%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU852^5 : 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 : n017.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 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 437 ( 151 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 481 ( 109 ~; 108 |; 47 &; 179 @)
% ( 11 <=>; 25 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 69 !; 21 ?; 90 :)
% 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,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ( X0 @ X3 )
& ( X2 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X1 @ X3 ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM36_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ( X0 @ X3 )
& ( X2 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X1 @ X3 ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) )
& ! [X4: a] :
( ( X1 @ X4 )
=> ( X0 @ X4 ) ) )
=> ( ! [X5: a] :
( ( ( X1 @ X5 )
& ( X0 @ X5 )
& ~ ( X2 @ X5 ) )
=> ( X2 @ X5 ) )
<=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
=> ( $true
= ( X0 @ X4 ) ) ) )
=> ( ! [X5: a] :
( ( ( $true
= ( X1 @ X5 ) )
& ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) )
=> ( $true
= ( X2 @ X5 ) ) )
<=> ! [X6: a] :
( ( $true
= ( X1 @ X6 ) )
=> ( $true
= ( X2 @ X6 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
=> ( $true
= ( X0 @ X4 ) ) ) )
=> ( ! [X6: a] :
( ( $true
= ( X1 @ X6 ) )
=> ( $true
= ( X2 @ X6 ) ) )
<=> ! [X5: a] :
( ( ( $true
= ( X0 @ X5 ) )
& ( $true
= ( X1 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) )
=> ( $true
= ( X2 @ X5 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X2 @ X6 ) ) )
<~> ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
| ( $true
!= ( X0 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X2 @ X6 ) ) )
<~> ! [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ? [X5: a] :
( ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) )
& ( $true
= ( X1 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) )
| ? [X6: a] :
( ( $true
= ( X1 @ X6 ) )
& ( $true
!= ( X2 @ X6 ) ) ) )
& ( ! [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) )
| ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X2 @ X6 ) ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f9,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ? [X5: a] :
( ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) )
& ( $true
= ( X1 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) )
| ? [X6: a] :
( ( $true
= ( X1 @ X6 ) )
& ( $true
!= ( X2 @ X6 ) ) ) )
& ( ! [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) )
| ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X2 @ X6 ) ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X1 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true ) )
| ? [X4: a] :
( ( $true
= ( X0 @ X4 ) )
& ( $true
!= ( X2 @ X4 ) ) ) )
& ( ! [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X2 @ X5 ) )
| ( $true
!= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) )
| ! [X6: a] :
( ( $true
!= ( X0 @ X6 ) )
| ( $true
= ( X2 @ X6 ) ) ) )
& ! [X7: a] :
( ( $true
= ( X1 @ X7 ) )
| ( $true
!= ( X0 @ X7 ) ) )
& ! [X8: a] :
( ( $true
!= ( X2 @ X8 ) )
| ( $true
= ( X1 @ X8 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ( ( $true
= ( sK1 @ sK3 ) )
& ( $true
!= ( sK2 @ sK3 ) )
& ( $true
= ( sK0 @ sK3 ) )
& ( $true
!= ( sK2 @ sK3 ) ) )
| ( ( $true
= ( sK0 @ sK4 ) )
& ( $true
!= ( sK2 @ sK4 ) ) ) )
& ( ! [X5: a] :
( ( ( sK1 @ X5 )
!= $true )
| ( ( sK2 @ X5 )
= $true )
| ( $true
!= ( sK0 @ X5 ) )
| ( ( sK2 @ X5 )
= $true ) )
| ! [X6: a] :
( ( $true
!= ( sK0 @ X6 ) )
| ( $true
= ( sK2 @ X6 ) ) ) )
& ! [X7: a] :
( ( ( sK1 @ X7 )
= $true )
| ( $true
!= ( sK0 @ X7 ) ) )
& ! [X8: a] :
( ( $true
!= ( sK2 @ X8 ) )
| ( $true
= ( sK1 @ X8 ) ) ) ),
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)],[f10]) ).
thf(f13,plain,
! [X7: a] :
( ( $true
!= ( sK0 @ X7 ) )
| ( ( sK1 @ X7 )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
! [X6: a,X5: a] :
( ( ( sK2 @ X5 )
= $true )
| ( $true
!= ( sK0 @ X5 ) )
| ( $true
!= ( sK0 @ X6 ) )
| ( ( sK1 @ X5 )
!= $true )
| ( $true
= ( sK2 @ X6 ) )
| ( ( sK2 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
!= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK2 @ sK4 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ( $true
!= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f25,plain,
! [X6: a,X5: a] :
( ( $true
!= ( sK0 @ X6 ) )
| ( ( sK1 @ X5 )
!= $true )
| ( $true
!= ( sK0 @ X5 ) )
| ( ( sK2 @ X5 )
= $true )
| ( $true
= ( sK2 @ X6 ) ) ),
inference(duplicate_literal_removal,[],[f14]) ).
thf(f27,definition,
( spl5_1
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f29,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| spl5_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl5_2
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f33,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f36,definition,
( spl5_3
<=> ! [X6: a] :
( ( $true
!= ( sK0 @ X6 ) )
| ( $true
= ( sK2 @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f37,plain,
( ! [X6: a] :
( ( $true
!= ( sK0 @ X6 ) )
| ( $true
= ( sK2 @ X6 ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,definition,
( spl5_4
<=> ! [X5: a] :
( ( ( sK1 @ X5 )
!= $true )
| ( ( sK2 @ X5 )
= $true )
| ( $true
!= ( sK0 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f40,plain,
( ! [X5: a] :
( ( ( sK1 @ X5 )
!= $true )
| ( $true
!= ( sK0 @ X5 ) )
| ( ( sK2 @ X5 )
= $true ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f41,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f25,f39,f36]) ).
thf(f43,definition,
( spl5_5
<=> ( $true
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f45,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| spl5_5 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f48,definition,
( spl5_6
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
( spl5_6
| spl5_2 ),
inference(avatar_split_clause,[],[f18,f31,f48]) ).
thf(f57,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f19,f43,f27]) ).
thf(f58,plain,
( ~ spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f17,f48,f43]) ).
thf(f60,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f16,f31,f27]) ).
thf(f63,plain,
( ( $true != $true )
| ( $true
= ( sK2 @ sK4 ) )
| ~ spl5_2
| ~ spl5_3 ),
inference(constrained_superposition,[],[f37,f33]) ).
thf(f64,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ~ spl5_2
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f65,plain,
( $false
| ~ spl5_2
| ~ spl5_3
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f64,f45]) ).
thf(f66,plain,
( ~ spl5_2
| ~ spl5_3
| spl5_5 ),
inference(avatar_contradiction_clause,[],[f65]) ).
thf(f67,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true != $true )
| ~ spl5_3
| ~ spl5_6 ),
inference(constrained_superposition,[],[f37,f50]) ).
thf(f70,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl5_3
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f71,plain,
( $false
| spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(forward_subsumption_resolution,[],[f70,f29]) ).
thf(f72,plain,
( spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f71]) ).
thf(f73,plain,
( ! [X5: a] :
( ( $true
!= ( sK0 @ X5 ) )
| ( ( sK2 @ X5 )
= $true ) )
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f40,f13]) ).
thf(f74,plain,
( spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f73,f39,f36]) ).
cnf(s2,plain,
( spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f41]) ).
cnf(s4,plain,
( spl5_2
| spl5_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
( ~ spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f58]) ).
cnf(s9,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s10,plain,
( ~ spl5_2
| ~ spl5_3
| spl5_5 ),
inference(sat_conversion,[],[f66]) ).
cnf(s11,plain,
( spl5_1
| ~ spl5_3
| ~ spl5_6 ),
inference(sat_conversion,[],[f72]) ).
cnf(s12,plain,
( spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f74]) ).
cnf(s13,plain,
spl5_3,
inference(rat,[],[s2,s12]) ).
cnf(s14,plain,
spl5_6,
inference(rat,[],[s10,s4,s7,s13]) ).
cnf(s15,plain,
spl5_1,
inference(rat,[],[s11,s13,s14]) ).
cnf(s16,plain,
spl5_2,
inference(rat,[],[s9,s15]) ).
cnf(s17,plain,
~ spl5_5,
inference(rat,[],[s6,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s10,s13,s17,s16]) ).
thf(f75,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU852^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n017.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
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:35:23 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.22/0.27 % (421472)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (421477)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1516300923:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.27 % (421477) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-421472-421477"...
% 0.22/0.27 % (421477)...printing done.
% 0.22/0.27 % (421477)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (421477)------------------------------
% 0.22/0.27 % (421477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (421477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (421477)CaDiCaL version: 2.1.3
% 0.22/0.27 % (421477)Termination reason: Refutation
% 0.22/0.27 % (421477)Time elapsed: 0.002 s
% 0.22/0.27 % (421477)Peak memory usage: 13 MB
% 0.22/0.27 % (421477)Instructions burned: 4 (million)
% 0.22/0.27 % (421472)Success in time 0.025 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------