ) )
& ( ! [X2: b] :
( ( ( f @ X2 )
!= X0 )
| ( $true
!= ( x @ X2 ) ) )
| ! [X3: b] :
( ( $true
!= ( y @ X3 ) )
| ( ( f @ X3 )
!= X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( $true
= ( y @ sK1 ) )
& ( ( f @ sK1 )
= sK0 )
& ( $true
= ( x @ sK1 ) )
& ( ! [X2: b] :
( ( sK0
!= ( f @ X2 ) )
| ( $true
!= ( x @ X2 ) ) )
| ! [X3: b] :
( ( $true
!= ( y @ X3 ) )
| ( sK0
!= ( f @ X3 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
! [X2: b,X3: b] :
( ( sK0
!= ( f @ X2 ) )
| ( $true
!= ( x @ X2 ) )
| ( $true
!= ( y @ X3 ) )
| ( sK0
!= ( f @ X3 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( $true
= ( x @ sK1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( f @ sK1 )
= sK0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( $true
= ( y @ sK1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: b] :
( ( $true
!= ( x @ sK1 ) )
| ( sK0 != sK0 )
| ( sK0
!= ( f @ X0 ) )
| ( $true
!= ( y @ X0 ) ) ),
inference(superposition,[],[f8,f10]) ).
thf(f14,plain,
! [X0: b] :
( ( $true
!= ( x @ sK1 ) )
| ( $true
!= ( y @ X0 ) )
| ( sK0
!= ( f @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f13]) ).
thf(f15,plain,
! [X0: b] :
( ( $true
!= ( y @ X0 ) )
| ( sK0
!= ( f @ X0 ) ) ),
inference(forward_subsumption_resolution,[],[f14,f9]) ).
thf(f16,plain,
( ( ( f @ sK1 )
!= sK0 )
| ( $true != $true ) ),
inference(superposition,[],[f15,f11]) ).
thf(f17,plain,
( ( f @ sK1 )
!= sK0 ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f18,plain,
$false,
inference(forward_subsumption_resolution,[],[f17,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU886^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n012.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:42:48 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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
% 0.09/0.25 % (196023)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.25 % (196034)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.25 % (196034)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
% 0.09/0.25 % (196029)lrs+10_16_si=on:nwc=1.5:random_seed=1875956582:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.25 % (196034)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=3401627481:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.25 % (196032)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=283608297:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.25 % (196033)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4138921170:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.25 % (196031)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=543168407: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)
% 0.09/0.25 % (196030)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=114830540:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.25 % (196028)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2384602672:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.25 % (196032) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-196023-196032"...
% 0.09/0.25 % (196028) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-196023-196028"...
% 0.09/0.25 % (196030) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-196023-196030"...
% 0.09/0.25 % (196029) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-196023-196029"...
% 0.09/0.25 % (196031) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-196023-196031"...
% 0.09/0.25 % (196033) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-196023-196033"...
% 0.09/0.25 % (196032)...printing done.
% 0.09/0.25 % (196029)...printing done.
% 0.09/0.25 % (196030)...printing done.
% 0.09/0.25 % (196028)...printing done.
% 0.09/0.25 % (196033)...printing done.
% 0.09/0.25 % (196031)...printing done.
% 0.09/0.25 % (196034) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-196023-196034"...
% 0.09/0.25 % (196032)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (196032)------------------------------
% 0.09/0.25 % (196032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (196032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (196032)CaDiCaL version: 2.1.3
% 0.09/0.25 % (196032)Termination reason: Refutation
% 0.09/0.25 % (196032)Time elapsed: 0.002 s
% 0.09/0.25 % (196032)Peak memory usage: 12 MB
% 0.09/0.25 % (196032)Instructions burned: 1 (million)
% 0.09/0.25 % (196023)Success in time 0.035 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------