%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET593^5 : TPTP v9.3.1. Released v4.0.0.
% 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 08:23:19 AM UTC 2026
% Result : Theorem 0.22s 0.26s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 6 unt; 0 typ; 6 def)
% Number of atoms : 321 ( 96 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 347 ( 90 ~; 75 |; 35 &; 121 @)
% ( 6 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 35 !; 15 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: a > $o ).
thf(func_def_6,type,
sK3: a ).
thf(func_def_7,type,
sK4: a ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( ( X2 @ X3 )
| ( X1 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X2 @ X3 ) )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_52_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( ( X2 @ X3 )
| ( X1 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X2 @ X3 ) )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( ( X2 @ X3 )
| ( X0 @ X3 ) ) )
=> ( ! [X4: a] :
( ( ( X1 @ X4 )
& ~ ( X0 @ X4 ) )
=> ( X2 @ X4 ) )
& ! [X5: a] :
( ( ( X1 @ X5 )
& ~ ( X2 @ X5 ) )
=> ( X0 @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) ) )
=> ( ! [X4: a] :
( ( ( ( X1 @ X4 )
= $true )
& ( ( X0 @ X4 )
!= $true ) )
=> ( ( X2 @ X4 )
= $true ) )
& ! [X5: a] :
( ( ( ( X1 @ X5 )
= $true )
& ( ( X2 @ X5 )
!= $true ) )
=> ( ( X0 @ X5 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) ) )
=> ( ! [X4: a] :
( ( ( ( X0 @ X4 )
!= $true )
& ( ( X1 @ X4 )
= $true ) )
=> ( ( X2 @ X4 )
= $true ) )
& ! [X5: a] :
( ( ( ( X1 @ X5 )
= $true )
& ( ( X2 @ X5 )
!= $true ) )
=> ( ( X0 @ X5 )
= $true ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ? [X4: a] :
( ( ( X2 @ X4 )
!= $true )
& ( ( X0 @ X4 )
!= $true )
& ( ( X1 @ X4 )
= $true ) )
| ? [X5: a] :
( ( ( X0 @ X5 )
!= $true )
& ( ( X1 @ X5 )
= $true )
& ( ( X2 @ X5 )
!= $true ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X4: a] :
( ( ( X0 @ X4 )
!= $true )
& ( ( X1 @ X4 )
= $true )
& ( ( X2 @ X4 )
!= $true ) )
| ? [X5: a] :
( ( ( X2 @ X5 )
!= $true )
& ( ( X0 @ X5 )
!= $true )
& ( ( X1 @ X5 )
= $true ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( ( X2 @ X4 )
!= $true )
& ( ( X0 @ X4 )
!= $true )
& ( ( X1 @ X4 )
= $true ) ) )
& ! [X5: a] :
( ( ( X1 @ X5 )
!= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X0 @ X5 )
= $true ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( ( $true
!= ( sK0 @ sK3 ) )
& ( ( sK1 @ sK3 )
= $true )
& ( $true
!= ( sK2 @ sK3 ) ) )
| ( ( $true
!= ( sK2 @ sK4 ) )
& ( ( sK0 @ sK4 )
!= $true )
& ( $true
= ( sK1 @ sK4 ) ) ) )
& ! [X5: a] :
( ( ( sK1 @ X5 )
!= $true )
| ( $true
= ( sK2 @ X5 ) )
| ( ( sK0 @ X5 )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f8]) ).
thf(f10,plain,
! [X5: a] :
( ( $true
= ( sK2 @ X5 ) )
| ( ( sK1 @ X5 )
!= $true )
| ( ( sK0 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK4 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ( $true
!= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK4 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
( ( ( sK0 @ sK4 )
!= $true )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f22,definition,
( spl5_1
<=> ( $true
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f24,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| spl5_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f26,definition,
( spl5_2
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| spl5_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f29,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f19,f26,f22]) ).
thf(f31,definition,
( spl5_3
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f33,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
( spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f16,f22,f31]) ).
thf(f36,definition,
( spl5_4
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| spl5_4 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl5_5
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f43,plain,
( ~ spl5_4
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f12,f40,f36]) ).
thf(f44,plain,
( ~ spl5_4
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f13,f22,f36]) ).
thf(f45,plain,
( spl5_3
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f15,f40,f31]) ).
thf(f46,plain,
( ~ spl5_5
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f18,f26,f40]) ).
thf(f48,definition,
( spl5_6
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f51,plain,
( ~ spl5_4
| spl5_6 ),
inference(avatar_split_clause,[],[f11,f48,f36]) ).
thf(f52,plain,
( spl5_6
| spl5_3 ),
inference(avatar_split_clause,[],[f14,f31,f48]) ).
thf(f53,plain,
( ~ spl5_2
| spl5_6 ),
inference(avatar_split_clause,[],[f17,f48,f26]) ).
thf(f54,plain,
( ( $true != $true )
| ( ( sK0 @ sK4 )
= $true )
| ( $true
!= ( sK1 @ sK4 ) )
| spl5_1 ),
inference(superposition,[],[f24,f10]) ).
thf(f55,plain,
( ( $true
!= ( sK1 @ sK4 ) )
| ( ( sK0 @ sK4 )
= $true )
| spl5_1 ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
( ~ spl5_6
| spl5_5
| spl5_1 ),
inference(avatar_split_clause,[],[f55,f22,f40,f48]) ).
thf(f57,plain,
( ( ( sK1 @ sK3 )
!= $true )
| ( $true != $true )
| ( $true
= ( sK0 @ sK3 ) )
| spl5_4 ),
inference(superposition,[],[f38,f10]) ).
thf(f58,plain,
( ( ( sK1 @ sK3 )
!= $true )
| ( $true
= ( sK0 @ sK3 ) )
| spl5_4 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f59,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl5_3
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f58,f33]) ).
thf(f60,plain,
( $false
| spl5_2
| ~ spl5_3
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f59,f28]) ).
thf(f61,plain,
( spl5_2
| ~ spl5_3
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
( ~ spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f34]) ).
cnf(s3,plain,
( ~ spl5_4
| ~ spl5_5 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
( spl5_3
| ~ spl5_5 ),
inference(sat_conversion,[],[f45]) ).
cnf(s6,plain,
( ~ spl5_2
| ~ spl5_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s7,plain,
( ~ spl5_4
| spl5_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s8,plain,
( spl5_3
| spl5_6 ),
inference(sat_conversion,[],[f52]) ).
cnf(s9,plain,
( ~ spl5_2
| spl5_6 ),
inference(sat_conversion,[],[f53]) ).
cnf(s10,plain,
( spl5_1
| spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f56]) ).
cnf(s11,plain,
( spl5_2
| ~ spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f61]) ).
cnf(s12,plain,
( spl5_3
| spl5_1 ),
inference(rat,[],[s10,s5,s8]) ).
cnf(s13,plain,
( ~ spl5_4
| spl5_1 ),
inference(rat,[],[s10,s3,s7]) ).
cnf(s14,plain,
spl5_1,
inference(rat,[],[s10,s6,s9,s11,s13,s12]) ).
cnf(s15,plain,
~ spl5_4,
inference(rat,[],[s4,s14]) ).
cnf(s16,plain,
spl5_3,
inference(rat,[],[s2,s14]) ).
cnf(s17,plain,
~ spl5_2,
inference(rat,[],[s1,s14]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s11,s16,s17,s15]) ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET593^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:38:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.22/0.26 % (101901)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.26 % (101909)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=2130067481: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)
% 0.22/0.26 % (101909) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-101901-101909"...
% 0.22/0.26 % (101909)...printing done.
% 0.22/0.26 % (101909)Refutation found. Thanks to Tanya!
% 0.22/0.26 % SZS status Theorem for theBenchmark
% 0.22/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.26 % (101909)------------------------------
% 0.22/0.26 % (101909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.26 % (101909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.26 % (101909)CaDiCaL version: 2.1.3
% 0.22/0.26 % (101909)Termination reason: Refutation
% 0.22/0.26 % (101909)Time elapsed: 0.002 s
% 0.22/0.26 % (101909)Peak memory usage: 13 MB
% 0.22/0.26 % (101909)Instructions burned: 3 (million)
% 0.22/0.26 % (101901)Success in time 0.025 s
% 0.22/0.26 % Vampire exiting
%------------------------------------------------------------------------------