%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM003-1 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 : Tue Sep 29 09:38:59 AM UTC 2026
% Result : Unsatisfiable 3.15s 1.06s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 69
% Syntax : Number of formulae : 272 ( 12 unt; 27 def)
% Number of atoms : 1054 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1485 ( 703 ~; 755 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 34 ( 33 usr; 28 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 152 ( 0 sgn 152 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ algorithm(X0)
| program(f2(X0))
| program(c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_1_1) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ algorithm(X0)
| program(f2(X0))
| ~ program(X1)
| decides(c1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_1_2) ).
fof(f3,axiom,
! [X0] :
( ~ algorithm(X0)
| ~ decides(X0,f2(X0),f1(X0))
| program(c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_1_3) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ algorithm(X0)
| ~ decides(X0,f2(X0),f1(X0))
| ~ program(X1)
| decides(c1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_1_4) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ program(X0)
| program(f4(X0))
| ~ program(X1)
| ~ halts2(X1,X2)
| halts3(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_2_1) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ program(X0)
| program(f4(X0))
| ~ program(X1)
| ~ halts2(X1,X2)
| outputs(X0,good) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_2_2) ).
fof(f7,axiom,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| program(f4(X0))
| ~ program(X1)
| halts2(X1,X2)
| ~ program(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_2_3) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ program(X0)
| program(f4(X0))
| ~ program(X1)
| halts2(X1,X2)
| outputs(X0,bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_2_4) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ program(X0)
| ~ decides(X0,f4(X0),f3(X0))
| ~ program(X1)
| ~ halts2(X1,X2)
| halts3(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_2_5) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ program(X0)
| ~ decides(X0,f4(X0),f3(X0))
| ~ program(X1)
| ~ halts2(X1,X2)
| outputs(X0,good) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_2_6) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ decides(X0,f4(X0),f3(X0))
| ~ program(X0)
| ~ program(X1)
| halts2(X1,X2)
| halts3(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_2_7) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ program(X0)
| ~ decides(X0,f4(X0),f3(X0))
| ~ program(X1)
| halts2(X1,X2)
| outputs(X0,bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_2_8) ).
fof(f13,axiom,
! [X0] :
( ~ program(X0)
| program(f5(X0))
| program(c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_1) ).
fof(f14,axiom,
! [X0,X1] :
( ~ program(X0)
| program(f5(X0))
| ~ program(X1)
| ~ halts2(X1,X1)
| halts2(c2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_2) ).
fof(f15,axiom,
! [X0,X1] :
( ~ program(X0)
| program(f5(X0))
| ~ program(X1)
| ~ halts2(X1,X1)
| outputs(c2,good) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_3) ).
fof(f16,axiom,
! [X0,X1] :
( ~ program(X0)
| program(f5(X0))
| ~ program(X1)
| halts2(X1,X1)
| halts2(c2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_4) ).
fof(f17,axiom,
! [X0,X1] :
( ~ program(X0)
| program(f5(X0))
| ~ program(X1)
| halts2(X1,X1)
| outputs(c2,bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_5) ).
fof(f18,axiom,
! [X0] :
( ~ program(X0)
| halts2(f5(X0),f5(X0))
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,bad)
| program(c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_6) ).
fof(f19,axiom,
! [X0,X1] :
( ~ program(X0)
| halts2(f5(X0),f5(X0))
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,bad)
| ~ program(X1)
| ~ halts2(X1,X1)
| halts2(c2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_7) ).
fof(f20,axiom,
! [X0,X1] :
( ~ program(X0)
| halts2(f5(X0),f5(X0))
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,bad)
| ~ program(X1)
| ~ halts2(X1,X1)
| outputs(c2,good) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_8) ).
fof(f21,axiom,
! [X0,X1] :
( ~ program(X0)
| halts2(f5(X0),f5(X0))
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,bad)
| ~ program(X1)
| halts2(X1,X1)
| halts2(c2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_9) ).
fof(f22,axiom,
! [X0,X1] :
( ~ program(X0)
| halts2(f5(X0),f5(X0))
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,bad)
| ~ program(X1)
| halts2(X1,X1)
| outputs(c2,bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_10) ).
fof(f23,axiom,
! [X0] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ halts2(f5(X0),f5(X0))
| program(c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_11) ).
fof(f24,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ halts2(f5(X0),f5(X0))
| ~ program(X1)
| ~ halts2(X1,X1)
| halts2(c2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_12) ).
fof(f25,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ halts2(f5(X0),f5(X0))
| ~ program(X1)
| ~ halts2(X1,X1)
| outputs(c2,good) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_13) ).
fof(f26,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ halts2(f5(X0),f5(X0))
| ~ program(X1)
| halts2(X1,X1)
| halts2(c2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_14) ).
fof(f27,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ halts2(f5(X0),f5(X0))
| ~ program(X1)
| halts2(X1,X1)
| outputs(c2,bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_15) ).
fof(f28,axiom,
! [X0] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_16) ).
fof(f29,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(X1)
| ~ halts2(X1,X1)
| halts2(c2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_17) ).
fof(f30,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(X1)
| ~ halts2(X1,X1)
| outputs(c2,good) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_18) ).
fof(f31,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(X1)
| halts2(X1,X1)
| halts2(c2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_19) ).
fof(f32,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(X1)
| halts2(X1,X1)
| outputs(c2,bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_3_20) ).
fof(f33,axiom,
! [X0] :
( ~ program(X0)
| program(f6(X0))
| program(c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_4_1) ).
fof(f34,axiom,
! [X0,X1] :
( ~ program(X0)
| program(f6(X0))
| ~ program(X1)
| ~ halts2(X1,X1)
| ~ halts2(c3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_4_2) ).
fof(f35,axiom,
! [X0,X1] :
( ~ program(X0)
| program(f6(X0))
| ~ program(X1)
| halts2(X1,X1)
| halts2(c3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_4_3) ).
fof(f41,axiom,
! [X0] :
( ~ program(X0)
| ~ halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ halts2(f6(X0),f6(X0))
| program(c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_4_9) ).
fof(f42,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ halts2(f6(X0),f6(X0))
| ~ program(X1)
| ~ halts2(X1,X1)
| ~ halts2(c3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_4_10) ).
fof(f45,axiom,
! [X0] :
( ~ program(X0)
| ~ halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_4_13) ).
fof(f46,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(X1)
| ~ halts2(X1,X1)
| ~ halts2(c3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_4_14) ).
fof(f47,axiom,
! [X0,X1] :
( ~ program(X0)
| ~ halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(X1)
| halts2(X1,X1)
| halts2(c3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_4_15) ).
fof(f49,negated_conjecture,
algorithm(c4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_deciding_algorithm) ).
fof(f50,negated_conjecture,
! [X0,X1] :
( decides(c4,X0,X1)
| ~ program(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_the_algorithm_doesnt_exist) ).
fof(f56,definition,
( spl0_2
<=> ! [X1] :
( ~ program(X1)
| halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f57,plain,
( ! [X1] :
( halts2(X1,X1)
| ~ program(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,definition,
( spl0_3
<=> ! [X0] :
( ~ program(X0)
| ~ outputs(X0,bad)
| ~ outputs(X0,good)
| ~ halts2(X0,f6(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f60,plain,
( ! [X0] :
( ~ halts2(X0,f6(X0))
| ~ outputs(X0,bad)
| ~ outputs(X0,good)
| ~ program(X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl0_4
<=> ! [X1] :
( ~ program(X1)
| halts2(c3,X1)
| halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f64,plain,
( ! [X1] :
( halts2(c3,X1)
| halts2(X1,X1)
| ~ program(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f47,f59,f63]) ).
fof(f67,definition,
( spl0_5
<=> ! [X1] :
( ~ program(X1)
| ~ halts2(c3,X1)
| ~ halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f68,plain,
( ! [X1] :
( ~ halts2(c3,X1)
| ~ program(X1)
| ~ halts2(X1,X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f46,f59,f67]) ).
fof(f71,definition,
( spl0_6
<=> program(c3) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f73,plain,
( program(c3)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl0_6
| spl0_3 ),
inference(avatar_split_clause,[],[f45,f59,f71]) ).
fof(f76,definition,
( spl0_7
<=> ! [X0] :
( ~ program(X0)
| ~ halts2(f6(X0),f6(X0))
| ~ outputs(X0,good)
| ~ halts2(X0,f6(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f77,plain,
( ! [X0] :
( ~ halts2(f6(X0),f6(X0))
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(X0,f6(X0)) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,plain,
( spl0_5
| spl0_7 ),
inference(avatar_split_clause,[],[f42,f76,f67]) ).
fof(f81,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f41,f76,f71]) ).
fof(f90,definition,
( spl0_9
<=> ! [X0] :
( ~ program(X0)
| program(f6(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f91,plain,
( ! [X0] :
( program(f6(X0))
| ~ program(X0) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f35,f90,f63]) ).
fof(f94,plain,
( spl0_5
| spl0_9 ),
inference(avatar_split_clause,[],[f34,f90,f67]) ).
fof(f95,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f33,f90,f71]) ).
fof(f97,definition,
( spl0_10
<=> outputs(c2,bad) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f99,plain,
( outputs(c2,bad)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl0_11
<=> ! [X0] :
( ~ program(X0)
| ~ outputs(X0,bad)
| ~ outputs(X0,good)
| ~ halts3(X0,f5(X0),f5(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f102,plain,
( ! [X0] :
( ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,bad)
| ~ outputs(X0,good)
| ~ program(X0) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( spl0_10
| spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f32,f101,f56,f97]) ).
fof(f105,definition,
( spl0_12
<=> ! [X1] :
( ~ program(X1)
| halts2(c2,X1)
| halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f106,plain,
( ! [X1] :
( halts2(c2,X1)
| halts2(X1,X1)
| ~ program(X1) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( spl0_12
| spl0_11 ),
inference(avatar_split_clause,[],[f31,f101,f105]) ).
fof(f109,definition,
( spl0_13
<=> outputs(c2,good) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f111,plain,
( outputs(c2,good)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_14
<=> ! [X1] :
( ~ program(X1)
| ~ halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f114,plain,
( ! [X1] :
( ~ halts2(X1,X1)
| ~ program(X1) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( spl0_13
| spl0_14
| spl0_11 ),
inference(avatar_split_clause,[],[f30,f101,f113,f109]) ).
fof(f117,definition,
( spl0_15
<=> ! [X1] :
( ~ program(X1)
| halts2(c2,X1)
| ~ halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f118,plain,
( ! [X1] :
( ~ program(X1)
| halts2(c2,X1)
| ~ halts2(X1,X1) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( spl0_15
| spl0_11 ),
inference(avatar_split_clause,[],[f29,f101,f117]) ).
fof(f121,definition,
( spl0_16
<=> program(c2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f123,plain,
( program(c2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_16
| spl0_11 ),
inference(avatar_split_clause,[],[f28,f101,f121]) ).
fof(f126,definition,
( spl0_17
<=> ! [X0] :
( ~ program(X0)
| ~ halts2(f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ halts3(X0,f5(X0),f5(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f127,plain,
( ! [X0] :
( ~ halts3(X0,f5(X0),f5(X0))
| ~ halts2(f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ program(X0) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f128,plain,
( spl0_10
| spl0_2
| spl0_17 ),
inference(avatar_split_clause,[],[f27,f126,f56,f97]) ).
fof(f129,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f126,f105]) ).
fof(f130,plain,
( spl0_13
| spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f25,f126,f113,f109]) ).
fof(f131,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f126,f117]) ).
fof(f132,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f23,f126,f121]) ).
fof(f134,definition,
( spl0_18
<=> ! [X0] :
( ~ program(X0)
| ~ outputs(X0,bad)
| ~ halts3(X0,f5(X0),f5(X0))
| halts2(f5(X0),f5(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f135,plain,
( ! [X0] :
( ~ halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,bad)
| ~ program(X0)
| halts2(f5(X0),f5(X0)) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f136,plain,
( spl0_10
| spl0_2
| spl0_18 ),
inference(avatar_split_clause,[],[f22,f134,f56,f97]) ).
fof(f137,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f21,f134,f105]) ).
fof(f138,plain,
( spl0_13
| spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f20,f134,f113,f109]) ).
fof(f139,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f19,f134,f117]) ).
fof(f140,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f18,f134,f121]) ).
fof(f142,definition,
( spl0_19
<=> ! [X0] :
( ~ program(X0)
| program(f5(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f143,plain,
( ! [X0] :
( program(f5(X0))
| ~ program(X0) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f144,plain,
( spl0_10
| spl0_2
| spl0_19 ),
inference(avatar_split_clause,[],[f17,f142,f56,f97]) ).
fof(f145,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f16,f142,f105]) ).
fof(f146,plain,
( spl0_13
| spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f15,f142,f113,f109]) ).
fof(f147,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f14,f142,f117]) ).
fof(f148,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f13,f142,f121]) ).
fof(f150,definition,
( spl0_20
<=> ! [X2,X1] :
( ~ program(X1)
| halts2(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f151,plain,
( ! [X2,X1] :
( halts2(X1,X2)
| ~ program(X1) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,definition,
( spl0_21
<=> ! [X0] :
( ~ program(X0)
| outputs(X0,bad)
| ~ decides(X0,f4(X0),f3(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f154,plain,
( ! [X0] :
( ~ decides(X0,f4(X0),f3(X0))
| outputs(X0,bad)
| ~ program(X0) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( spl0_20
| spl0_21 ),
inference(avatar_split_clause,[],[f12,f153,f150]) ).
fof(f157,definition,
( spl0_22
<=> ! [X2,X1] :
( ~ program(X1)
| ~ halts2(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f158,plain,
( ! [X2,X1] :
( ~ halts2(X1,X2)
| ~ program(X1) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,definition,
( spl0_23
<=> ! [X0] :
( ~ program(X0)
| outputs(X0,good)
| ~ decides(X0,f4(X0),f3(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f161,plain,
( ! [X0] :
( ~ decides(X0,f4(X0),f3(X0))
| outputs(X0,good)
| ~ program(X0) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f162,plain,
( spl0_22
| spl0_23 ),
inference(avatar_split_clause,[],[f10,f160,f157]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ decides(X0,f4(X0),f3(X0))
| ~ program(X0)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f9,f11]) ).
fof(f165,definition,
( spl0_24
<=> ! [X0] :
( ~ program(X0)
| outputs(X0,bad)
| program(f4(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f166,plain,
( ! [X0] :
( outputs(X0,bad)
| ~ program(X0)
| program(f4(X0)) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f167,plain,
( spl0_20
| spl0_24 ),
inference(avatar_split_clause,[],[f8,f165,f150]) ).
fof(f169,definition,
( spl0_25
<=> ! [X0] :
( ~ program(X0)
| outputs(X0,good)
| program(f4(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f170,plain,
( ! [X0] :
( outputs(X0,good)
| ~ program(X0)
| program(f4(X0)) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f171,plain,
( spl0_22
| spl0_25 ),
inference(avatar_split_clause,[],[f6,f169,f157]) ).
fof(f172,plain,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| program(f4(X0))
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[],[f5,f7]) ).
fof(f174,definition,
( spl0_26
<=> ! [X2,X1] :
( ~ program(X1)
| decides(c1,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f175,plain,
( ! [X2,X1] :
( decides(c1,X1,X2)
| ~ program(X1) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,definition,
( spl0_27
<=> ! [X0] :
( ~ algorithm(X0)
| ~ decides(X0,f2(X0),f1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f178,plain,
( ! [X0] :
( ~ decides(X0,f2(X0),f1(X0))
| ~ algorithm(X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f179,plain,
( spl0_26
| spl0_27 ),
inference(avatar_split_clause,[],[f4,f177,f174]) ).
fof(f181,definition,
( spl0_28
<=> program(c1) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f183,plain,
( program(c1)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl0_28
| spl0_27 ),
inference(avatar_split_clause,[],[f3,f177,f181]) ).
fof(f186,definition,
( spl0_29
<=> ! [X0] :
( ~ algorithm(X0)
| program(f2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f187,plain,
( ! [X0] :
( program(f2(X0))
| ~ algorithm(X0) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f188,plain,
( spl0_26
| spl0_29 ),
inference(avatar_split_clause,[],[f2,f186,f174]) ).
fof(f189,plain,
( spl0_28
| spl0_29 ),
inference(avatar_split_clause,[],[f1,f186,f181]) ).
fof(f190,plain,
( ! [X1] :
( ~ halts2(c3,X1)
| ~ program(X1) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f68,f57]) ).
fof(f192,plain,
( ! [X1] : ~ program(X1)
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f158,f151]) ).
fof(f195,plain,
( $false
| ~ spl0_20
| ~ spl0_22
| ~ spl0_28 ),
inference(resolution,[],[f192,f183]) ).
fof(f196,plain,
( ~ spl0_20
| ~ spl0_22
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f195]) ).
fof(f199,plain,
( ! [X0] :
( ~ program(X0)
| ~ program(X0) )
| ~ spl0_2
| ~ spl0_22 ),
inference(resolution,[],[f158,f57]) ).
fof(f200,plain,
( ! [X0] : ~ program(X0)
| ~ spl0_2
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f199]) ).
fof(f201,plain,
( ~ program(c3)
| ~ program(c3)
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f190,f57]) ).
fof(f202,plain,
( ~ program(c3)
| ~ spl0_2
| ~ spl0_5 ),
inference(duplicate_literal_removal,[],[f201]) ).
fof(f205,plain,
( $false
| ~ spl0_2
| ~ spl0_22
| ~ spl0_28 ),
inference(resolution,[],[f200,f183]) ).
fof(f206,plain,
( ~ spl0_2
| ~ spl0_22
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f205]) ).
fof(f209,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f202,f73]) ).
fof(f210,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f209]) ).
fof(f211,plain,
( ! [X1] :
( halts2(c2,X1)
| ~ program(X1) )
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f118,f106]) ).
fof(f212,plain,
( halts2(c3,c3)
| ~ program(c3)
| ~ spl0_4 ),
inference(factoring,[],[f64]) ).
fof(f213,plain,
( halts2(c3,c3)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f212,f73]) ).
fof(f215,plain,
( ~ program(c3)
| ~ halts2(c3,c3)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(resolution,[],[f68,f213]) ).
fof(f217,plain,
( ~ halts2(c3,c3)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f215,f73]) ).
fof(f218,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f217,f213]) ).
fof(f219,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f224,plain,
( outputs(c1,bad)
| ~ program(c1)
| ~ program(f4(c1))
| ~ spl0_21
| ~ spl0_26 ),
inference(resolution,[],[f154,f175]) ).
fof(f225,plain,
( outputs(c1,bad)
| ~ program(c1)
| ~ spl0_21
| ~ spl0_24
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f224,f166]) ).
fof(f227,plain,
( outputs(c1,bad)
| ~ spl0_21
| ~ spl0_24
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f225,f183]) ).
fof(f238,plain,
( outputs(c1,good)
| ~ program(c1)
| ~ program(f4(c1))
| ~ spl0_23
| ~ spl0_26 ),
inference(resolution,[],[f161,f175]) ).
fof(f239,plain,
( outputs(c1,good)
| ~ program(c1)
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f238,f170]) ).
fof(f241,plain,
( outputs(c1,good)
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f239,f183]) ).
fof(f242,plain,
( ~ outputs(c2,bad)
| ~ outputs(c2,good)
| ~ program(c2)
| ~ program(f6(c2))
| ~ spl0_3
| ~ spl0_12
| ~ spl0_15 ),
inference(resolution,[],[f60,f211]) ).
fof(f243,plain,
( ~ outputs(c2,bad)
| ~ outputs(c2,good)
| ~ program(c2)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f242,f91]) ).
fof(f244,plain,
( ~ outputs(c2,good)
| ~ program(c2)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f243,f99]) ).
fof(f259,plain,
( ! [X0] :
( ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(X0,f6(X0))
| ~ program(f6(X0)) )
| ~ spl0_2
| ~ spl0_7 ),
inference(resolution,[],[f77,f57]) ).
fof(f263,plain,
( ! [X0] :
( ~ halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ program(X0) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f259,f91]) ).
fof(f265,plain,
( ~ outputs(c2,good)
| ~ program(c2)
| ~ program(f6(c2))
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_15 ),
inference(resolution,[],[f263,f211]) ).
fof(f266,plain,
( ~ outputs(c2,good)
| ~ program(c2)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f265,f91]) ).
fof(f267,plain,
( ~ program(c2)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f266,f111]) ).
fof(f268,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f267,f123]) ).
fof(f269,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f268]) ).
fof(f280,plain,
( ! [X0,X1] :
( ~ program(c1)
| ~ program(X0)
| halts3(c1,X0,X1)
| ~ program(f4(c1)) )
| ~ spl0_26 ),
inference(resolution,[],[f163,f175]) ).
fof(f281,plain,
( ! [X0,X1] :
( ~ program(c1)
| ~ program(X0)
| halts3(c1,X0,X1) )
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f280,f172]) ).
fof(f283,plain,
( ! [X0,X1] :
( halts3(c1,X0,X1)
| ~ program(X0) )
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f281,f183]) ).
fof(f288,plain,
( ~ program(f5(c1))
| ~ halts2(f5(c1),f5(c1))
| ~ outputs(c1,good)
| ~ program(c1)
| ~ spl0_17
| ~ spl0_26
| ~ spl0_28 ),
inference(resolution,[],[f283,f127]) ).
fof(f289,plain,
( ~ program(f5(c1))
| ~ outputs(c1,bad)
| ~ outputs(c1,good)
| ~ program(c1)
| ~ spl0_11
| ~ spl0_26
| ~ spl0_28 ),
inference(resolution,[],[f283,f102]) ).
fof(f290,plain,
( ~ outputs(c1,bad)
| ~ outputs(c1,good)
| ~ program(c1)
| ~ spl0_11
| ~ spl0_19
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f289,f143]) ).
fof(f291,plain,
( ~ halts2(f5(c1),f5(c1))
| ~ outputs(c1,good)
| ~ program(c1)
| ~ spl0_17
| ~ spl0_19
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f288,f143]) ).
fof(f292,plain,
( ~ outputs(c1,good)
| ~ program(c1)
| ~ spl0_11
| ~ spl0_19
| ~ spl0_21
| ~ spl0_24
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f290,f227]) ).
fof(f293,plain,
( ~ halts2(f5(c1),f5(c1))
| ~ program(c1)
| ~ spl0_17
| ~ spl0_19
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f291,f241]) ).
fof(f294,plain,
( ~ program(c1)
| ~ spl0_11
| ~ spl0_19
| ~ spl0_21
| ~ spl0_23
| ~ spl0_24
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f292,f241]) ).
fof(f295,plain,
( ~ halts2(f5(c1),f5(c1))
| ~ spl0_17
| ~ spl0_19
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f293,f183]) ).
fof(f296,plain,
( $false
| ~ spl0_11
| ~ spl0_19
| ~ spl0_21
| ~ spl0_23
| ~ spl0_24
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f294,f183]) ).
fof(f297,plain,
( ~ spl0_11
| ~ spl0_19
| ~ spl0_21
| ~ spl0_23
| ~ spl0_24
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f296]) ).
fof(f298,plain,
( ~ algorithm(c4)
| ~ program(f2(c4))
| ~ spl0_27 ),
inference(resolution,[],[f178,f50]) ).
fof(f299,plain,
( ~ program(f2(c4))
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f298,f49]) ).
fof(f304,plain,
( ~ algorithm(c4)
| ~ spl0_27
| ~ spl0_29 ),
inference(resolution,[],[f299,f187]) ).
fof(f305,plain,
( $false
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f304,f49]) ).
fof(f306,plain,
( ~ spl0_27
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f346,plain,
( ~ program(f5(c1))
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(resolution,[],[f295,f151]) ).
fof(f351,plain,
( ~ program(c1)
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(resolution,[],[f346,f143]) ).
fof(f352,plain,
( $false
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f351,f183]) ).
fof(f353,plain,
( ~ spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f397,plain,
( ~ spl0_16
| ~ spl0_13
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f244,f117,f105,f97,f90,f59,f109,f121]) ).
fof(f410,plain,
( ~ outputs(c1,bad)
| ~ program(c1)
| halts2(f5(c1),f5(c1))
| ~ program(f5(c1))
| ~ spl0_18
| ~ spl0_26
| ~ spl0_28 ),
inference(resolution,[],[f135,f283]) ).
fof(f413,plain,
( ~ outputs(c1,bad)
| ~ program(c1)
| ~ program(f5(c1))
| ~ spl0_18
| ~ spl0_22
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f410,f158]) ).
fof(f414,plain,
( ~ outputs(c1,bad)
| ~ program(c1)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_22
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f413,f143]) ).
fof(f415,plain,
( ~ program(c1)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| ~ spl0_22
| ~ spl0_24
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f414,f227]) ).
fof(f416,plain,
( $false
| ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| ~ spl0_22
| ~ spl0_24
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f415,f183]) ).
fof(f417,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| ~ spl0_22
| ~ spl0_24
| ~ spl0_26
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f416]) ).
fof(f433,plain,
( ~ program(c2)
| ~ program(c2)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(resolution,[],[f114,f211]) ).
fof(f437,plain,
( ~ program(c2)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(duplicate_literal_removal,[],[f433]) ).
fof(f439,plain,
( $false
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f437,f123]) ).
fof(f440,plain,
( ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f439]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f69]) ).
cnf(s4,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f74]) ).
cnf(s7,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f80]) ).
cnf(s8,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f81]) ).
cnf(s14,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f93]) ).
cnf(s15,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f94]) ).
cnf(s16,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f95]) ).
cnf(s17,plain,
( spl0_2
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f103]) ).
cnf(s18,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f107]) ).
cnf(s19,plain,
( spl0_11
| spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f115]) ).
cnf(s20,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f119]) ).
cnf(s21,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f124]) ).
cnf(s22,plain,
( spl0_2
| spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f128]) ).
cnf(s23,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f129]) ).
cnf(s24,plain,
( spl0_13
| spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f130]) ).
cnf(s25,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f131]) ).
cnf(s26,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f132]) ).
cnf(s27,plain,
( spl0_2
| spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f136]) ).
cnf(s28,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f137]) ).
cnf(s29,plain,
( spl0_13
| spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f138]) ).
cnf(s30,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f139]) ).
cnf(s31,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f140]) ).
cnf(s32,plain,
( spl0_2
| spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f144]) ).
cnf(s33,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f145]) ).
cnf(s34,plain,
( spl0_13
| spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f146]) ).
cnf(s35,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f147]) ).
cnf(s36,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f148]) ).
cnf(s37,plain,
( spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f155]) ).
cnf(s38,plain,
( spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f162]) ).
cnf(s39,plain,
( spl0_20
| spl0_24 ),
inference(sat_conversion,[],[f167]) ).
cnf(s40,plain,
( spl0_22
| spl0_25 ),
inference(sat_conversion,[],[f171]) ).
cnf(s41,plain,
( spl0_26
| spl0_27 ),
inference(sat_conversion,[],[f179]) ).
cnf(s42,plain,
( spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f184]) ).
cnf(s43,plain,
( spl0_26
| spl0_29 ),
inference(sat_conversion,[],[f188]) ).
cnf(s44,plain,
( spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f189]) ).
cnf(s45,plain,
( ~ spl0_20
| ~ spl0_22
| ~ spl0_28 ),
inference(sat_conversion,[],[f196]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_22
| ~ spl0_28 ),
inference(sat_conversion,[],[f206]) ).
cnf(s51,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f210]) ).
cnf(s52,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f219]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f269]) ).
cnf(s56,plain,
( ~ spl0_11
| ~ spl0_19
| ~ spl0_21
| ~ spl0_23
| ~ spl0_24
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(sat_conversion,[],[f297]) ).
cnf(s57,plain,
( ~ spl0_27
| ~ spl0_29 ),
inference(sat_conversion,[],[f306]) ).
cnf(s59,plain,
( ~ spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| ~ spl0_28 ),
inference(sat_conversion,[],[f353]) ).
cnf(s61,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f397]) ).
cnf(s64,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_21
| ~ spl0_22
| ~ spl0_24
| ~ spl0_26
| ~ spl0_28 ),
inference(sat_conversion,[],[f417]) ).
cnf(s65,plain,
( ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f440]) ).
cnf(s66,plain,
spl0_26,
inference(rat,[],[s57,s41,s43]) ).
cnf(s67,plain,
spl0_28,
inference(rat,[],[s57,s42,s44]) ).
cnf(s68,plain,
( spl0_20
| ~ spl0_11
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s56,s38,s40,s64,s37,s39,s66,s67]) ).
cnf(s69,plain,
( spl0_10
| spl0_2 ),
inference(rat,[],[s59,s38,s40,s45,s68,s17,s22,s27,s32,s67,s66]) ).
cnf(s70,plain,
( spl0_17
| ~ spl0_10
| ~ spl0_3
| ~ spl0_9 ),
inference(rat,[],[s24,s61,s65,s23,s25,s26]) ).
cnf(s71,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_11
| ~ spl0_17 ),
inference(rat,[],[s59,s38,s40,s45,s68,s66,s67]) ).
cnf(s72,plain,
( spl0_19
| ~ spl0_10
| ~ spl0_3
| ~ spl0_9 ),
inference(rat,[],[s34,s61,s65,s33,s35,s36]) ).
cnf(s73,plain,
( spl0_18
| ~ spl0_10
| ~ spl0_3
| ~ spl0_9 ),
inference(rat,[],[s29,s61,s65,s28,s30,s31]) ).
cnf(s74,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s19,s61,s65,s18,s20,s21,s71,s73,s72,s70]) ).
cnf(s76,plain,
( spl0_7
| ~ spl0_2 ),
inference(rat,[],[s51,s7,s8]) ).
cnf(s77,plain,
( spl0_19
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s34,s55,s65,s33,s35,s36,s76]) ).
cnf(s78,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s19,s55,s65,s18,s20,s21,s76]) ).
cnf(s79,plain,
( spl0_20
| ~ spl0_11
| ~ spl0_19
| spl0_22 ),
inference(rat,[],[s56,s37,s39,s40,s38,s66,s67]) ).
cnf(s80,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s24,s55,s65,s23,s25,s26,s59,s79,s78,s77,s40,s38,s48,s76,s66,s67]) ).
cnf(s81,plain,
~ spl0_2,
inference(rat,[],[s51,s15,s16,s80]) ).
cnf(s83,plain,
spl0_10,
inference(rat,[],[s69,s81]) ).
cnf(s84,plain,
spl0_3,
inference(rat,[],[s52,s2,s3,s4]) ).
cnf(s85,plain,
~ spl0_9,
inference(rat,[],[s74,s83,s84]) ).
cnf(s86,plain,
spl0_6,
inference(rat,[],[s16,s85]) ).
cnf(s87,plain,
spl0_5,
inference(rat,[],[s15,s85]) ).
cnf(s88,plain,
spl0_4,
inference(rat,[],[s14,s85]) ).
cnf(s89,plain,
$false,
inference(rat,[],[s52,s88,s86,s87]) ).
fof(f441,plain,
$false,
inference(avatar_sat_refutation,[],[s89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM003-1 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:42:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.15/1.06 % (3520932)Input is clausal, will run a generic CNF schedule.
% 3.15/1.06 % (3520939)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4123456398:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.15/1.06 % (3520937)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=596609742:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.15/1.06 % (3520941)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=424457981:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.15/1.06 % (3520940)lrs+10_1_sil=8000:sp=occurrence:random_seed=2778162967:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.15/1.06 % (3520943)dis-21_1_sil=8000:lcm=predicate:random_seed=3918477634:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.15/1.06 % (3520938)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=792724359:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.15/1.06 % (3520942)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4181304901:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.15/1.06 % (3520940)First to succeed.
% 3.15/1.06 % (3520941)Also succeeded, but the first one will report.
% 3.15/1.06 % (3520943)Also succeeded, but the first one will report.
% 3.15/1.06 % (3520940)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3520932"
% 3.15/1.06 % (3520942)Also succeeded, but the first one will report.
% 3.15/1.06 % (3520940)Refutation found. Thanks to Tanya!
% 3.15/1.06 % SZS status Unsatisfiable for theBenchmark
% 3.15/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.24 % (3520940)------------------------------
% 3.51/1.24 % (3520940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.24 % (3520940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.24 % (3520940)CaDiCaL version: 2.1.3
% 3.51/1.24 % (3520940)Termination reason: Refutation
% 3.51/1.24 % (3520940)Time elapsed: 0.010 s
% 3.51/1.24 % (3520940)Peak memory usage: 89 MB
% 3.51/1.24 % (3520940)Instructions burned: 13 (million)
% 3.51/1.24 % (3520940)------------------------------
% 3.51/1.24 % (3520940)------------------------------
% 3.51/1.24 % (3520932)Success in time 0.413 s
% 3.51/1.24 % Vampire exiting
%------------------------------------------------------------------------------