%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM003+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 01:04:14 PM UTC 2026
% Result : Theorem 2.91s 6.28s
% Output : CNFRefutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of formulae : 211 ( 12 unt; 6 def)
% Number of atoms : 952 ( 2 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1232 ( 501 ~; 527 |; 167 &)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 22 ( 20 usr; 13 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 334 ( 0 sgn 290 !; 44 ?; 143 :)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
( ? [X0] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,bad)
& halts3(X0,X1,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,good)
& halts3(X0,X1,X1) ) ) )
& program(X0) )
=> ? [X2] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X2,bad)
& halts2(X2,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X2,good)
& halts2(X2,X1) ) ) )
& program(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
( ? [X0] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,bad)
& halts2(X0,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,good)
& halts2(X0,X1) ) ) )
& program(X0) )
=> ? [X2] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X2,bad)
& halts2(X2,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ~ halts2(X2,X1) ) )
& program(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f5,conjecture,
~ ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f6,negated_conjecture,
~ ~ ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,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(f8,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(f9,plain,
( ? [X0] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,bad)
& halts3(X0,X1,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,good)
& halts3(X0,X1,X1) ) ) )
& program(X0) )
=> ? [X2] :
( ! [X3] :
( ( ( ~ halts2(X3,X3)
& program(X3) )
=> ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ( halts2(X3,X3)
& program(X3) )
=> ( outputs(X2,good)
& halts2(X2,X3) ) ) )
& program(X2) ) ),
inference(rectify,[],[f3]) ).
fof(f10,plain,
( ? [X0] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,bad)
& halts2(X0,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,good)
& halts2(X0,X1) ) ) )
& program(X0) )
=> ? [X2] :
( ! [X3] :
( ( ( ~ halts2(X3,X3)
& program(X3) )
=> ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ( halts2(X3,X3)
& program(X3) )
=> ~ halts2(X2,X3) ) )
& program(X2) ) ),
inference(rectify,[],[f4]) ).
fof(f11,plain,
? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(flattening,[],[f6]) ).
fof(f12,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,[],[f7]) ).
fof(f13,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,[],[f8]) ).
fof(f14,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,[],[f13]) ).
fof(f15,plain,
( ! [X0] :
( ? [X1] :
( ( ~ halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) ) )
| ( halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X1) ) ) )
| ~ program(X0) )
| ? [X2] :
( ! [X3] :
( ( halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ~ halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,good)
& halts2(X2,X3) ) ) )
& program(X2) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,plain,
( ! [X0] :
( ? [X1] :
( ( ~ halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) ) )
| ( halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X1) ) ) )
| ~ program(X0) )
| ? [X2] :
( ! [X3] :
( ( halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ~ halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,good)
& halts2(X2,X3) ) ) )
& program(X2) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
( ! [X0] :
( ? [X1] :
( ( ~ halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts2(X0,X1) ) )
| ( halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts2(X0,X1) ) ) )
| ~ program(X0) )
| ? [X2] :
( ! [X3] :
( ( halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ~ halts2(X3,X3)
| ~ program(X3)
| ~ halts2(X2,X3) ) )
& program(X2) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f18,plain,
( ! [X0] :
( ? [X1] :
( ( ~ halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts2(X0,X1) ) )
| ( halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts2(X0,X1) ) ) )
| ~ program(X0) )
| ? [X2] :
( ! [X3] :
( ( halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ~ halts2(X3,X3)
| ~ program(X3)
| ~ halts2(X2,X3) ) )
& program(X2) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0] :
( ! [X1] :
( ~ program(X1)
| ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f26,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,[],[f12]) ).
fof(f27,plain,
( ! [X3] :
( ( program(sK5(X3))
& ~ decides(X3,sK5(X3),sK6(X3)) )
| ~ algorithm(X3) )
| ( ! [X1] :
( ~ program(X1)
| ! [X2] : decides(sK4,X1,X2) )
& program(sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X4,sK5(X3)),skolemize(X5,sK6(X3))],[f26]) ).
fof(f28,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,[],[f14]) ).
fof(f29,plain,
! [X0] :
( ( program(sK7(X0))
& ~ decides(X0,sK7(X0),sK8(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,[sK7,sK8]),skolemize(X3,sK7(X0)),skolemize(X4,sK8(X0))],[f28]) ).
fof(f30,plain,
( ~ sP1
| ? [X2] :
( ! [X3] :
( ( halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ~ halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,good)
& halts2(X2,X3) ) ) )
& program(X2) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f31,plain,
( ~ sP1
| ? [X0] :
( ! [X1] :
( ( halts2(X1,X1)
| ~ program(X1)
| ( outputs(X0,bad)
& halts2(X0,X1) ) )
& ( ~ halts2(X1,X1)
| ~ program(X1)
| ( outputs(X0,good)
& halts2(X0,X1) ) ) )
& program(X0) ) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
( ~ sP1
| ( ! [X1] :
( ( halts2(X1,X1)
| ~ program(X1)
| ( outputs(sK9,bad)
& halts2(sK9,X1) ) )
& ( ~ halts2(X1,X1)
| ~ program(X1)
| ( outputs(sK9,good)
& halts2(sK9,X1) ) ) )
& program(sK9) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f31]) ).
fof(f35,plain,
( ! [X0] :
( sP0(sK10(X0),X0)
| ( halts2(sK10(X0),sK10(X0))
& program(sK10(X0))
& ( ~ outputs(X0,good)
| ~ halts3(X0,sK10(X0),sK10(X0)) ) )
| ~ program(X0) )
| sP1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f22]) ).
fof(f36,plain,
( ~ sP3
| ? [X2] :
( ! [X3] :
( ( halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ~ halts2(X3,X3)
| ~ program(X3)
| ~ halts2(X2,X3) ) )
& program(X2) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f37,plain,
( ~ sP3
| ? [X0] :
( ! [X1] :
( ( halts2(X1,X1)
| ~ program(X1)
| ( outputs(X0,bad)
& halts2(X0,X1) ) )
& ( ~ halts2(X1,X1)
| ~ program(X1)
| ~ halts2(X0,X1) ) )
& program(X0) ) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
( ~ sP3
| ( ! [X1] :
( ( halts2(X1,X1)
| ~ program(X1)
| ( outputs(sK11,bad)
& halts2(sK11,X1) ) )
& ( ~ halts2(X1,X1)
| ~ program(X1)
| ~ halts2(sK11,X1) ) )
& program(sK11) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f37]) ).
fof(f41,plain,
( ! [X0] :
( sP2(sK12(X0),X0)
| ( halts2(sK12(X0),sK12(X0))
& program(sK12(X0))
& ( ~ outputs(X0,good)
| ~ halts2(X0,sK12(X0)) ) )
| ~ program(X0) )
| sP3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f25]) ).
fof(f42,plain,
( ! [X1] :
( ~ program(X1)
| ! [X2] : decides(sK13,X1,X2) )
& algorithm(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f19]) ).
fof(f43,plain,
! [X2,X3,X1] :
( program(sK5(X3))
| ~ algorithm(X3)
| ~ program(X1)
| decides(sK4,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f44,plain,
! [X2,X3,X1] :
( ~ decides(X3,sK5(X3),sK6(X3))
| ~ algorithm(X3)
| ~ program(X1)
| decides(sK4,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X3] :
( program(sK5(X3))
| ~ algorithm(X3)
| program(sK4) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X3] :
( ~ decides(X3,sK5(X3),sK6(X3))
| ~ algorithm(X3)
| program(sK4) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X2,X0,X1] :
( program(sK7(X0))
| ~ program(X0)
| halts2(X1,X2)
| ~ program(X1)
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ decides(X0,sK7(X0),sK8(X0))
| ~ program(X0)
| halts2(X1,X2)
| ~ program(X1)
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X2,X0,X1] :
( program(sK7(X0))
| ~ program(X0)
| halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ decides(X0,sK7(X0),sK8(X0))
| ~ program(X0)
| halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X2,X0,X1] :
( program(sK7(X0))
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| outputs(X0,good) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ decides(X0,sK7(X0),sK8(X0))
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| outputs(X0,good) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
! [X2,X0,X1] :
( program(sK7(X0))
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ decides(X0,sK7(X0),sK8(X0))
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f55,plain,
! [X1] :
( ~ sP1
| halts2(X1,X1)
| ~ program(X1)
| outputs(sK9,bad) ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
! [X1] :
( ~ sP1
| halts2(X1,X1)
| ~ program(X1)
| halts2(sK9,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
! [X1] :
( ~ sP1
| ~ halts2(X1,X1)
| ~ program(X1)
| outputs(sK9,good) ),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
! [X1] :
( ~ sP1
| ~ halts2(X1,X1)
| ~ program(X1)
| halts2(sK9,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f59,plain,
( ~ sP1
| program(sK9) ),
inference(cnf_transformation,[],[f32]) ).
fof(f63,plain,
! [X0] :
( sP0(sK10(X0),X0)
| halts2(sK10(X0),sK10(X0))
| ~ program(X0)
| sP1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f64,plain,
! [X0] :
( sP0(sK10(X0),X0)
| program(sK10(X0))
| ~ program(X0)
| sP1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X0] :
( sP0(sK10(X0),X0)
| ~ outputs(X0,good)
| ~ halts3(X0,sK10(X0),sK10(X0))
| ~ program(X0)
| sP1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
! [X1] :
( ~ sP3
| halts2(X1,X1)
| ~ program(X1)
| outputs(sK11,bad) ),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
! [X1] :
( ~ sP3
| halts2(X1,X1)
| ~ program(X1)
| halts2(sK11,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f68,plain,
! [X1] :
( ~ sP3
| ~ halts2(X1,X1)
| ~ program(X1)
| ~ halts2(sK11,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f69,plain,
( ~ sP3
| program(sK11) ),
inference(cnf_transformation,[],[f38]) ).
fof(f74,plain,
! [X0] :
( sP2(sK12(X0),X0)
| program(sK12(X0))
| ~ program(X0)
| sP3 ),
inference(cnf_transformation,[],[f41]) ).
fof(f75,plain,
! [X0] :
( sP2(sK12(X0),X0)
| ~ outputs(X0,good)
| ~ halts2(X0,sK12(X0))
| ~ program(X0)
| sP3 ),
inference(cnf_transformation,[],[f41]) ).
fof(f76,plain,
! [X2,X1] :
( ~ program(X1)
| decides(sK13,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f77,plain,
algorithm(sK13),
inference(cnf_transformation,[],[f42]) ).
tcf(c_49,plain,
! [X0: $i] :
( program(sK4)
| ~ algorithm(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_50,plain,
! [X0: $i] :
( program(sK4)
| program(sK5(X0))
| ~ algorithm(X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( decides(sK4,X1,X2)
| ~ algorithm(X0)
| ~ program(X1)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(sK5(X1))
| decides(sK4,X0,X2)
| ~ algorithm(X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(sK7(X2))
| halts3(X2,X0,X1)
| ~ program(X2)
| ~ program(X0)
| ~ halts2(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( outputs(X0,good)
| ~ program(X1)
| ~ program(X0)
| ~ halts2(X1,X2)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( outputs(X2,good)
| program(sK7(X2))
| ~ program(X2)
| ~ program(X0)
| ~ halts2(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts2(X1,X2)
| halts3(X0,X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(sK7(X1))
| halts2(X0,X2)
| halts3(X1,X0,X2)
| ~ program(X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( outputs(X0,bad)
| halts2(X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( outputs(X1,bad)
| program(sK7(X1))
| halts2(X0,X2)
| ~ program(X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_61,plain,
( program(sK9)
| ~ sP1 ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_62,plain,
! [X0: $i] :
( halts2(sK9,X0)
| ~ sP1
| ~ program(X0)
| ~ halts2(X0,X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_63,plain,
! [X0: $i] :
( outputs(sK9,good)
| ~ sP1
| ~ program(X0)
| ~ halts2(X0,X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_64,plain,
! [X0: $i] :
( halts2(sK9,X0)
| halts2(X0,X0)
| ~ sP1
| ~ program(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_65,plain,
! [X0: $i] :
( outputs(sK9,bad)
| halts2(X0,X0)
| ~ sP1
| ~ program(X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_69,plain,
! [X0: $i] :
( sP1
| sP0(sK10(X0),X0)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts3(X0,sK10(X0),sK10(X0)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_70,plain,
! [X0: $i] :
( sP1
| program(sK10(X0))
| sP0(sK10(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_71,plain,
! [X0: $i] :
( sP1
| sP0(sK10(X0),X0)
| halts2(sK10(X0),sK10(X0))
| ~ program(X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_72,plain,
( program(sK11)
| ~ sP3 ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_73,plain,
! [X0: $i] :
( ~ sP3
| ~ program(X0)
| ~ halts2(sK11,X0)
| ~ halts2(X0,X0) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_74,plain,
! [X0: $i] :
( halts2(sK11,X0)
| halts2(X0,X0)
| ~ sP3
| ~ program(X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_75,plain,
! [X0: $i] :
( outputs(sK11,bad)
| halts2(X0,X0)
| ~ sP3
| ~ program(X0) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_79,plain,
! [X0: $i] :
( sP3
| sP2(sK12(X0),X0)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(X0,sK12(X0)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_80,plain,
! [X0: $i] :
( sP3
| program(sK12(X0))
| sP2(sK12(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_82,negated_conjecture,
algorithm(sK13),
inference(cnf_transformation,[],[f77]) ).
tcf(c_83,negated_conjecture,
! [X0: $i,X1: $i] :
( decides(sK13,X0,X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_115,plain,
! [X0: $i] :
( halts2(sK9,X0)
| ~ program(X0)
| ~ sP1 ),
inference(global_subsumption_just,[status(thm)],[c_64,c_64,c_62]) ).
tcf(c_116,plain,
! [X0: $i] :
( halts2(sK9,X0)
| ~ sP1
| ~ program(X0) ),
inference(renaming,[status(thm)],[c_115]) ).
tcf(c_118,plain,
! [X0: $i] :
( halts2(sK9,X0)
| ~ sP1
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_116]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ decides(X0,sK7(X0),sK8(X0))
| ~ program(X0)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_57,c_53]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(renaming,[status(thm)],[c_120]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ program(X0)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_121]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i] :
( program(sK7(X1))
| halts3(X1,X0,X2)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58,c_54]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i] :
( decides(sK4,X0,X1)
| ~ program(X0)
| ~ decides(sK13,sK5(sK13),sK6(sK13)) ),
inference(resolution,[status(thm)],[c_51,c_82]) ).
tcf(c_371,plain,
( program(sK4)
| program(sK5(sK13)) ),
inference(resolution,[status(thm)],[c_50,c_82]) ).
tcf(c_378,plain,
( program(sK4)
| ~ decides(sK13,sK5(sK13),sK6(sK13)) ),
inference(resolution,[status(thm)],[c_49,c_82]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i] :
( program(sK5(sK13))
| decides(sK4,X0,X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c_52,c_82]) ).
tcf(c_423,plain,
! [X0: $i] :
( sP1
| sP0(sK10(X0),X0)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ program(sK10(X0))
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(resolution,[status(thm)],[c_123,c_69]) ).
tcf(c_425,plain,
! [X0: $i] :
( sP1
| sP0(sK10(X0),X0)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_423,c_70,c_423]) ).
tcf(c_459,plain,
! [X0: $i] :
( sP1
| program(sK7(X0))
| sP0(sK10(X0),X0)
| ~ program(X0)
| ~ outputs(X0,good)
| ~ program(sK10(X0)) ),
inference(resolution,[status(thm)],[c_306,c_69]) ).
tcf(c_461,plain,
! [X0: $i] :
( sP1
| program(sK7(X0))
| sP0(sK10(X0),X0)
| ~ program(X0)
| ~ outputs(X0,good) ),
inference(global_subsumption_just,[status(thm)],[c_459,c_70,c_459]) ).
tcf(c_2643,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ program(X0)
| halts2(X0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_75]) ).
tcf(c_2645,plain,
( iPr_def_10
| outputs(sK9,bad)
| ~ sP1 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_65]) ).
tcf(c_2646,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ program(X0)
| ~ halts2(X0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_63]) ).
tcf(c_2647,plain,
( iPr_def_11
| outputs(sK9,good)
| ~ sP1 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_63]) ).
tcf(c_2648,plain,
! [X0: $i] :
( ~ iPr_def_12
| program(sK7(X0))
| ~ program(X0)
| outputs(X0,bad) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_60]) ).
tcf(c_2649,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_13
| ~ program(X0)
| halts2(X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_60]) ).
tcf(c_2650,plain,
( iPr_def_13
| iPr_def_12 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_60]) ).
tcf(c_2651,plain,
! [X0: $i] :
( ~ iPr_def_14
| ~ program(X0)
| outputs(X0,bad)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_59]) ).
tcf(c_2652,plain,
( iPr_def_14
| iPr_def_13 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_59]) ).
tcf(c_2653,plain,
! [X0: $i] :
( ~ iPr_def_15
| program(sK7(X0))
| ~ program(X0)
| outputs(X0,good) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_56]) ).
tcf(c_2654,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_16
| ~ program(X0)
| ~ halts2(X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_16])],[c_56]) ).
tcf(c_2655,plain,
( iPr_def_16
| iPr_def_15 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_56]) ).
tcf(c_2656,plain,
! [X0: $i] :
( ~ iPr_def_17
| ~ program(X0)
| outputs(X0,good)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_17])],[c_55]) ).
tcf(c_2657,plain,
( iPr_def_17
| iPr_def_16 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_55]) ).
tcf(c_2658,definition,
iPr_def_18 = sK5(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_2659,definition,
iPr_def_19 = sK6(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_2660,plain,
! [X0: $i,X1: $i] :
( program(iPr_def_18)
| decides(sK4,X0,X1)
| ~ program(X0) ),
inference(demodulation,[status(thm)],[c_385,c_2658]) ).
tcf(c_2661,plain,
( program(sK4)
| ~ decides(sK13,iPr_def_18,iPr_def_19) ),
inference(demodulation,[status(thm)],[c_378,c_2659]) ).
tcf(c_2662,plain,
( program(iPr_def_18)
| program(sK4) ),
inference(demodulation,[status(thm)],[c_371]) ).
tcf(c_2663,plain,
! [X0: $i,X1: $i] :
( decides(sK4,X0,X1)
| ~ program(X0)
| ~ decides(sK13,iPr_def_18,iPr_def_19) ),
inference(demodulation,[status(thm)],[c_360]) ).
tcf(c_2664,negated_conjecture,
! [X0: $i,X1: $i] :
( decides(sK13,X0,X1)
| ~ program(X0) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_3293,plain,
( program(sK4)
| ~ program(iPr_def_18) ),
inference(superposition,[status(thm)],[c_2664,c_2661]) ).
tcf(c_3296,plain,
program(sK4),
inference(global_subsumption_just,[status(thm)],[c_3293,c_2662,c_3293]) ).
tcf(c_3310,plain,
! [X0: $i,X1: $i] :
( decides(sK4,X0,X1)
| ~ program(iPr_def_18)
| ~ program(X0) ),
inference(superposition,[status(thm)],[c_2664,c_2663]) ).
tcf(c_3315,plain,
! [X0: $i,X1: $i] :
( decides(sK4,X0,X1)
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3310,c_2660,c_3310]) ).
tcf(c_3440,plain,
( halts2(sK11,sK11)
| ~ sP3
| ~ program(sK11) ),
inference(equality_factoring,[status(thm)],[c_74]) ).
tcf(c_3485,plain,
( halts2(sK11,sK11)
| ~ sP3 ),
inference(global_subsumption_just,[status(thm)],[c_3440,c_72,c_3440]) ).
tcf(c_3491,plain,
( ~ sP3
| ~ program(sK11)
| ~ halts2(sK11,sK11) ),
inference(superposition,[status(thm)],[c_3485,c_73]) ).
tcf(c_3517,plain,
( ~ iPr_def_11
| ~ sP1
| ~ program(sK9) ),
inference(superposition,[status(thm)],[c_118,c_2646]) ).
tcf(c_3572,plain,
( ~ iPr_def_11
| ~ sP1 ),
inference(global_subsumption_just,[status(thm)],[c_3517,c_61,c_3517]) ).
tcf(c_3578,plain,
( outputs(sK9,good)
| ~ sP1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_2647,c_3572]) ).
tcf(c_3594,plain,
! [X0: $i] :
( sP1
| sP0(sK10(X0),X0)
| ~ iPr_def_16
| ~ program(X0)
| ~ program(sK10(X0)) ),
inference(superposition,[status(thm)],[c_71,c_2654]) ).
tcf(c_3764,plain,
! [X0: $i] :
( sP1
| sP0(sK10(X0),X0)
| ~ program(X0)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_425,c_70,c_425,c_2656,c_2657,c_3594]) ).
tcf(c_3776,plain,
( sP1
| sP0(sK10(sK4),sK4)
| ~ program(sK4)
| ~ program(sK7(sK4)) ),
inference(superposition,[status(thm)],[c_3315,c_3764]) ).
tcf(c_3777,plain,
( sP1
| sP0(sK10(sK4),sK4)
| ~ program(sK7(sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3776,c_3296]) ).
tcf(c_3972,plain,
! [X0: $i] :
( sP1
| program(sK7(X0))
| sP0(sK10(X0),X0)
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_461,c_70,c_461,c_2653,c_2655,c_3594]) ).
tcf(c_4082,plain,
( outputs(sK4,bad)
| ~ iPr_def_14
| ~ program(sK4)
| ~ program(sK7(sK4)) ),
inference(superposition,[status(thm)],[c_3315,c_2651]) ).
tcf(c_4083,plain,
( outputs(sK4,bad)
| ~ iPr_def_14
| ~ program(sK7(sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4082,c_3296]) ).
fof(f20,definition,
! [X1,X0] :
( ~ sP0(X1,X0)
| ( ~ halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f21,definition,
( ~ sP1
| ? [X2] :
( ! [X3] :
( ( halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ~ halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,good)
& halts2(X2,X3) ) ) )
& program(X2) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f22,plain,
( ! [X0] :
( ? [X1] :
( sP0(X1,X0)
| ( halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X1) ) ) )
| ~ program(X0) )
| sP1 ),
inference(definition_folding,[],[f16,f21,f20]) ).
fof(f23,definition,
! [X1,X0] :
( ~ sP2(X1,X0)
| ( ~ halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts2(X0,X1) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f24,definition,
( ~ sP3
| ? [X2] :
( ! [X3] :
( ( halts2(X3,X3)
| ~ program(X3)
| ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ~ halts2(X3,X3)
| ~ program(X3)
| ~ halts2(X2,X3) ) )
& program(X2) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f25,plain,
( ! [X0] :
( ? [X1] :
( sP2(X1,X0)
| ( halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,good)
| ~ halts2(X0,X1) ) ) )
| ~ program(X0) )
| sP3 ),
inference(definition_folding,[],[f18,f24,f23]) ).
fof(f33,plain,
! [X1,X0] :
( ~ sP0(X1,X0)
| ( ~ halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) ) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( ~ halts2(X0,X0)
& program(X0)
& ( ~ outputs(X1,bad)
| ~ halts3(X1,X0,X0) ) ) ),
inference(rectify,[],[f33]) ).
fof(f39,plain,
! [X1,X0] :
( ~ sP2(X1,X0)
| ( ~ halts2(X1,X1)
& program(X1)
& ( ~ outputs(X0,bad)
| ~ halts2(X0,X1) ) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ( ~ halts2(X0,X0)
& program(X0)
& ( ~ outputs(X1,bad)
| ~ halts2(X1,X0) ) ) ),
inference(rectify,[],[f39]) ).
fof(f60,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ halts2(X0,X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| program(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f62,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ outputs(X1,bad)
| ~ halts3(X1,X0,X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ halts2(X0,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f71,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| program(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f72,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ outputs(X1,bad)
| ~ halts2(X1,X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ~ outputs(X0,bad)
| ~ sP0(X1,X0)
| ~ halts3(X0,X1,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( program(X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0,X1)
| ~ halts2(X0,X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ~ outputs(X0,bad)
| ~ sP2(X1,X0)
| ~ halts2(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( program(X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ~ sP2(X0,X1)
| ~ halts2(X0,X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_144,plain,
! [X0: $i] :
( sP3
| program(sK12(X0))
| ~ program(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_80,c_77]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i] :
( ~ program(X1)
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ sP0(X1,X0)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(resolution,[status(thm)],[c_123,c_66]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i] :
( ~ program(X0)
| ~ outputs(X0,bad)
| ~ sP0(X1,X0)
| ~ decides(X0,sK7(X0),sK8(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_406,c_67]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i] :
( program(sK7(X1))
| ~ program(X1)
| ~ program(X0)
| ~ outputs(X1,bad)
| ~ sP0(X0,X1) ),
inference(resolution,[status(thm)],[c_306,c_66]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] :
( program(sK7(X1))
| ~ program(X1)
| ~ sP0(X0,X1)
| ~ outputs(X1,bad) ),
inference(global_subsumption_just,[status(thm)],[c_443,c_67,c_443]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i] :
( program(sK7(X1))
| ~ program(X1)
| ~ outputs(X1,bad)
| ~ sP0(X0,X1) ),
inference(renaming,[status(thm)],[c_445]) ).
tcf(c_514,plain,
! [X0: $i] :
( sP3
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ outputs(X0,good)
| ~ halts2(X0,sK12(X0)) ),
inference(resolution,[status(thm)],[c_76,c_79]) ).
tcf(c_532,plain,
! [X0: $i] :
( sP3
| ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(X0,sK12(X0))
| ~ halts2(sK12(X0),sK12(X0)) ),
inference(resolution,[status(thm)],[c_78,c_79]) ).
tcf(c_3412,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_13
| ~ program(X0)
| ~ sP0(X0,X1) ),
inference(superposition,[status(thm)],[c_2649,c_68]) ).
tcf(c_3492,plain,
! [X0: $i] :
( ~ sP3
| ~ sP0(sK11,X0) ),
inference(superposition,[status(thm)],[c_3485,c_68]) ).
tcf(c_3499,plain,
~ sP3,
inference(global_subsumption_just,[status(thm)],[c_3492,c_72,c_3485,c_3491]) ).
tcf(c_3651,plain,
! [X0: $i] :
( ~ program(sK4)
| ~ outputs(sK4,bad)
| ~ program(sK7(sK4))
| ~ sP0(X0,sK4) ),
inference(superposition,[status(thm)],[c_3315,c_418]) ).
tcf(c_3652,plain,
! [X0: $i] :
( ~ outputs(sK4,bad)
| ~ program(sK7(sK4))
| ~ sP0(X0,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3651,c_3296]) ).
tcf(c_3676,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_13
| ~ sP0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3412,c_67,c_3412]) ).
tcf(c_3825,plain,
( sP1
| ~ iPr_def_13
| ~ program(sK7(sK4)) ),
inference(superposition,[status(thm)],[c_3777,c_3676]) ).
tcf(c_3885,plain,
! [X0: $i,X1: $i] :
( program(sK7(X1))
| ~ iPr_def_12
| ~ program(X1)
| ~ sP0(X0,X1) ),
inference(superposition,[status(thm)],[c_2648,c_446]) ).
tcf(c_3917,plain,
! [X0: $i,X1: $i] :
( program(sK7(X1))
| ~ sP0(X0,X1)
| ~ program(X1) ),
inference(global_subsumption_just,[status(thm)],[c_3885,c_67,c_2650,c_3412,c_3885]) ).
tcf(c_3918,plain,
! [X0: $i,X1: $i] :
( program(sK7(X1))
| ~ program(X1)
| ~ sP0(X0,X1) ),
inference(renaming,[status(thm)],[c_3917]) ).
tcf(c_3979,plain,
! [X0: $i] :
( sP1
| program(sK7(X0))
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3972,c_3918]) ).
tcf(c_4007,plain,
( sP1
| ~ iPr_def_13
| ~ program(sK4) ),
inference(superposition,[status(thm)],[c_3979,c_3825]) ).
tcf(c_4008,plain,
! [X0: $i] :
( sP1
| ~ program(sK4)
| ~ outputs(sK4,bad)
| ~ sP0(X0,sK4) ),
inference(superposition,[status(thm)],[c_3979,c_3652]) ).
tcf(c_4009,plain,
( sP1
| ~ iPr_def_13 ),
inference(forward_subsumption_resolution,[status(thm)],[c_4007,c_3296]) ).
tcf(c_4018,plain,
! [X0: $i] :
( sP1
| ~ outputs(sK4,bad)
| ~ sP0(X0,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4008,c_3296]) ).
tcf(c_4092,plain,
( sP3
| program(sK12(sK9))
| ~ program(sK9) ),
inference(instantiation,[status(thm)],[c_144]) ).
tcf(c_4242,plain,
! [X0: $i] :
( ~ halts2(X0,sK12(X0))
| ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_514,c_72,c_514,c_3485,c_3491]) ).
tcf(c_4243,plain,
! [X0: $i] :
( ~ program(X0)
| ~ outputs(X0,bad)
| ~ outputs(X0,good)
| ~ halts2(X0,sK12(X0)) ),
inference(renaming,[status(thm)],[c_4242]) ).
tcf(c_4254,plain,
( ~ sP1
| ~ program(sK9)
| ~ outputs(sK9,bad)
| ~ outputs(sK9,good)
| ~ program(sK12(sK9)) ),
inference(superposition,[status(thm)],[c_118,c_4243]) ).
tcf(c_4300,plain,
( sP1
| outputs(sK4,bad)
| ~ iPr_def_14
| ~ program(sK4) ),
inference(superposition,[status(thm)],[c_3979,c_4083]) ).
tcf(c_4301,plain,
( sP1
| outputs(sK4,bad)
| ~ iPr_def_14 ),
inference(forward_subsumption_resolution,[status(thm)],[c_4300,c_3296]) ).
tcf(c_4305,plain,
( sP1
| outputs(sK4,bad) ),
inference(global_subsumption_just,[status(thm)],[c_4301,c_2652,c_4009,c_4301]) ).
tcf(c_4311,plain,
! [X0: $i] :
( sP1
| ~ sP0(X0,sK4) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4018,c_4305]) ).
tcf(c_4321,plain,
( sP1
| ~ program(sK7(sK4)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3777,c_4311]) ).
tcf(c_4328,plain,
( sP1
| ~ program(sK4) ),
inference(superposition,[status(thm)],[c_3979,c_4321]) ).
tcf(c_4329,plain,
sP1,
inference(forward_subsumption_resolution,[status(thm)],[c_4328,c_3296]) ).
tcf(c_4332,plain,
outputs(sK9,good),
inference(backward_subsumption_resolution,[status(thm)],[c_3578,c_4329]) ).
tcf(c_4333,plain,
( iPr_def_10
| outputs(sK9,bad) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2645,c_4329]) ).
tcf(c_4334,plain,
! [X0: $i] :
( halts2(sK9,X0)
| ~ program(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_118,c_4329]) ).
tcf(c_4335,plain,
program(sK9),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_4329]) ).
tcf(c_4353,plain,
! [X0: $i] :
( ~ halts2(sK12(X0),sK12(X0))
| ~ halts2(X0,sK12(X0))
| ~ outputs(X0,good)
| ~ program(X0) ),
inference(global_subsumption_just,[status(thm)],[c_532,c_72,c_532,c_3485,c_3491]) ).
tcf(c_4354,plain,
! [X0: $i] :
( ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(X0,sK12(X0))
| ~ halts2(sK12(X0),sK12(X0)) ),
inference(renaming,[status(thm)],[c_4353]) ).
tcf(c_4365,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ program(X0)
| ~ outputs(X0,good)
| ~ program(sK12(X0))
| ~ halts2(X0,sK12(X0)) ),
inference(superposition,[status(thm)],[c_2643,c_4354]) ).
tcf(c_4381,plain,
iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_4333,c_61,c_2645,c_3499,c_3578,c_4092,c_4254,c_4329]) ).
tcf(c_4384,plain,
! [X0: $i] :
( halts2(X0,X0)
| ~ program(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2643,c_4381]) ).
tcf(c_4410,plain,
! [X0: $i] :
( ~ program(X0)
| ~ outputs(X0,good)
| ~ program(sK12(X0))
| ~ halts2(X0,sK12(X0)) ),
inference(superposition,[status(thm)],[c_4384,c_4354]) ).
tcf(c_4492,plain,
! [X0: $i] :
( ~ program(X0)
| ~ outputs(X0,good)
| ~ halts2(X0,sK12(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_4410,c_61,c_144,c_2645,c_3499,c_3578,c_4092,c_4254,c_4329,c_4365]) ).
tcf(c_4502,plain,
( ~ program(sK9)
| ~ outputs(sK9,good)
| ~ program(sK12(sK9)) ),
inference(superposition,[status(thm)],[c_4334,c_4492]) ).
tcf(c_4506,plain,
~ program(sK12(sK9)),
inference(forward_subsumption_resolution,[status(thm)],[c_4502,c_4335,c_4332]) ).
tcf(c_4507,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4506,c_4329,c_4092,c_3499,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.37 % Computer : n016.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 07:48:20 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.40 Running first-order theorem proving
% 0.16/5.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.41
% 0.16/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.41
% 0.16/5.41 % Detected problem language: tptp
% 0.16/5.43 % Proving...
% 2.91/6.28 % SZS status Started for theBenchmark.p
% 2.91/6.28 % SZS status Theorem for theBenchmark.p
% 2.91/6.28
% 2.91/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.91/6.28
% 2.91/6.28 % ------ iProver source info
% 2.91/6.28
% 2.91/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.91/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.91/6.28 % git: non_committed_changes: false
% 2.91/6.28
% 2.91/6.28 % ------ Parsing...
% 2.91/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.91/6.28
% 2.91/6.28 % ------ 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 %
% 2.91/6.28
% 2.91/6.28 % ------ Preprocessing... gs_s sp: 11 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.91/6.28
% 2.91/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.91/6.28 % ------ Proving...
% 2.91/6.28 % ------ Problem Properties
% 2.91/6.28
% 2.91/6.28 %
% 2.91/6.28 % clauses 39
% 2.91/6.28 % conjectures 1
% 2.91/6.28 % EPR 23
% 2.91/6.28 % Horn 21
% 2.91/6.28 % unary 2
% 2.91/6.28 % binary 11
% 2.91/6.28 % lits 121
% 2.91/6.28 % lits eq 2
% 2.91/6.28 % fd_pure 0
% 2.91/6.28 % fd_pseudo 0
% 2.91/6.28 % fd_cond 0
% 2.91/6.28 % fd_pseudo_cond 0
% 2.91/6.28 % AC symbols 0
% 2.91/6.28
% 2.91/6.28 % ------ Schedule dynamic 5 is on
% 2.91/6.28
% 2.91/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.91/6.28
% 2.91/6.28
% 2.91/6.28 % ------
% 2.91/6.28 % Current options:
% 2.91/6.28 % ------
% 2.91/6.28
% 2.91/6.28
% 2.91/6.28 %
% 2.91/6.28
% 2.91/6.28 % ------ Proving...
% 2.91/6.28 %
% 2.91/6.28
% 2.91/6.28 % SZS status Theorem for theBenchmark.p
% 2.91/6.28
% 2.91/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.91/6.29
% 2.91/6.29
%------------------------------------------------------------------------------