%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU850^5 : 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 : n015.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 08:31:48 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 308 ( 100 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 288 ( 64 ~; 74 |; 32 &; 99 @)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 24 !; 18 ?; 42 :)
% 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(func_def_8,type,
sK5: a ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( X0 = X1 )
& ( X1 = X2 ) )
=> ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM9_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( X0 = X1 )
& ( X1 = X2 ) )
=> ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( X0 = X2 )
& ( X1 = X2 ) )
=> ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X2 @ X4 ) )
& ! [X5: a] :
( ( X1 @ X5 )
=> ( X0 @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ( X0 = X2 )
& ( X1 = X2 ) )
=> ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) )
& ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
=> ( $true
= ( X0 @ X5 ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
=> ( $true
= ( X2 @ X4 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ? [X5: a] :
( ( $true
= ( X1 @ X5 ) )
& ( $true
!= ( X0 @ X5 ) ) )
| ? [X3: a] :
( ( ( X2 @ X3 )
= $true )
& ( ( X1 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( $true
= ( X0 @ X4 ) )
& ( $true
!= ( X2 @ X4 ) ) ) )
& ( X0 = X2 )
& ( X1 = X2 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( X0 = X2 )
& ( X1 = X2 )
& ( ? [X5: a] :
( ( $true
= ( X1 @ X5 ) )
& ( $true
!= ( X0 @ X5 ) ) )
| ? [X3: a] :
( ( ( X2 @ X3 )
= $true )
& ( ( X1 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( $true
= ( X0 @ X4 ) )
& ( $true
!= ( X2 @ X4 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( X1 = X2 )
& ( X0 = X1 )
& ( ? [X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( $true
= ( X1 @ X4 ) )
& ( $true
!= ( X0 @ X4 ) ) )
| ? [X5: a] :
( ( $true
= ( X2 @ X5 ) )
& ( $true
!= ( X1 @ X5 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( sK1 = sK2 )
& ( sK1 = sK0 )
& ( ( ( $true
= ( sK0 @ sK3 ) )
& ( $true
!= ( sK2 @ sK3 ) ) )
| ( ( $true
= ( sK1 @ sK4 ) )
& ( $true
!= ( sK0 @ sK4 ) ) )
| ( ( $true
= ( sK2 @ sK5 ) )
& ( $true
!= ( sK1 @ sK5 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f7]) ).
thf(f9,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( $true
!= ( sK0 @ sK4 ) )
| ( $true
!= ( sK1 @ sK5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( $true
!= ( sK0 @ sK4 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( $true
!= ( sK1 @ sK5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK0 @ sK4 ) )
| ( $true
!= ( sK1 @ sK5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK0 @ sK4 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( $true
!= ( sK1 @ sK5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
sK1 = sK0,
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
sK1 = sK2,
inference(cnf_transformation,[],[f8]) ).
thf(f21,plain,
sK0 = sK2,
inference(definition_unfolding,[],[f18,f17]) ).
thf(f22,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(definition_unfolding,[],[f16,f17,f21]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK0 @ sK5 ) ) ),
inference(definition_unfolding,[],[f15,f17,f17]) ).
thf(f24,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(definition_unfolding,[],[f14,f21]) ).
thf(f25,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ( $true
!= ( sK0 @ sK5 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(definition_unfolding,[],[f13,f17]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(definition_unfolding,[],[f12,f21,f17,f21]) ).
thf(f27,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
!= ( sK0 @ sK3 ) )
| ( $true
!= ( sK0 @ sK5 ) ) ),
inference(definition_unfolding,[],[f11,f21,f17,f17]) ).
thf(f28,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true
!= ( sK0 @ sK3 ) )
| ( $true
!= ( sK0 @ sK4 ) ) ),
inference(definition_unfolding,[],[f10,f21,f21]) ).
thf(f29,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ( $true
!= ( sK0 @ sK4 ) )
| ( $true
!= ( sK0 @ sK5 ) ) ),
inference(definition_unfolding,[],[f9,f21,f17]) ).
thf(f31,definition,
( spl6_1
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f34,definition,
( spl6_2
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f37,definition,
( spl6_3
<=> ( $true
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f39,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f27,f37,f34,f31]) ).
thf(f41,plain,
( ~ spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f29,f37,f34,f31]) ).
thf(f44,plain,
( ~ spl6_2
| spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f24,f31,f37,f34]) ).
thf(f45,plain,
( spl6_3
| ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f28,f34,f31,f37]) ).
thf(f46,plain,
( spl6_1
| ~ spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f23,f34,f37,f31]) ).
thf(f47,plain,
( spl6_1
| spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f22,f34,f37,f31]) ).
thf(f48,plain,
( ~ spl6_3
| ~ spl6_2
| spl6_1 ),
inference(avatar_split_clause,[],[f25,f31,f34,f37]) ).
thf(f49,plain,
( ~ spl6_1
| spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f26,f34,f37,f31]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f41]) ).
cnf(s3,plain,
( spl6_1
| ~ spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f44]) ).
cnf(s4,plain,
( ~ spl6_1
| ~ spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f45]) ).
cnf(s5,plain,
( spl6_1
| spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s6,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s7,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s8,plain,
( ~ spl6_1
| spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f49]) ).
cnf(s9,plain,
( spl6_2
| spl6_1 ),
inference(rat,[],[s5,s6]) ).
cnf(s10,plain,
( ~ spl6_2
| spl6_1 ),
inference(rat,[],[s7,s3]) ).
cnf(s11,plain,
spl6_1,
inference(rat,[],[s10,s9]) ).
cnf(s12,plain,
spl6_2,
inference(rat,[],[s1,s8,s11]) ).
cnf(s13,plain,
spl6_3,
inference(rat,[],[s4,s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s11,s12,s13]) ).
thf(f50,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU850^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:43:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.08/0.26 % (3614527)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (3614540)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1957665658:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.26 % (3614540) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3614527-3614540"...
% 0.08/0.26 % (3614540)...printing done.
% 0.08/0.26 % (3614540)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (3614540)------------------------------
% 0.08/0.26 % (3614540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3614540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3614540)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3614540)Termination reason: Refutation
% 0.08/0.26 % (3614540)Time elapsed: 0.001 s
% 0.08/0.26 % (3614540)Peak memory usage: 12 MB
% 0.08/0.26 % (3614540)Instructions burned: 3 (million)
% 0.08/0.26 % (3614527)Success in time 0.016 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------