%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.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 : Fri Sep 25 01:04:15 PM UTC 2026
% Result : Theorem 2.95s 6.31s
% Output : CNFRefutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 175 ( 7 unt; 4 def)
% Number of atoms : 832 ( 2 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 1136 ( 489 ~; 515 |; 105 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 9 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-1 aty)
% Number of variables : 316 ( 0 sgn 283 !; 33 ?; 150 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) )
=> ? [X3] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X3,X1,X2) )
& program(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& program(X0) )
=> ! [X1,X2] :
( ( ( ~ halts2(X1,X2)
& program(X1) )
=> ( outputs(X0,bad)
& halts3(X0,X1,X2) ) )
& ( ( halts2(X1,X2)
& program(X1) )
=> ( outputs(X0,good)
& halts3(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ( ! [X1,X2] :
( ( ( ~ halts2(X1,X2)
& program(X1) )
=> ( outputs(X0,bad)
& halts3(X0,X1,X2) ) )
& ( ( halts2(X1,X2)
& program(X1) )
=> ( outputs(X0,good)
& halts3(X0,X1,X2) ) ) )
& program(X0) )
=> ? [X3] :
( ! [X1] :
( ( ( outputs(X0,bad)
& halts3(X0,X1,X1)
& program(X1) )
=> ( outputs(X3,bad)
& halts2(X3,X1) ) )
& ( ( outputs(X0,good)
& halts3(X0,X1,X1)
& program(X1) )
=> ~ halts2(X3,X1) ) )
& program(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f4,conjecture,
~ ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f5,negated_conjecture,
~ ~ ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
( ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) )
=> ? [X3] :
( ! [X4] :
( program(X4)
=> ! [X5] : decides(X3,X4,X5) )
& program(X3) ) ),
inference(rectify,[],[f1]) ).
fof(f7,plain,
! [X0] :
( ( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& program(X0) )
=> ! [X3,X4] :
( ( ( ~ halts2(X3,X4)
& program(X3) )
=> ( outputs(X0,bad)
& halts3(X0,X3,X4) ) )
& ( ( halts2(X3,X4)
& program(X3) )
=> ( outputs(X0,good)
& halts3(X0,X3,X4) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f8,plain,
! [X0] :
( ( ! [X1,X2] :
( ( ( ~ halts2(X1,X2)
& program(X1) )
=> ( outputs(X0,bad)
& halts3(X0,X1,X2) ) )
& ( ( halts2(X1,X2)
& program(X1) )
=> ( outputs(X0,good)
& halts3(X0,X1,X2) ) ) )
& program(X0) )
=> ? [X3] :
( ! [X4] :
( ( ( outputs(X0,bad)
& halts3(X0,X4,X4)
& program(X4) )
=> ( outputs(X3,bad)
& halts2(X3,X4) ) )
& ( ( outputs(X0,good)
& halts3(X0,X4,X4)
& program(X4) )
=> ~ halts2(X3,X4) ) )
& program(X3) ) ),
inference(rectify,[],[f3]) ).
fof(f9,plain,
? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(flattening,[],[f5]) ).
fof(f10,plain,
( ! [X0] :
( ? [X1] :
( program(X1)
& ? [X2] : ~ decides(X0,X1,X2) )
| ~ algorithm(X0) )
| ? [X3] :
( ! [X4] :
( ~ program(X4)
| ! [X5] : decides(X3,X4,X5) )
& program(X3) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f11,plain,
! [X0] :
( ? [X1] :
( program(X1)
& ? [X2] : ~ decides(X0,X1,X2) )
| ~ program(X0)
| ! [X3,X4] :
( ( halts2(X3,X4)
| ~ program(X3)
| ( outputs(X0,bad)
& halts3(X0,X3,X4) ) )
& ( ~ halts2(X3,X4)
| ~ program(X3)
| ( outputs(X0,good)
& halts3(X0,X3,X4) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0] :
( ? [X1] :
( program(X1)
& ? [X2] : ~ decides(X0,X1,X2) )
| ~ program(X0)
| ! [X3,X4] :
( ( halts2(X3,X4)
| ~ program(X3)
| ( outputs(X0,bad)
& halts3(X0,X3,X4) ) )
& ( ~ halts2(X3,X4)
| ~ program(X3)
| ( outputs(X0,good)
& halts3(X0,X3,X4) ) ) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ? [X1,X2] :
( ( ~ halts2(X1,X2)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X2) ) )
| ( halts2(X1,X2)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X2) ) ) )
| ~ program(X0)
| ? [X3] :
( ! [X4] :
( ( ~ outputs(X0,bad)
| ~ halts3(X0,X4,X4)
| ~ program(X4)
| ( outputs(X3,bad)
& halts2(X3,X4) ) )
& ( ~ outputs(X0,good)
| ~ halts3(X0,X4,X4)
| ~ program(X4)
| ~ halts2(X3,X4) ) )
& program(X3) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
! [X0] :
( ? [X1,X2] :
( ( ~ halts2(X1,X2)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X2) ) )
| ( halts2(X1,X2)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X2) ) ) )
| ~ program(X0)
| ? [X3] :
( ! [X4] :
( ( ~ outputs(X0,bad)
| ~ halts3(X0,X4,X4)
| ~ program(X4)
| ( outputs(X3,bad)
& halts2(X3,X4) ) )
& ( ~ outputs(X0,good)
| ~ halts3(X0,X4,X4)
| ~ program(X4)
| ~ halts2(X3,X4) ) )
& program(X3) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
? [X0] :
( ! [X1] :
( ~ program(X1)
| ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f19,plain,
( ! [X3] :
( ? [X4] :
( program(X4)
& ? [X5] : ~ decides(X3,X4,X5) )
| ~ algorithm(X3) )
| ? [X0] :
( ! [X1] :
( ~ program(X1)
| ! [X2] : decides(X0,X1,X2) )
& program(X0) ) ),
inference(rectify,[],[f10]) ).
fof(f20,plain,
( ! [X3] :
( ( program(sK3(X3))
& ~ decides(X3,sK3(X3),sK4(X3)) )
| ~ algorithm(X3) )
| ( ! [X1] :
( ~ program(X1)
| ! [X2] : decides(sK2,X1,X2) )
& program(sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X4,sK3(X3)),skolemize(X5,sK4(X3))],[f19]) ).
fof(f21,plain,
! [X0] :
( ? [X3] :
( program(X3)
& ? [X4] : ~ decides(X0,X3,X4) )
| ~ program(X0)
| ! [X1,X2] :
( ( halts2(X1,X2)
| ~ program(X1)
| ( outputs(X0,bad)
& halts3(X0,X1,X2) ) )
& ( ~ halts2(X1,X2)
| ~ program(X1)
| ( outputs(X0,good)
& halts3(X0,X1,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f22,plain,
! [X0] :
( ( program(sK5(X0))
& ~ decides(X0,sK5(X0),sK6(X0)) )
| ~ program(X0)
| ! [X1,X2] :
( ( halts2(X1,X2)
| ~ program(X1)
| ( outputs(X0,bad)
& halts3(X0,X1,X2) ) )
& ( ~ halts2(X1,X2)
| ~ program(X1)
| ( outputs(X0,good)
& halts3(X0,X1,X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X3,sK5(X0)),skolemize(X4,sK6(X0))],[f21]) ).
fof(f23,plain,
! [X0] :
( ~ sP1(X0)
| ? [X3] :
( ! [X4] :
( ( ~ outputs(X0,bad)
| ~ halts3(X0,X4,X4)
| ~ program(X4)
| ( outputs(X3,bad)
& halts2(X3,X4) ) )
& ( ~ outputs(X0,good)
| ~ halts3(X0,X4,X4)
| ~ program(X4)
| ~ halts2(X3,X4) ) )
& program(X3) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f24,plain,
! [X0] :
( ~ sP1(X0)
| ? [X1] :
( ! [X2] :
( ( ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| ( outputs(X1,bad)
& halts2(X1,X2) ) )
& ( ~ outputs(X0,good)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| ~ halts2(X1,X2) ) )
& program(X1) ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ sP1(X0)
| ( ! [X2] :
( ( ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| ( outputs(sK7(X0),bad)
& halts2(sK7(X0),X2) ) )
& ( ~ outputs(X0,good)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| ~ halts2(sK7(X0),X2) ) )
& program(sK7(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f24]) ).
fof(f28,plain,
! [X0] :
( sP0(sK9(X0),sK8(X0),X0)
| ( halts2(sK8(X0),sK9(X0))
& program(sK8(X0))
& ( ~ outputs(X0,good)
| ~ halts3(X0,sK8(X0),sK9(X0)) ) )
| ~ program(X0)
| sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X1,sK8(X0)),skolemize(X2,sK9(X0))],[f18]) ).
fof(f29,plain,
( ! [X1] :
( ~ program(X1)
| ! [X2] : decides(sK10,X1,X2) )
& algorithm(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f15]) ).
fof(f30,plain,
! [X2,X3,X1] :
( program(sK3(X3))
| ~ algorithm(X3)
| ~ program(X1)
| decides(sK2,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X2,X3,X1] :
( ~ decides(X3,sK3(X3),sK4(X3))
| ~ algorithm(X3)
| ~ program(X1)
| decides(sK2,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X3] :
( program(sK3(X3))
| ~ algorithm(X3)
| program(sK2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X3] :
( ~ decides(X3,sK3(X3),sK4(X3))
| ~ algorithm(X3)
| program(sK2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X2,X0,X1] :
( program(sK5(X0))
| ~ program(X0)
| halts2(X1,X2)
| ~ program(X1)
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ decides(X0,sK5(X0),sK6(X0))
| ~ program(X0)
| halts2(X1,X2)
| ~ program(X1)
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X0,X1] :
( program(sK5(X0))
| ~ program(X0)
| halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ decides(X0,sK5(X0),sK6(X0))
| ~ program(X0)
| halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( program(sK5(X0))
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| outputs(X0,good) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ decides(X0,sK5(X0),sK6(X0))
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| outputs(X0,good) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0,X1] :
( program(sK5(X0))
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ decides(X0,sK5(X0),sK6(X0))
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X2,X0] :
( ~ sP1(X0)
| ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| outputs(sK7(X0),bad) ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X2,X0] :
( ~ sP1(X0)
| ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| halts2(sK7(X0),X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
! [X2,X0] :
( ~ sP1(X0)
| ~ outputs(X0,good)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| ~ halts2(sK7(X0),X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0] :
( ~ sP1(X0)
| program(sK7(X0)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f49,plain,
! [X0] :
( sP0(sK9(X0),sK8(X0),X0)
| halts2(sK8(X0),sK9(X0))
| ~ program(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X0] :
( sP0(sK9(X0),sK8(X0),X0)
| program(sK8(X0))
| ~ program(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0] :
( sP0(sK9(X0),sK8(X0),X0)
| ~ outputs(X0,good)
| ~ halts3(X0,sK8(X0),sK9(X0))
| ~ program(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X2,X1] :
( ~ program(X1)
| decides(sK10,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
algorithm(sK10),
inference(cnf_transformation,[],[f29]) ).
tcf(c_49,plain,
! [X0: $i] :
( program(sK2)
| ~ algorithm(X0)
| ~ decides(X0,sK3(X0),sK4(X0)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_50,plain,
! [X0: $i] :
( program(sK2)
| program(sK3(X0))
| ~ algorithm(X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( decides(sK2,X1,X2)
| ~ algorithm(X0)
| ~ program(X1)
| ~ decides(X0,sK3(X0),sK4(X0)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(sK3(X1))
| decides(sK2,X0,X2)
| ~ algorithm(X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(sK5(X2))
| halts3(X2,X0,X1)
| ~ program(X2)
| ~ program(X0)
| ~ halts2(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( outputs(X0,good)
| ~ program(X1)
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( outputs(X2,good)
| program(sK5(X2))
| ~ program(X2)
| ~ program(X0)
| ~ halts2(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts2(X1,X2)
| halts3(X0,X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(sK5(X1))
| halts2(X0,X2)
| halts3(X1,X0,X2)
| ~ program(X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( outputs(X0,bad)
| halts2(X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( outputs(X1,bad)
| program(sK5(X1))
| halts2(X0,X2)
| ~ program(X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_61,plain,
! [X0: $i] :
( program(sK7(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ~ sP1(X0)
| ~ program(X1)
| ~ outputs(X0,good)
| ~ halts2(sK7(X0),X1)
| ~ halts3(X0,X1,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( halts2(sK7(X0),X1)
| ~ sP1(X0)
| ~ program(X1)
| ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( outputs(sK7(X0),bad)
| ~ sP1(X0)
| ~ program(X1)
| ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_68,plain,
! [X0: $i] :
( sP1(X0)
| sP0(sK9(X0),sK8(X0),X0)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts3(X0,sK8(X0),sK9(X0)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_69,plain,
! [X0: $i] :
( sP1(X0)
| program(sK8(X0))
| sP0(sK9(X0),sK8(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_70,plain,
! [X0: $i] :
( sP1(X0)
| halts2(sK8(X0),sK9(X0))
| sP0(sK9(X0),sK8(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_71,negated_conjecture,
algorithm(sK10),
inference(cnf_transformation,[],[f53]) ).
tcf(c_72,negated_conjecture,
! [X0: $i,X1: $i] :
( decides(sK10,X0,X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ decides(X0,sK5(X0),sK6(X0))
| ~ program(X0)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_57,c_53]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(renaming,[status(thm)],[c_96]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_97]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(sK5(X1))
| halts3(X1,X0,X2)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58,c_54]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] :
( decides(sK2,X0,X1)
| ~ program(X0)
| ~ decides(sK10,sK3(sK10),sK4(sK10)) ),
inference(resolution,[status(thm)],[c_51,c_71]) ).
tcf(c_287,plain,
( program(sK2)
| program(sK3(sK10)) ),
inference(resolution,[status(thm)],[c_50,c_71]) ).
tcf(c_294,plain,
( program(sK2)
| ~ decides(sK10,sK3(sK10),sK4(sK10)) ),
inference(resolution,[status(thm)],[c_49,c_71]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i] :
( program(sK3(sK10))
| decides(sK2,X0,X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c_52,c_71]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| halts2(sK7(X0),X1)
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(resolution,[status(thm)],[c_202,c_63]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(sK7(X0),X1) ),
inference(resolution,[status(thm)],[c_202,c_62]) ).
tcf(c_2500,plain,
! [X0: $i] :
( ~ iPr_def_10
| program(sK5(X0))
| ~ program(X0)
| outputs(X0,bad) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_60]) ).
tcf(c_2501,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ~ program(X0)
| halts2(X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_60]) ).
tcf(c_2502,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_60]) ).
tcf(c_2503,plain,
! [X0: $i] :
( ~ iPr_def_12
| ~ program(X0)
| outputs(X0,bad)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_59]) ).
tcf(c_2504,plain,
( iPr_def_12
| iPr_def_11 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_59]) ).
tcf(c_2505,plain,
! [X0: $i] :
( ~ iPr_def_13
| program(sK5(X0))
| ~ program(X0)
| outputs(X0,good) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_56]) ).
tcf(c_2506,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_14
| ~ program(X0)
| ~ halts2(X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_56]) ).
tcf(c_2507,plain,
( iPr_def_14
| iPr_def_13 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_56]) ).
tcf(c_2508,plain,
! [X0: $i] :
( ~ iPr_def_15
| ~ program(X0)
| outputs(X0,good)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_55]) ).
tcf(c_2509,plain,
( iPr_def_15
| iPr_def_14 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_55]) ).
tcf(c_2510,definition,
iPr_def_16 = sK3(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2511,definition,
iPr_def_17 = sK4(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2512,plain,
! [X0: $i,X1: $i] :
( program(iPr_def_16)
| decides(sK2,X0,X1)
| ~ program(X0) ),
inference(demodulation,[status(thm)],[c_301,c_2510]) ).
tcf(c_2513,plain,
( program(sK2)
| ~ decides(sK10,iPr_def_16,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_294,c_2511]) ).
tcf(c_2514,plain,
( program(iPr_def_16)
| program(sK2) ),
inference(demodulation,[status(thm)],[c_287]) ).
tcf(c_2515,plain,
! [X0: $i,X1: $i] :
( decides(sK2,X0,X1)
| ~ program(X0)
| ~ decides(sK10,iPr_def_16,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_276]) ).
tcf(c_2516,negated_conjecture,
! [X0: $i,X1: $i] :
( decides(sK10,X0,X1)
| ~ program(X0) ),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_3011,plain,
( program(sK2)
| ~ program(iPr_def_16) ),
inference(superposition,[status(thm)],[c_2516,c_2513]) ).
tcf(c_3014,plain,
program(sK2),
inference(global_subsumption_just,[status(thm)],[c_3011,c_2514,c_3011]) ).
tcf(c_3028,plain,
! [X0: $i,X1: $i] :
( decides(sK2,X0,X1)
| ~ program(iPr_def_16)
| ~ program(X0) ),
inference(superposition,[status(thm)],[c_2516,c_2515]) ).
tcf(c_3033,plain,
! [X0: $i,X1: $i] :
( decides(sK2,X0,X1)
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3028,c_2512,c_3028]) ).
tcf(c_3086,plain,
! [X0: $i] :
( ~ iPr_def_14
| ~ iPr_def_11
| ~ program(X0) ),
inference(superposition,[status(thm)],[c_2501,c_2506]) ).
tcf(c_3097,plain,
( ~ iPr_def_14
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_3014,c_3086]) ).
tcf(c_3108,plain,
( iPr_def_10
| ~ iPr_def_14 ),
inference(superposition,[status(thm)],[c_2502,c_3097]) ).
tcf(c_3115,plain,
( iPr_def_13
| iPr_def_10 ),
inference(superposition,[status(thm)],[c_2507,c_3108]) ).
tcf(c_3147,plain,
( outputs(sK2,bad)
| ~ iPr_def_12
| ~ program(sK2)
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3033,c_2503]) ).
tcf(c_3148,plain,
( outputs(sK2,bad)
| ~ iPr_def_12
| ~ program(sK5(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3147,c_3014]) ).
tcf(c_3166,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(sK7(X0),X1) ),
inference(superposition,[status(thm)],[c_202,c_62]) ).
tcf(c_3182,plain,
! [X0: $i,X1: $i] :
( halts3(sK2,X0,X1)
| ~ program(sK2)
| ~ program(X0)
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3033,c_99]) ).
tcf(c_3183,plain,
! [X0: $i,X1: $i] :
( halts3(sK2,X0,X1)
| ~ program(X0)
| ~ program(sK5(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3182,c_3014]) ).
tcf(c_3203,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| halts2(sK7(X0),X1)
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(superposition,[status(thm)],[c_202,c_63]) ).
tcf(c_3220,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| outputs(sK7(X0),bad)
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(superposition,[status(thm)],[c_202,c_64]) ).
tcf(c_3234,plain,
! [X0: $i] :
( halts2(sK7(sK2),X0)
| ~ sP1(sK2)
| ~ program(X0)
| ~ outputs(sK2,bad)
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3183,c_63]) ).
tcf(c_3235,plain,
! [X0: $i] :
( ~ sP1(sK2)
| ~ program(X0)
| ~ outputs(sK2,good)
| ~ program(sK5(sK2))
| ~ halts2(sK7(sK2),X0) ),
inference(superposition,[status(thm)],[c_3183,c_62]) ).
tcf(c_3312,plain,
( outputs(sK2,good)
| ~ iPr_def_15
| ~ program(sK2)
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3033,c_2508]) ).
tcf(c_3313,plain,
( outputs(sK2,good)
| ~ iPr_def_15
| ~ program(sK5(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3312,c_3014]) ).
tcf(c_3421,plain,
! [X0: $i] :
( ~ iPr_def_14
| ~ sP1(sK2)
| ~ program(X0)
| ~ outputs(sK2,bad)
| ~ program(sK7(sK2))
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3234,c_2506]) ).
tcf(c_3494,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ sP1(sK2)
| ~ program(X0)
| ~ outputs(sK2,good)
| ~ program(sK7(sK2))
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_2501,c_3235]) ).
tcf(c_3495,plain,
! [X0: $i] :
( ~ sP1(sK2)
| ~ program(X0)
| ~ outputs(sK2,bad)
| ~ outputs(sK2,good)
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3234,c_3235]) ).
tcf(c_3551,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ iPr_def_14
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ program(sK7(X0)) ),
inference(superposition,[status(thm)],[c_3203,c_2506]) ).
tcf(c_3820,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ outputs(X0,bad)
| ~ program(X0)
| ~ program(X1)
| ~ sP1(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3220,c_61,c_533,c_553,c_2505,c_2507,c_3551]) ).
tcf(c_3821,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(renaming,[status(thm)],[c_3820]) ).
tcf(c_3833,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ iPr_def_10
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0) ),
inference(superposition,[status(thm)],[c_2500,c_3821]) ).
tcf(c_3884,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ halts2(sK7(X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_3166,c_553,c_2505,c_3115,c_3833]) ).
tcf(c_3897,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ iPr_def_11
| ~ sP1(X0)
| ~ program(X1)
| ~ program(X0)
| ~ program(sK7(X0)) ),
inference(superposition,[status(thm)],[c_2501,c_3884]) ).
tcf(c_4035,plain,
( program(sK7(sK2))
| ~ sP1(sK2) ),
inference(instantiation,[status(thm)],[c_61]) ).
fof(f16,definition,
! [X2,X1,X0] :
( ~ sP0(X2,X1,X0)
| ( ~ halts2(X1,X2)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X2) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f17,definition,
! [X0] :
( ~ sP1(X0)
| ? [X3] :
( ! [X4] :
( ( ~ outputs(X0,bad)
| ~ halts3(X0,X4,X4)
| ~ program(X4)
| ( outputs(X3,bad)
& halts2(X3,X4) ) )
& ( ~ outputs(X0,good)
| ~ halts3(X0,X4,X4)
| ~ program(X4)
| ~ halts2(X3,X4) ) )
& program(X3) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f18,plain,
! [X0] :
( ? [X1,X2] :
( sP0(X2,X1,X0)
| ( halts2(X1,X2)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X2) ) ) )
| ~ program(X0)
| sP1(X0) ),
inference(definition_folding,[],[f14,f17,f16]) ).
fof(f26,plain,
! [X2,X1,X0] :
( ~ sP0(X2,X1,X0)
| ( ~ halts2(X1,X2)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ sP0(X0,X1,X2)
| ( ~ halts2(X1,X0)
& program(X1)
& ( ~ outputs(X2,bad)
| ~ halts3(X2,X1,X0) ) ) ),
inference(rectify,[],[f26]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ halts2(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| program(X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ outputs(X2,bad)
| ~ halts3(X2,X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ outputs(X0,bad)
| ~ sP0(X2,X1,X0)
| ~ halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ halts2(X1,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_110,plain,
! [X0: $i] :
( sP1(X0)
| program(sK8(X0))
| ~ program(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_69,c_66]) ).
tcf(c_322,plain,
! [X0: $i] :
( sP1(X0)
| halts2(sK8(X0),sK9(X0))
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ halts3(X0,sK8(X0),sK9(X0)) ),
inference(resolution,[status(thm)],[c_65,c_70]) ).
tcf(c_339,plain,
! [X0: $i] :
( sP1(X0)
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ outputs(X0,good)
| ~ halts3(X0,sK8(X0),sK9(X0)) ),
inference(resolution,[status(thm)],[c_65,c_68]) ).
tcf(c_357,plain,
! [X0: $i] :
( sP1(X0)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(sK8(X0),sK9(X0))
| ~ halts3(X0,sK8(X0),sK9(X0)) ),
inference(resolution,[status(thm)],[c_67,c_68]) ).
tcf(c_573,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| ~ program(X0)
| ~ outputs(X0,good)
| ~ program(sK8(X0))
| ~ halts2(sK8(X0),sK9(X0)) ),
inference(resolution,[status(thm)],[c_202,c_357]) ).
tcf(c_575,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(sK8(X0),sK9(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_573,c_110,c_573]) ).
tcf(c_613,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| halts2(sK8(X0),sK9(X0))
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ program(sK8(X0)) ),
inference(resolution,[status(thm)],[c_202,c_322]) ).
tcf(c_615,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| halts2(sK8(X0),sK9(X0))
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(global_subsumption_just,[status(thm)],[c_613,c_110,c_613]) ).
tcf(c_3439,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| halts2(sK8(X0),sK9(X0))
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ program(sK8(X0)) ),
inference(superposition,[status(thm)],[c_202,c_322]) ).
tcf(c_3441,plain,
( sP1(sK2)
| halts2(sK8(sK2),sK9(sK2))
| ~ program(sK2)
| ~ outputs(sK2,bad)
| ~ program(sK8(sK2))
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3183,c_322]) ).
tcf(c_3453,plain,
( sP1(sK2)
| halts2(sK8(sK2),sK9(sK2))
| ~ outputs(sK2,bad)
| ~ program(sK8(sK2))
| ~ program(sK5(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3441,c_3014]) ).
tcf(c_3521,plain,
( sP1(sK2)
| ~ program(sK2)
| ~ outputs(sK2,bad)
| ~ outputs(sK2,good)
| ~ program(sK8(sK2))
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3183,c_339]) ).
tcf(c_3533,plain,
( sP1(sK2)
| ~ outputs(sK2,bad)
| ~ outputs(sK2,good)
| ~ program(sK8(sK2))
| ~ program(sK5(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3521,c_3014]) ).
tcf(c_3664,plain,
( sP1(sK2)
| ~ iPr_def_14
| ~ outputs(sK2,bad)
| ~ program(sK8(sK2))
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_3453,c_2506]) ).
tcf(c_3672,plain,
( sP1(sK2)
| ~ iPr_def_14
| ~ program(sK5(sK2))
| ~ program(sK8(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_3664,c_2504,c_3097,c_3148,c_3664]) ).
tcf(c_3673,plain,
( sP1(sK2)
| ~ iPr_def_14
| ~ program(sK8(sK2))
| ~ program(sK5(sK2)) ),
inference(renaming,[status(thm)],[c_3672]) ).
tcf(c_3682,plain,
( sP1(sK2)
| program(sK8(sK2))
| ~ program(sK2) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_3707,plain,
! [X0: $i] :
( ~ program(sK5(sK2))
| ~ outputs(sK2,good)
| ~ outputs(sK2,bad)
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3495,c_2514,c_3011,c_3495,c_3533,c_3682]) ).
tcf(c_3708,plain,
! [X0: $i] :
( ~ program(X0)
| ~ outputs(sK2,bad)
| ~ outputs(sK2,good)
| ~ program(sK5(sK2)) ),
inference(renaming,[status(thm)],[c_3707]) ).
tcf(c_3777,plain,
! [X0: $i] :
( ~ iPr_def_14
| ~ program(sK7(sK2))
| ~ program(sK5(sK2))
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3421,c_2504,c_2514,c_3011,c_3097,c_3148,c_3421,c_3673,c_3682]) ).
tcf(c_3778,plain,
! [X0: $i] :
( ~ iPr_def_14
| ~ program(X0)
| ~ program(sK7(sK2))
| ~ program(sK5(sK2)) ),
inference(renaming,[status(thm)],[c_3777]) ).
tcf(c_3798,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| ~ program(X0)
| ~ outputs(X0,good)
| ~ program(sK8(X0))
| ~ halts2(sK8(X0),sK9(X0)) ),
inference(superposition,[status(thm)],[c_202,c_357]) ).
tcf(c_3800,plain,
( sP1(sK2)
| ~ program(sK2)
| ~ outputs(sK2,good)
| ~ program(sK8(sK2))
| ~ program(sK5(sK2))
| ~ halts2(sK8(sK2),sK9(sK2)) ),
inference(superposition,[status(thm)],[c_3183,c_357]) ).
tcf(c_3812,plain,
( sP1(sK2)
| ~ outputs(sK2,good)
| ~ program(sK8(sK2))
| ~ program(sK5(sK2))
| ~ halts2(sK8(sK2),sK9(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3800,c_3014]) ).
tcf(c_3916,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| halts2(sK8(X0),sK9(X0))
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(global_subsumption_just,[status(thm)],[c_3439,c_615]) ).
tcf(c_3928,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| ~ iPr_def_14
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ program(sK8(X0)) ),
inference(superposition,[status(thm)],[c_3916,c_2506]) ).
tcf(c_4168,plain,
( sP1(sK2)
| ~ program(sK5(sK2))
| ~ halts2(sK8(sK2),sK9(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_3812,c_2509,c_2514,c_3011,c_3313,c_3673,c_3682,c_3812]) ).
tcf(c_4181,plain,
( sP1(sK2)
| ~ iPr_def_11
| ~ program(sK8(sK2))
| ~ program(sK5(sK2)) ),
inference(superposition,[status(thm)],[c_2501,c_4168]) ).
tcf(c_4203,plain,
! [X0: $i] :
( ~ program(sK5(sK2))
| ~ program(X0)
| ~ sP1(sK2) ),
inference(global_subsumption_just,[status(thm)],[c_3494,c_2504,c_2509,c_3148,c_3313,c_3494,c_3708,c_3778,c_4035]) ).
tcf(c_4204,plain,
! [X0: $i] :
( ~ sP1(sK2)
| ~ program(X0)
| ~ program(sK5(sK2)) ),
inference(renaming,[status(thm)],[c_4203]) ).
tcf(c_4206,plain,
! [X0: $i] :
( ~ program(sK5(sK2))
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_4204,c_2504,c_2514,c_3011,c_3148,c_3453,c_3682,c_4168,c_4181,c_4204]) ).
tcf(c_4207,plain,
! [X0: $i] :
( ~ program(X0)
| ~ program(sK5(sK2)) ),
inference(renaming,[status(thm)],[c_4206]) ).
tcf(c_4213,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| ~ program(X0)
| ~ halts2(sK8(X0),sK9(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_3798,c_110,c_575,c_2500,c_2505,c_2507,c_3115,c_3928]) ).
tcf(c_4224,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3916,c_4213]) ).
tcf(c_4230,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| ~ iPr_def_11
| ~ program(X0)
| ~ program(sK8(X0)) ),
inference(superposition,[status(thm)],[c_2501,c_4213]) ).
tcf(c_4242,plain,
! [X0: $i] :
( sP1(X0)
| program(sK5(X0))
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_4224,c_110,c_2500,c_2502,c_4224,c_4230]) ).
tcf(c_4252,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ program(X1)
| ~ program(X0)
| ~ halts2(sK7(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3884,c_4242]) ).
tcf(c_4289,plain,
! [X0: $i,X1: $i] :
( program(sK5(X0))
| ~ program(X1)
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_4252,c_61,c_2502,c_3833,c_3897,c_4242]) ).
tcf(c_4298,plain,
! [X0: $i] :
( program(sK5(X0))
| ~ program(X0) ),
inference(superposition,[status(thm)],[c_3014,c_4289]) ).
tcf(c_4343,plain,
! [X0: $i] :
( ~ program(sK2)
| ~ program(X0) ),
inference(superposition,[status(thm)],[c_4298,c_4207]) ).
tcf(c_4346,plain,
! [X0: $i] : ~ program(X0),
inference(forward_subsumption_resolution,[status(thm)],[c_4343,c_3014]) ).
tcf(c_4347,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_3014,c_4346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n018.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Fri Sep 25 07:46:25 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 2.95/6.31 % SZS status Started for theBenchmark.p
% 2.95/6.31 % SZS status Theorem for theBenchmark.p
% 2.95/6.31
% 2.95/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.95/6.31
% 2.95/6.31 % ------ iProver source info
% 2.95/6.31
% 2.95/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.95/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.95/6.31 % git: non_committed_changes: false
% 2.95/6.31
% 2.95/6.31 % ------ Parsing...
% 2.95/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.95/6.31
% 2.95/6.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.95/6.31
% 2.95/6.31 % ------ Preprocessing... gs_s sp: 8 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.95/6.31
% 2.95/6.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.95/6.31 % ------ Proving...
% 2.95/6.31 % ------ Problem Properties
% 2.95/6.31
% 2.95/6.31 %
% 2.95/6.31 % clauses 27
% 2.95/6.31 % conjectures 1
% 2.95/6.31 % EPR 11
% 2.95/6.31 % Horn 16
% 2.95/6.31 % unary 2
% 2.95/6.31 % binary 8
% 2.95/6.31 % lits 87
% 2.95/6.31 % lits eq 2
% 2.95/6.31 % fd_pure 0
% 2.95/6.31 % fd_pseudo 0
% 2.95/6.31 % fd_cond 0
% 2.95/6.31 % fd_pseudo_cond 0
% 2.95/6.31 % AC symbols 0
% 2.95/6.31
% 2.95/6.31 % ------ Schedule dynamic 5 is on
% 2.95/6.31
% 2.95/6.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.95/6.31
% 2.95/6.31
% 2.95/6.31 % ------
% 2.95/6.31 % Current options:
% 2.95/6.31 % ------
% 2.95/6.31
% 2.95/6.31
% 2.95/6.31 %
% 2.95/6.31
% 2.95/6.31 % ------ Proving...
% 2.95/6.31 %
% 2.95/6.31
% 2.95/6.31 % SZS status Theorem for theBenchmark.p
% 2.95/6.31
% 2.95/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.95/6.32
% 2.95/6.32
%------------------------------------------------------------------------------