%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU538^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:29:59 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 21 unt; 0 typ; 10 def)
% Number of atoms : 290 ( 68 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 226 ( 64 ~; 44 |; 11 &; 91 @)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 27 !; 11 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $o ).
thf(func_def_7,type,
sF3: $o ).
thf(func_def_8,type,
sF4: $o ).
thf(func_def_9,type,
sF5: $i > $o ).
thf(func_def_10,type,
sF6: $i > $o ).
thf(f1,conjecture,
! [X1: $i > $o,X0: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(f2,negated_conjecture,
~ ! [X1: $i > $o,X0: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $o,X1: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ~ ( X0 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i > $o,X1: $i] :
( ~ ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( X0 @ X2 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( $true
!= ( X0 @ X3 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i > $o,X1: $i] :
( ~ ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( X0 @ X2 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( $true
!= ( X0 @ X3 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: $i > $o,X1: $i] :
( ? [X3: $i] :
( ( $true
= ( X0 @ X3 ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( X0 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( X0 @ X2 ) )
& ( ( in @ X2 @ X1 )
= $true ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
!= ( X0 @ X3 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
= ( sK0 @ sK2 ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
thf(f9,plain,
! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,definition,
( sF3
= ( sK0 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f15,plain,
( ( sK0 @ sK2 )
= sF3 ),
inference(reorient_equations,[],[f14]) ).
thf(f16,plain,
$true = sF3,
inference(definition_folding,[],[f11,f15]) ).
thf(f17,definition,
( sF4
= ( in @ sK2 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f18,plain,
( ( in @ sK2 @ sK1 )
= sF4 ),
inference(reorient_equations,[],[f17]) ).
thf(f19,plain,
$true = sF4,
inference(definition_folding,[],[f10,f18]) ).
thf(f20,definition,
! [X3: $i] :
( ( sF5 @ X3 )
= ( in @ X3 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f21,definition,
! [X3: $i] :
( ( sF6 @ X3 )
= ( sK0 @ X3 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f22,plain,
! [X3: $i] :
( ( sK0 @ X3 )
= ( sF6 @ X3 ) ),
inference(reorient_equations,[],[f21]) ).
thf(f23,plain,
! [X3: $i] :
( ( $true
!= ( sF6 @ X3 ) )
| ( $true
!= ( sF5 @ X3 ) ) ),
inference(definition_folding,[],[f9,f22,f20]) ).
thf(f24,plain,
! [X3: $i] :
( ( $false
= ( in @ X3 @ sK1 ) )
| ( $true
= ( sF5 @ X3 ) ) ),
inference(iff_proxy_clausification,[],[f20]) ).
thf(f27,plain,
! [X3: $i] :
( ( $true
= ( sF6 @ X3 ) )
| ( $false
= ( sK0 @ X3 ) ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f28,plain,
( ( $false = sF4 )
| ( $true
= ( in @ sK2 @ sK1 ) ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f30,plain,
( ( $false = sF3 )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f37,definition,
( spl7_2
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f39,plain,
( ( $true = sF4 )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f42,definition,
( spl7_3
<=> ( $true
= ( in @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f44,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f46,definition,
( spl7_4
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f48,plain,
( ( $false = sF4 )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f28,f46,f42]) ).
thf(f51,definition,
( spl7_5
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f53,plain,
( ( $true = sF3 )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f60,definition,
( spl7_7
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f62,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f64,definition,
( spl7_8
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f66,plain,
( ( $false = sF3 )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f67,plain,
( spl7_7
| spl7_8 ),
inference(avatar_split_clause,[],[f30,f64,f60]) ).
thf(f68,plain,
spl7_5,
inference(avatar_split_clause,[],[f16,f51]) ).
thf(f69,plain,
spl7_2,
inference(avatar_split_clause,[],[f19,f37]) ).
thf(f85,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( sF5 @ X0 )
!= $true )
| ( $false
= ( sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f23,f27]) ).
thf(f86,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( ( sF5 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f92,plain,
( ( $true
!= ( sF5 @ sK2 ) )
| ( $false = $true )
| ~ spl7_7 ),
inference(constrained_superposition,[],[f62,f86]) ).
thf(f94,plain,
( ( $true
!= ( sF5 @ sK2 ) )
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f106,plain,
( ( $false = $true )
| ( $true
= ( sF5 @ sK2 ) )
| ~ spl7_3 ),
inference(constrained_superposition,[],[f44,f24]) ).
thf(f109,plain,
( ( $true
= ( sF5 @ sK2 ) )
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f112,plain,
( $false
| ~ spl7_3
| ~ spl7_7 ),
inference(forward_subsumption_resolution,[],[f109,f94]) ).
thf(f113,plain,
( ~ spl7_3
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f112]) ).
thf(f114,plain,
( ( $false = $true )
| ~ spl7_5
| ~ spl7_8 ),
inference(forward_demodulation,[],[f66,f53]) ).
thf(f115,plain,
( $false
| ~ spl7_5
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f116,plain,
( ~ spl7_5
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f115]) ).
thf(f117,plain,
( ( $false = $true )
| ~ spl7_2
| ~ spl7_4 ),
inference(forward_demodulation,[],[f48,f39]) ).
thf(f118,plain,
( $false
| ~ spl7_2
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f119,plain,
( ~ spl7_2
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f118]) ).
cnf(s2,plain,
( spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f49]) ).
cnf(s4,plain,
( spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f67]) ).
cnf(s5,plain,
spl7_5,
inference(sat_conversion,[],[f68]) ).
cnf(s6,plain,
spl7_2,
inference(sat_conversion,[],[f69]) ).
cnf(s8,plain,
( ~ spl7_3
| ~ spl7_7 ),
inference(sat_conversion,[],[f113]) ).
cnf(s9,plain,
( ~ spl7_5
| ~ spl7_8 ),
inference(sat_conversion,[],[f116]) ).
cnf(s10,plain,
( ~ spl7_2
| ~ spl7_4 ),
inference(sat_conversion,[],[f119]) ).
cnf(s11,plain,
~ spl7_4,
inference(rat,[],[s10,s6]) ).
cnf(s12,plain,
~ spl7_8,
inference(rat,[],[s9,s5]) ).
cnf(s13,plain,
spl7_7,
inference(rat,[],[s4,s12]) ).
cnf(s14,plain,
~ spl7_3,
inference(rat,[],[s8,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s2,s11,s14]) ).
thf(f121,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU538^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n011.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:49:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.19/0.27 % (125582)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (125593)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.27 % (125593)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
% 0.19/0.27 % (125593)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=177152154:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.27 % (125589)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=292668461:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.27 % (125588)lrs+10_16_si=on:nwc=1.5:random_seed=3626805718:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (125587)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2305151026:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (125590)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=1198546789: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)
% 0.19/0.27 % (125591)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3814421967:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.27 % (125593) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-125582-125593"...
% 0.19/0.27 % (125589) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-125582-125589"...
% 0.19/0.27 % (125588) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-125582-125588"...
% 0.19/0.27 % (125587) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-125582-125587"...
% 0.19/0.27 % (125591) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-125582-125591"...
% 0.19/0.27 % (125590) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-125582-125590"...
% 0.19/0.27 % (125593)...printing done.
% 0.19/0.27 % (125589)...printing done.
% 0.19/0.27 % (125587)...printing done.
% 0.19/0.27 % (125588)...printing done.
% 0.19/0.27 % (125593)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (125593)------------------------------
% 0.19/0.27 % (125593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (125593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (125593)CaDiCaL version: 2.1.3
% 0.19/0.27 % (125593)Termination reason: Refutation
% 0.19/0.27 % (125593)Time elapsed: 0.003 s
% 0.19/0.27 % (125593)Peak memory usage: 13 MB
% 0.19/0.27 % (125593)Instructions burned: 5 (million)
% 0.19/0.27 % (125582)Success in time 0.039 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------