%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n010.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 09:40:05 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 70
% Syntax : Number of formulae : 332 ( 21 unt; 33 def)
% Number of atoms : 1231 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1501 ( 602 ~; 866 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 40 ( 39 usr; 34 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 212 ( 0 sgn 212 !; 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] :
( ~ program(X0)
| program(f4(X0))
| ~ program(X1)
| halts2(X1,X2)
| halts3(X0,X1,X2) ),
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] :
( ~ 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_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(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(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(f43,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_11) ).
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] :
( ~ program(X0)
| decides(c4,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_the_algorithm_doesnt_exist) ).
fof(f51,plain,
! [X0] :
( algorithm(X0)
| ~ program(f2(X0))
| ~ program(c1) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f52,plain,
! [X2,X0,X1] :
( algorithm(X0)
| ~ program(f2(X0))
| program(X1)
| ~ decides(c1,X1,X2) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f53,plain,
! [X0] :
( algorithm(X0)
| decides(X0,f2(X0),f1(X0))
| ~ program(c1) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f54,plain,
! [X2,X0,X1] :
( algorithm(X0)
| decides(X0,f2(X0),f1(X0))
| program(X1)
| ~ decides(c1,X1,X2) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ halts3(X0,X1,X2)
| ~ program(f4(X0))
| program(X1)
| halts2(X1,X2)
| program(X0) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f56,plain,
! [X2,X0,X1] :
( program(X0)
| ~ program(f4(X0))
| program(X1)
| halts2(X1,X2)
| outputs(X0,good) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f57,plain,
! [X2,X0,X1] :
( program(X0)
| ~ program(f4(X0))
| program(X1)
| ~ halts2(X1,X2)
| ~ halts3(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f58,plain,
! [X2,X0,X1] :
( program(X0)
| ~ program(f4(X0))
| program(X1)
| ~ halts2(X1,X2)
| outputs(X0,bad) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ halts3(X0,X1,X2)
| decides(X0,f4(X0),f3(X0))
| program(X1)
| halts2(X1,X2)
| program(X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f60,plain,
! [X2,X0,X1] :
( program(X0)
| decides(X0,f4(X0),f3(X0))
| program(X1)
| halts2(X1,X2)
| outputs(X0,good) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f61,plain,
! [X2,X0,X1] :
( program(X0)
| decides(X0,f4(X0),f3(X0))
| program(X1)
| ~ halts2(X1,X2)
| ~ halts3(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f62,plain,
! [X2,X0,X1] :
( program(X0)
| decides(X0,f4(X0),f3(X0))
| program(X1)
| ~ halts2(X1,X2)
| outputs(X0,bad) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f63,plain,
! [X0] :
( program(X0)
| ~ program(f5(X0))
| ~ program(c2) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f64,plain,
! [X0,X1] :
( program(X0)
| ~ program(f5(X0))
| program(X1)
| halts2(X1,X1)
| ~ halts2(c2,X1) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f65,plain,
! [X0,X1] :
( program(X0)
| ~ program(f5(X0))
| program(X1)
| halts2(X1,X1)
| outputs(c2,good) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f66,plain,
! [X0,X1] :
( program(X0)
| ~ program(f5(X0))
| program(X1)
| ~ halts2(X1,X1)
| ~ halts2(c2,X1) ),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f67,plain,
! [X0,X1] :
( program(X0)
| ~ program(f5(X0))
| program(X1)
| ~ halts2(X1,X1)
| outputs(c2,bad) ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f68,plain,
! [X0] :
( program(X0)
| ~ halts2(f5(X0),f5(X0))
| halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,bad)
| ~ program(c2) ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f69,plain,
! [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) ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f71,plain,
! [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) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f72,plain,
! [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) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f78,plain,
! [X0] :
( program(X0)
| halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(c2) ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f79,plain,
! [X0,X1] :
( program(X0)
| halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(X1)
| halts2(X1,X1)
| ~ halts2(c2,X1) ),
inference(consistent_polarity_flipping,[],[f29]) ).
fof(f80,plain,
! [X0,X1] :
( program(X0)
| halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(X1)
| halts2(X1,X1)
| outputs(c2,good) ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f81,plain,
! [X0,X1] :
( program(X0)
| halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(X1)
| ~ halts2(X1,X1)
| ~ halts2(c2,X1) ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f82,plain,
! [X0,X1] :
( program(X0)
| halts3(X0,f5(X0),f5(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(X1)
| ~ halts2(X1,X1)
| outputs(c2,bad) ),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f83,plain,
! [X0] :
( program(X0)
| ~ program(f6(X0))
| ~ program(c3) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f84,plain,
! [X0,X1] :
( program(X0)
| ~ program(f6(X0))
| program(X1)
| halts2(X1,X1)
| halts2(c3,X1) ),
inference(consistent_polarity_flipping,[],[f34]) ).
fof(f85,plain,
! [X0,X1] :
( program(X0)
| ~ program(f6(X0))
| program(X1)
| ~ halts2(X1,X1)
| ~ halts2(c3,X1) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f91,plain,
! [X0] :
( program(X0)
| halts2(X0,f6(X0))
| ~ outputs(X0,good)
| halts2(f6(X0),f6(X0))
| ~ program(c3) ),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f92,plain,
! [X0,X1] :
( program(X0)
| halts2(X0,f6(X0))
| ~ outputs(X0,good)
| halts2(f6(X0),f6(X0))
| program(X1)
| halts2(X1,X1)
| halts2(c3,X1) ),
inference(consistent_polarity_flipping,[],[f42]) ).
fof(f93,plain,
! [X0,X1] :
( program(X0)
| halts2(X0,f6(X0))
| ~ outputs(X0,good)
| halts2(f6(X0),f6(X0))
| program(X1)
| ~ halts2(X1,X1)
| ~ halts2(c3,X1) ),
inference(consistent_polarity_flipping,[],[f43]) ).
fof(f95,plain,
! [X0] :
( program(X0)
| halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(c3) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f96,plain,
! [X0,X1] :
( program(X0)
| halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(X1)
| halts2(X1,X1)
| halts2(c3,X1) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f97,plain,
! [X0,X1] :
( program(X0)
| halts2(X0,f6(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(X1)
| ~ halts2(X1,X1)
| ~ halts2(c3,X1) ),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f99,plain,
~ algorithm(c4),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f100,plain,
! [X0,X1] :
( ~ decides(c4,X0,X1)
| program(X0) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f106,definition,
( spl0_2
<=> ! [X1] :
( program(X1)
| ~ halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f107,plain,
( ! [X1] :
( ~ halts2(X1,X1)
| program(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,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(f110,plain,
( ! [X0] :
( ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(X0)
| halts2(X0,f6(X0)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_4
<=> ! [X1] :
( program(X1)
| ~ halts2(c3,X1)
| ~ halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f114,plain,
( ! [X1] :
( ~ halts2(c3,X1)
| program(X1)
| ~ halts2(X1,X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f97,f109,f113]) ).
fof(f117,definition,
( spl0_5
<=> ! [X1] :
( program(X1)
| halts2(c3,X1)
| halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f118,plain,
( ! [X1] :
( halts2(c3,X1)
| halts2(X1,X1)
| program(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f96,f109,f117]) ).
fof(f121,definition,
( spl0_6
<=> program(c3) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f123,plain,
( ~ program(c3)
| spl0_6 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( ~ spl0_6
| spl0_3 ),
inference(avatar_split_clause,[],[f95,f109,f121]) ).
fof(f126,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(f127,plain,
( ! [X0] :
( halts2(f6(X0),f6(X0))
| program(X0)
| ~ outputs(X0,good)
| halts2(X0,f6(X0)) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f93,f126,f113]) ).
fof(f130,plain,
( spl0_5
| spl0_7 ),
inference(avatar_split_clause,[],[f92,f126,f117]) ).
fof(f131,plain,
( ~ spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f91,f126,f121]) ).
fof(f140,definition,
( spl0_9
<=> ! [X0] :
( program(X0)
| ~ program(f6(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f141,plain,
( ! [X0] :
( ~ program(f6(X0))
| program(X0) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f85,f140,f113]) ).
fof(f144,plain,
( spl0_5
| spl0_9 ),
inference(avatar_split_clause,[],[f84,f140,f117]) ).
fof(f145,plain,
( ~ spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f83,f140,f121]) ).
fof(f147,definition,
( spl0_10
<=> outputs(c2,bad) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f151,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(f152,plain,
( ! [X0] :
( ~ outputs(X0,good)
| ~ outputs(X0,bad)
| program(X0)
| halts3(X0,f5(X0),f5(X0)) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( spl0_10
| spl0_2
| spl0_11 ),
inference(avatar_split_clause,[],[f82,f151,f106,f147]) ).
fof(f155,definition,
( spl0_12
<=> ! [X1] :
( program(X1)
| ~ halts2(c2,X1)
| ~ halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f156,plain,
( ! [X1] :
( ~ halts2(c2,X1)
| program(X1)
| ~ halts2(X1,X1) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( spl0_12
| spl0_11 ),
inference(avatar_split_clause,[],[f81,f151,f155]) ).
fof(f159,definition,
( spl0_13
<=> outputs(c2,good) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f161,plain,
( outputs(c2,good)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f163,definition,
( spl0_14
<=> ! [X1] :
( program(X1)
| halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f164,plain,
( ! [X1] :
( halts2(X1,X1)
| program(X1) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f165,plain,
( spl0_13
| spl0_14
| spl0_11 ),
inference(avatar_split_clause,[],[f80,f151,f163,f159]) ).
fof(f167,definition,
( spl0_15
<=> ! [X1] :
( program(X1)
| ~ halts2(c2,X1)
| halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f168,plain,
( ! [X1] :
( program(X1)
| ~ halts2(c2,X1)
| halts2(X1,X1) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f169,plain,
( spl0_15
| spl0_11 ),
inference(avatar_split_clause,[],[f79,f151,f167]) ).
fof(f171,definition,
( spl0_16
<=> program(c2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f173,plain,
( ~ program(c2)
| spl0_16 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( ~ spl0_16
| spl0_11 ),
inference(avatar_split_clause,[],[f78,f151,f171]) ).
fof(f184,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(f185,plain,
( ! [X0] :
( ~ halts2(f5(X0),f5(X0))
| ~ outputs(X0,bad)
| halts3(X0,f5(X0),f5(X0))
| program(X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f186,plain,
( spl0_10
| spl0_2
| spl0_18 ),
inference(avatar_split_clause,[],[f72,f184,f106,f147]) ).
fof(f187,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f71,f184,f155]) ).
fof(f189,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f69,f184,f167]) ).
fof(f190,plain,
( ~ spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f68,f184,f171]) ).
fof(f192,definition,
( spl0_19
<=> ! [X0] :
( program(X0)
| ~ program(f5(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f193,plain,
( ! [X0] :
( ~ program(f5(X0))
| program(X0) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f194,plain,
( spl0_10
| spl0_2
| spl0_19 ),
inference(avatar_split_clause,[],[f67,f192,f106,f147]) ).
fof(f195,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f66,f192,f155]) ).
fof(f196,plain,
( spl0_13
| spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f65,f192,f163,f159]) ).
fof(f197,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f64,f192,f167]) ).
fof(f198,plain,
( ~ spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f63,f192,f171]) ).
fof(f200,definition,
( spl0_20
<=> ! [X2,X1] :
( program(X1)
| ~ halts2(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f201,plain,
( ! [X2,X1] :
( ~ halts2(X1,X2)
| program(X1) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,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(f204,plain,
( ! [X0] :
( decides(X0,f4(X0),f3(X0))
| outputs(X0,bad)
| program(X0) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f205,plain,
( spl0_20
| spl0_21 ),
inference(avatar_split_clause,[],[f62,f203,f200]) ).
fof(f207,definition,
( spl0_22
<=> ! [X2,X1] :
( program(X1)
| halts2(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f208,plain,
( ! [X2,X1] :
( halts2(X1,X2)
| program(X1) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f210,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(f211,plain,
( ! [X0] :
( decides(X0,f4(X0),f3(X0))
| outputs(X0,good)
| program(X0) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f212,plain,
( spl0_22
| spl0_23 ),
inference(avatar_split_clause,[],[f60,f210,f207]) ).
fof(f214,definition,
( spl0_24
<=> ! [X0] :
( program(X0)
| outputs(X0,bad)
| ~ program(f4(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f215,plain,
( ! [X0] :
( ~ program(f4(X0))
| outputs(X0,bad)
| program(X0) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( spl0_20
| spl0_24 ),
inference(avatar_split_clause,[],[f58,f214,f200]) ).
fof(f218,definition,
( spl0_25
<=> ! [X0] :
( program(X0)
| outputs(X0,good)
| ~ program(f4(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f219,plain,
( ! [X0] :
( ~ program(f4(X0))
| outputs(X0,good)
| program(X0) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f220,plain,
( spl0_22
| spl0_25 ),
inference(avatar_split_clause,[],[f56,f218,f207]) ).
fof(f222,definition,
( spl0_26
<=> ! [X2,X1] :
( program(X1)
| ~ decides(c1,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f223,plain,
( ! [X2,X1] :
( ~ decides(c1,X1,X2)
| program(X1) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,definition,
( spl0_27
<=> ! [X0] :
( algorithm(X0)
| decides(X0,f2(X0),f1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f226,plain,
( ! [X0] :
( decides(X0,f2(X0),f1(X0))
| algorithm(X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f227,plain,
( spl0_26
| spl0_27 ),
inference(avatar_split_clause,[],[f54,f225,f222]) ).
fof(f229,definition,
( spl0_28
<=> program(c1) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f231,plain,
( ~ program(c1)
| spl0_28 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f232,plain,
( ~ spl0_28
| spl0_27 ),
inference(avatar_split_clause,[],[f53,f225,f229]) ).
fof(f234,definition,
( spl0_29
<=> ! [X0] :
( algorithm(X0)
| ~ program(f2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f235,plain,
( ! [X0] :
( ~ program(f2(X0))
| algorithm(X0) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f236,plain,
( spl0_26
| spl0_29 ),
inference(avatar_split_clause,[],[f52,f234,f222]) ).
fof(f237,plain,
( ~ spl0_28
| spl0_29 ),
inference(avatar_split_clause,[],[f51,f234,f229]) ).
fof(f238,plain,
( ! [X1] : program(X1)
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f208,f201]) ).
fof(f241,plain,
( $false
| ~ spl0_20
| ~ spl0_22
| spl0_28 ),
inference(backward_subsumption_resolution,[],[f231,f238]) ).
fof(f244,plain,
( ~ spl0_20
| ~ spl0_22
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f241]) ).
fof(f245,plain,
( ! [X0] :
( program(X0)
| program(X0) )
| ~ spl0_2
| ~ spl0_22 ),
inference(resolution,[],[f208,f107]) ).
fof(f246,plain,
( ! [X0] : program(X0)
| ~ spl0_2
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f245]) ).
fof(f248,plain,
( outputs(c1,bad)
| program(c1)
| program(f4(c1))
| ~ spl0_21
| ~ spl0_26 ),
inference(resolution,[],[f204,f223]) ).
fof(f249,plain,
( outputs(c1,bad)
| program(c1)
| ~ spl0_21
| ~ spl0_24
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f248,f215]) ).
fof(f251,plain,
( outputs(c1,bad)
| ~ spl0_21
| ~ spl0_24
| ~ spl0_26
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f249,f231]) ).
fof(f282,plain,
( ! [X0] :
( halts2(f6(X0),f6(X0))
| program(X0)
| ~ outputs(X0,good) )
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f127,f201]) ).
fof(f290,plain,
( ! [X0] :
( program(X0)
| ~ outputs(X0,good)
| program(f6(X0)) )
| ~ spl0_7
| ~ spl0_20 ),
inference(resolution,[],[f282,f201]) ).
fof(f291,plain,
( ! [X0] :
( ~ outputs(X0,good)
| program(X0) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f290,f141]) ).
fof(f297,plain,
( ! [X0] :
( decides(X0,f4(X0),f3(X0))
| program(X0) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f211,f291]) ).
fof(f299,plain,
( program(c1)
| program(f4(c1))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_23
| ~ spl0_26 ),
inference(resolution,[],[f297,f223]) ).
fof(f300,plain,
( program(f4(c1))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_23
| ~ spl0_26
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f299,f231]) ).
fof(f318,plain,
( outputs(c1,good)
| program(c1)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28 ),
inference(resolution,[],[f300,f219]) ).
fof(f319,plain,
( program(c1)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f318,f291]) ).
fof(f321,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f319,f231]) ).
fof(f322,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f324,definition,
( spl0_34
<=> program(f4(c1)) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f325,plain,
( ~ program(f4(c1))
| spl0_34 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f328,plain,
( algorithm(c4)
| program(f2(c4))
| ~ spl0_27 ),
inference(resolution,[],[f226,f100]) ).
fof(f331,plain,
( program(f2(c4))
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f328,f99]) ).
fof(f332,plain,
( algorithm(c4)
| ~ spl0_27
| ~ spl0_29 ),
inference(resolution,[],[f331,f235]) ).
fof(f333,plain,
( $false
| ~ spl0_27
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f332,f99]) ).
fof(f334,plain,
( ~ spl0_27
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f336,definition,
( spl0_35
<=> outputs(c1,bad) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f338,plain,
( outputs(c1,bad)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f341,plain,
( spl0_35
| ~ spl0_21
| ~ spl0_24
| ~ spl0_26
| spl0_28 ),
inference(avatar_split_clause,[],[f251,f229,f222,f214,f203,f336]) ).
fof(f353,plain,
( halts2(c3,c3)
| program(c3)
| ~ spl0_5 ),
inference(factoring,[],[f118]) ).
fof(f355,plain,
( halts2(c3,c3)
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f353,f123]) ).
fof(f357,plain,
( ! [X1] :
( ~ halts2(c2,X1)
| program(X1) )
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f168,f156]) ).
fof(f364,plain,
( outputs(c1,good)
| program(c1)
| program(f4(c1))
| ~ spl0_23
| ~ spl0_26 ),
inference(resolution,[],[f211,f223]) ).
fof(f365,plain,
( outputs(c1,good)
| program(c1)
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f364,f219]) ).
fof(f367,plain,
( outputs(c1,good)
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f365,f231]) ).
fof(f368,plain,
! [X2,X0,X1] :
( ~ halts3(X0,X1,X2)
| ~ program(f4(X0))
| program(X1)
| program(X0) ),
inference(forward_subsumption_resolution,[],[f57,f55]) ).
fof(f372,plain,
( program(c3)
| ~ halts2(c3,c3)
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(resolution,[],[f355,f114]) ).
fof(f373,plain,
( ~ halts2(c3,c3)
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f372,f123]) ).
fof(f374,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f373,f355]) ).
fof(f375,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f374]) ).
fof(f376,plain,
( ~ outputs(c1,bad)
| program(c1)
| halts3(c1,f5(c1),f5(c1))
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28 ),
inference(resolution,[],[f367,f152]) ).
fof(f379,plain,
( program(c1)
| halts3(c1,f5(c1),f5(c1))
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f376,f338]) ).
fof(f381,plain,
( halts3(c1,f5(c1),f5(c1))
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f379,f231]) ).
fof(f385,definition,
( spl0_38
<=> halts3(c1,f5(c1),f5(c1)) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f387,plain,
( halts3(c1,f5(c1),f5(c1))
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f389,definition,
( spl0_39
<=> halts2(f5(c1),f5(c1)) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f390,plain,
( ~ halts2(f5(c1),f5(c1))
| spl0_39 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f391,plain,
( halts2(f5(c1),f5(c1))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f393,plain,
! [X2,X0,X1] :
( ~ halts3(X0,X1,X2)
| decides(X0,f4(X0),f3(X0))
| program(X1)
| program(X0) ),
inference(forward_subsumption_resolution,[],[f61,f59]) ).
fof(f425,plain,
( ~ outputs(c1,bad)
| halts3(c1,f5(c1),f5(c1))
| program(c1)
| ~ spl0_18
| ~ spl0_39 ),
inference(resolution,[],[f391,f185]) ).
fof(f426,plain,
( halts3(c1,f5(c1),f5(c1))
| program(c1)
| ~ spl0_18
| ~ spl0_35
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[],[f425,f338]) ).
fof(f427,plain,
( halts3(c1,f5(c1),f5(c1))
| ~ spl0_18
| spl0_28
| ~ spl0_35
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[],[f426,f231]) ).
fof(f428,plain,
( spl0_38
| ~ spl0_18
| spl0_28
| ~ spl0_35
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f427,f389,f336,f229,f184,f385]) ).
fof(f429,plain,
( spl0_38
| ~ spl0_11
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f381,f336,f229,f222,f218,f210,f151,f385]) ).
fof(f430,plain,
( decides(c1,f4(c1),f3(c1))
| program(f5(c1))
| program(c1)
| ~ spl0_38 ),
inference(resolution,[],[f387,f393]) ).
fof(f432,plain,
( ~ program(f4(c1))
| program(f5(c1))
| program(c1)
| ~ spl0_38 ),
inference(resolution,[],[f387,f368]) ).
fof(f434,plain,
( ~ program(f4(c1))
| program(c1)
| ~ spl0_19
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f432,f193]) ).
fof(f435,plain,
( decides(c1,f4(c1),f3(c1))
| program(c1)
| ~ spl0_19
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f430,f193]) ).
fof(f436,plain,
( ~ program(f4(c1))
| ~ spl0_19
| spl0_28
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f434,f231]) ).
fof(f437,plain,
( decides(c1,f4(c1),f3(c1))
| ~ spl0_19
| spl0_28
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f435,f231]) ).
fof(f438,plain,
( ~ spl0_34
| ~ spl0_19
| spl0_28
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f436,f385,f229,f192,f324]) ).
fof(f439,plain,
( program(f4(c1))
| ~ spl0_19
| ~ spl0_26
| spl0_28
| ~ spl0_38 ),
inference(resolution,[],[f437,f223]) ).
fof(f440,plain,
( $false
| ~ spl0_19
| ~ spl0_26
| spl0_28
| spl0_34
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[],[f439,f325]) ).
fof(f441,plain,
( ~ spl0_19
| ~ spl0_26
| spl0_28
| spl0_34
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f444,definition,
( spl0_45
<=> program(f5(c1)) ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f445,plain,
( ~ program(f5(c1))
| spl0_45 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f446,plain,
( program(f5(c1))
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f459,definition,
( spl0_48
<=> halts2(c2,f6(c2)) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f460,plain,
( ~ halts2(c2,f6(c2))
| spl0_48 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f461,plain,
( halts2(c2,f6(c2))
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f483,plain,
( program(c2)
| program(c2)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(resolution,[],[f164,f357]) ).
fof(f487,plain,
( program(c2)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(duplicate_literal_removal,[],[f483]) ).
fof(f489,plain,
( $false
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f487,f173]) ).
fof(f490,plain,
( ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f498,plain,
( ~ outputs(c2,bad)
| program(c2)
| halts2(c2,f6(c2))
| ~ spl0_3
| ~ spl0_13 ),
inference(resolution,[],[f161,f110]) ).
fof(f503,plain,
( program(f6(c2))
| ~ spl0_12
| ~ spl0_15
| ~ spl0_48 ),
inference(resolution,[],[f461,f357]) ).
fof(f510,definition,
( spl0_52
<=> program(f6(c2)) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f512,plain,
( program(f6(c2))
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f514,plain,
( spl0_52
| ~ spl0_12
| ~ spl0_15
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f503,f459,f167,f155,f510]) ).
fof(f515,plain,
( program(c2)
| ~ spl0_9
| ~ spl0_52 ),
inference(resolution,[],[f512,f141]) ).
fof(f516,plain,
( $false
| ~ spl0_9
| spl0_16
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f515,f173]) ).
fof(f517,plain,
( ~ spl0_9
| spl0_16
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f516]) ).
fof(f519,plain,
( ~ outputs(c2,bad)
| halts2(c2,f6(c2))
| ~ spl0_3
| ~ spl0_13
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f498,f173]) ).
fof(f521,plain,
( spl0_48
| ~ spl0_10
| ~ spl0_3
| ~ spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f519,f171,f159,f109,f147,f459]) ).
fof(f523,plain,
( ! [X0] :
( program(f6(X0))
| program(X0)
| ~ outputs(X0,good)
| halts2(X0,f6(X0)) )
| ~ spl0_2
| ~ spl0_7 ),
inference(resolution,[],[f107,f127]) ).
fof(f524,plain,
( ! [X0] :
( ~ outputs(X0,good)
| program(X0)
| halts2(X0,f6(X0)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f523,f141]) ).
fof(f527,plain,
( program(c2)
| halts2(c2,f6(c2))
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(resolution,[],[f524,f161]) ).
fof(f528,plain,
( halts2(c2,f6(c2))
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f527,f173]) ).
fof(f529,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_16
| spl0_48 ),
inference(forward_subsumption_resolution,[],[f528,f460]) ).
fof(f530,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_16
| spl0_48 ),
inference(avatar_contradiction_clause,[],[f529]) ).
fof(f532,plain,
( $false
| ~ spl0_2
| ~ spl0_22
| spl0_28 ),
inference(backward_subsumption_resolution,[],[f231,f246]) ).
fof(f541,plain,
( ~ spl0_2
| ~ spl0_22
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f532]) ).
fof(f545,plain,
( program(c1)
| ~ spl0_19
| ~ spl0_45 ),
inference(resolution,[],[f193,f446]) ).
fof(f546,plain,
( $false
| ~ spl0_19
| spl0_28
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f545,f231]) ).
fof(f547,plain,
( ~ spl0_19
| spl0_28
| ~ spl0_45 ),
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f550,plain,
( program(c2)
| ~ spl0_22
| spl0_48 ),
inference(resolution,[],[f208,f460]) ).
fof(f552,plain,
( $false
| spl0_16
| ~ spl0_22
| spl0_48 ),
inference(forward_subsumption_resolution,[],[f550,f173]) ).
fof(f553,plain,
( spl0_16
| ~ spl0_22
| spl0_48 ),
inference(avatar_contradiction_clause,[],[f552]) ).
fof(f561,plain,
( program(f5(c1))
| ~ spl0_22
| spl0_39 ),
inference(resolution,[],[f390,f208]) ).
fof(f562,plain,
( $false
| ~ spl0_22
| spl0_39
| spl0_45 ),
inference(forward_subsumption_resolution,[],[f561,f445]) ).
fof(f563,plain,
( ~ spl0_22
| spl0_39
| spl0_45 ),
inference(avatar_contradiction_clause,[],[f562]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f115]) ).
cnf(s3,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f119]) ).
cnf(s4,plain,
( spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f124]) ).
cnf(s6,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f129]) ).
cnf(s7,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f130]) ).
cnf(s8,plain,
( ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f131]) ).
cnf(s14,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f143]) ).
cnf(s15,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f144]) ).
cnf(s16,plain,
( ~ spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f145]) ).
cnf(s17,plain,
( spl0_2
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f153]) ).
cnf(s18,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f157]) ).
cnf(s19,plain,
( spl0_11
| spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f165]) ).
cnf(s20,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f169]) ).
cnf(s21,plain,
( spl0_11
| ~ spl0_16 ),
inference(sat_conversion,[],[f174]) ).
cnf(s27,plain,
( spl0_2
| spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f186]) ).
cnf(s28,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f187]) ).
cnf(s30,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f189]) ).
cnf(s31,plain,
( ~ spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f190]) ).
cnf(s32,plain,
( spl0_2
| spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f194]) ).
cnf(s33,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f195]) ).
cnf(s34,plain,
( spl0_13
| spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f196]) ).
cnf(s35,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f197]) ).
cnf(s36,plain,
( ~ spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f198]) ).
cnf(s37,plain,
( spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f205]) ).
cnf(s38,plain,
( spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f212]) ).
cnf(s39,plain,
( spl0_20
| spl0_24 ),
inference(sat_conversion,[],[f216]) ).
cnf(s40,plain,
( spl0_22
| spl0_25 ),
inference(sat_conversion,[],[f220]) ).
cnf(s41,plain,
( spl0_26
| spl0_27 ),
inference(sat_conversion,[],[f227]) ).
cnf(s42,plain,
( spl0_27
| ~ spl0_28 ),
inference(sat_conversion,[],[f232]) ).
cnf(s43,plain,
( spl0_26
| spl0_29 ),
inference(sat_conversion,[],[f236]) ).
cnf(s44,plain,
( ~ spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f237]) ).
cnf(s47,plain,
( ~ spl0_20
| ~ spl0_22
| spl0_28 ),
inference(sat_conversion,[],[f244]) ).
cnf(s60,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28 ),
inference(sat_conversion,[],[f322]) ).
cnf(s62,plain,
( ~ spl0_27
| ~ spl0_29 ),
inference(sat_conversion,[],[f334]) ).
cnf(s65,plain,
( ~ spl0_21
| ~ spl0_24
| ~ spl0_26
| spl0_28
| spl0_35 ),
inference(sat_conversion,[],[f341]) ).
cnf(s68,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f375]) ).
cnf(s74,plain,
( ~ spl0_18
| spl0_28
| ~ spl0_35
| spl0_38
| ~ spl0_39 ),
inference(sat_conversion,[],[f428]) ).
cnf(s75,plain,
( ~ spl0_11
| ~ spl0_23
| ~ spl0_25
| ~ spl0_26
| spl0_28
| ~ spl0_35
| spl0_38 ),
inference(sat_conversion,[],[f429]) ).
cnf(s76,plain,
( ~ spl0_19
| spl0_28
| ~ spl0_34
| ~ spl0_38 ),
inference(sat_conversion,[],[f438]) ).
cnf(s77,plain,
( ~ spl0_19
| ~ spl0_26
| spl0_28
| spl0_34
| ~ spl0_38 ),
inference(sat_conversion,[],[f441]) ).
cnf(s83,plain,
( ~ spl0_12
| ~ spl0_14
| ~ spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f490]) ).
cnf(s92,plain,
( ~ spl0_12
| ~ spl0_15
| ~ spl0_48
| spl0_52 ),
inference(sat_conversion,[],[f514]) ).
cnf(s93,plain,
( ~ spl0_9
| spl0_16
| ~ spl0_52 ),
inference(sat_conversion,[],[f517]) ).
cnf(s95,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_13
| spl0_16
| spl0_48 ),
inference(sat_conversion,[],[f521]) ).
cnf(s96,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| spl0_16
| spl0_48 ),
inference(sat_conversion,[],[f530]) ).
cnf(s97,plain,
( ~ spl0_2
| ~ spl0_22
| spl0_28 ),
inference(sat_conversion,[],[f541]) ).
cnf(s101,plain,
( ~ spl0_19
| spl0_28
| ~ spl0_45 ),
inference(sat_conversion,[],[f547]) ).
cnf(s102,plain,
( spl0_16
| ~ spl0_22
| spl0_48 ),
inference(sat_conversion,[],[f553]) ).
cnf(s104,plain,
( ~ spl0_22
| spl0_39
| spl0_45 ),
inference(sat_conversion,[],[f563]) ).
cnf(s105,plain,
spl0_26,
inference(rat,[],[s62,s41,s43]) ).
cnf(s106,plain,
( ~ spl0_38
| spl0_28
| ~ spl0_19 ),
inference(rat,[],[s76,s77,s105]) ).
cnf(s107,plain,
( spl0_28
| spl0_22
| spl0_20
| ~ spl0_11
| ~ spl0_19 ),
inference(rat,[],[s106,s75,s65,s39,s37,s40,s38,s105]) ).
cnf(s108,plain,
~ spl0_28,
inference(rat,[],[s62,s42,s44]) ).
cnf(s109,plain,
( spl0_20
| ~ spl0_11
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s74,s104,s65,s107,s37,s39,s101,s106,s108,s105]) ).
cnf(s110,plain,
( ~ spl0_20
| ~ spl0_7
| ~ spl0_9 ),
inference(rat,[],[s60,s38,s40,s47,s105,s108]) ).
cnf(s111,plain,
( spl0_10
| spl0_20
| spl0_2 ),
inference(rat,[],[s109,s17,s27,s32]) ).
cnf(s112,plain,
( ~ spl0_11
| ~ spl0_19
| spl0_20
| ~ spl0_9 ),
inference(rat,[],[s92,s102,s93,s28,s30,s31,s107,s109,s108]) ).
cnf(s113,plain,
( spl0_11
| ~ spl0_10
| ~ spl0_3
| ~ spl0_9 ),
inference(rat,[],[s95,s19,s92,s83,s93,s18,s20,s21]) ).
cnf(s115,plain,
spl0_9,
inference(rat,[],[s68,s14,s15,s16]) ).
cnf(s116,plain,
spl0_7,
inference(rat,[],[s68,s6,s7,s8]) ).
cnf(s117,plain,
~ spl0_20,
inference(rat,[],[s110,s115,s116]) ).
cnf(s121,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s96,s19,s92,s83,s93,s18,s20,s21,s116,s115]) ).
cnf(s122,plain,
~ spl0_2,
inference(rat,[],[s96,s34,s92,s83,s93,s33,s35,s36,s107,s121,s97,s116,s115,s108,s117]) ).
cnf(s123,plain,
spl0_10,
inference(rat,[],[s111,s122,s117]) ).
cnf(s125,plain,
spl0_3,
inference(rat,[],[s68,s2,s3,s4]) ).
cnf(s126,plain,
spl0_11,
inference(rat,[],[s113,s115,s123,s125]) ).
cnf(s127,plain,
~ spl0_19,
inference(rat,[],[s112,s115,s117,s126]) ).
cnf(s128,plain,
~ spl0_16,
inference(rat,[],[s36,s127]) ).
cnf(s129,plain,
spl0_15,
inference(rat,[],[s35,s127]) ).
cnf(s130,plain,
spl0_12,
inference(rat,[],[s33,s127]) ).
cnf(s131,plain,
~ spl0_52,
inference(rat,[],[s93,s115,s128]) ).
cnf(s132,plain,
~ spl0_14,
inference(rat,[],[s83,s128,s130,s129]) ).
cnf(s133,plain,
~ spl0_48,
inference(rat,[],[s92,s131,s130,s129]) ).
cnf(s134,plain,
spl0_13,
inference(rat,[],[s34,s127,s132]) ).
cnf(s136,plain,
$false,
inference(rat,[],[s95,s123,s125,s128,s133,s134]) ).
fof(f564,plain,
$false,
inference(avatar_sat_refutation,[],[s136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 SAT
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 21:44:09 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (2389151)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (2389157)% WARNING: option uhcvi not known.
% 0.20/0.27 % (2389157)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1184992416:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (2389157) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2389151-2389157"...
% 0.20/0.27 % (2389159)dis+10_1_sil=32000:sp=arity:random_seed=1049110769:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (2389158)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3503193682:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (2389156)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1262662967_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (2389160)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3420112164:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (2389157)...printing done.
% 0.20/0.27 % (2389157)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (2389157)------------------------------
% 0.20/0.28 % (2389157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2389157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2389157)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2389157)Termination reason: Refutation
% 0.20/0.28 % (2389157)Time elapsed: 0.007 s
% 0.20/0.28 % (2389157)Peak memory usage: 12 MB
% 0.20/0.28 % (2389157)Instructions burned: 15 (million)
% 0.20/0.28 % (2389151)Success in time 0.033 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------