%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 1.32s 16.50s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 96 ( 15 unt; 0 def)
% Number of atoms : 320 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 392 ( 168 ~; 155 |; 54 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 14 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 172 ( 0 sgn 149 !; 23 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( program_program_decides(X0)
<=> ( program_decides(X0)
& program(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_program_decides_def) ).
fof(f4,axiom,
! [X0,X1] :
( program_halts2(X0,X1)
<=> ( halts2(X0,X1)
& program(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_def) ).
fof(f6,axiom,
! [X0,X1] :
( program_not_halts2(X0,X1)
<=> ( ~ halts2(X0,X1)
& program(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_def) ).
fof(f7,axiom,
! [X0,X1,X2] :
( halts2_outputs(X0,X1,X2)
<=> ( outputs(X0,X2)
& halts2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts2_outputs_def) ).
fof(f11,axiom,
! [X0,X1,X2] :
( program_not_halts2_halts2_outputs(X0,X1,X2)
<=> ( program_not_halts2(X1,X1)
=> halts2_outputs(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs_def) ).
fof(f12,axiom,
( ? [X0] : algorithm_program_decides(X0)
=> ? [X1] : program_program_decides(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f13,axiom,
! [X0] :
( program_program_decides(X0)
=> ! [X1,X2] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
& program_halts2_halts3_outputs(X0,X1,X2,good) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f14,axiom,
( ? [X0] :
( ! [X1] :
( program_not_halts2_halts3_outputs(X0,X1,X1,bad)
& program_halts2_halts3_outputs(X0,X1,X1,good) )
& program(X0) )
=> ? [X2] :
( ! [X1] :
( program_not_halts2_halts2_outputs(X2,X1,bad)
& program_halts2_halts2_outputs(X2,X1,good) )
& program(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f15,axiom,
( ? [X0] :
( ! [X1] :
( program_not_halts2_halts2_outputs(X0,X1,bad)
& program_halts2_halts2_outputs(X0,X1,good) )
& program(X0) )
=> ? [X2] :
( ! [X1] :
( program_not_halts2_halts2_outputs(X2,X1,good)
& ( program_halts2(X1,X1)
=> ~ halts2(X2,X1) ) )
& program(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f16,conjecture,
~ ? [X0] : algorithm_program_decides(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f17,negated_conjecture,
~ ~ ? [X0] : algorithm_program_decides(X0),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
( ? [X0] :
( ! [X1] :
( program_not_halts2_halts3_outputs(X0,X1,X1,bad)
& program_halts2_halts3_outputs(X0,X1,X1,good) )
& program(X0) )
=> ? [X2] :
( ! [X3] :
( program_not_halts2_halts2_outputs(X2,X3,bad)
& program_halts2_halts2_outputs(X2,X3,good) )
& program(X2) ) ),
inference(rectify,[],[f14]) ).
fof(f19,plain,
( ? [X0] :
( ! [X1] :
( program_not_halts2_halts2_outputs(X0,X1,bad)
& program_halts2_halts2_outputs(X0,X1,good) )
& program(X0) )
=> ? [X2] :
( ! [X3] :
( program_not_halts2_halts2_outputs(X2,X3,good)
& ( program_halts2(X3,X3)
=> ~ halts2(X2,X3) ) )
& program(X2) ) ),
inference(rectify,[],[f15]) ).
fof(f20,plain,
? [X0] : algorithm_program_decides(X0),
inference(flattening,[],[f17]) ).
fof(f25,plain,
! [X0,X1,X2] :
( program_not_halts2_halts2_outputs(X0,X1,X2)
<=> ( ~ program_not_halts2(X1,X1)
| halts2_outputs(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f26,plain,
( ! [X0] : ~ algorithm_program_decides(X0)
| ? [X1] : program_program_decides(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0] :
( ~ program_program_decides(X0)
| ! [X1,X2] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
& program_halts2_halts3_outputs(X0,X1,X2,good) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f28,plain,
( ! [X0] :
( ? [X1] :
( ~ program_not_halts2_halts3_outputs(X0,X1,X1,bad)
| ~ program_halts2_halts3_outputs(X0,X1,X1,good) )
| ~ program(X0) )
| ? [X2] :
( ! [X3] :
( program_not_halts2_halts2_outputs(X2,X3,bad)
& program_halts2_halts2_outputs(X2,X3,good) )
& program(X2) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f29,plain,
( ! [X0] :
( ? [X1] :
( ~ program_not_halts2_halts2_outputs(X0,X1,bad)
| ~ program_halts2_halts2_outputs(X0,X1,good) )
| ~ program(X0) )
| ? [X2] :
( ! [X3] :
( program_not_halts2_halts2_outputs(X2,X3,good)
& ( ~ program_halts2(X3,X3)
| ~ halts2(X2,X3) ) )
& program(X2) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0] :
( ( ~ program_program_decides(X0)
| ( program_decides(X0)
& program(X0) ) )
& ( ~ program_decides(X0)
| ~ program(X0)
| program_program_decides(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] :
( ( ~ program_program_decides(X0)
| ( program_decides(X0)
& program(X0) ) )
& ( ~ program_decides(X0)
| ~ program(X0)
| program_program_decides(X0) ) ),
inference(flattening,[],[f33]) ).
fof(f37,plain,
! [X0,X1] :
( ( ~ program_halts2(X0,X1)
| ( halts2(X0,X1)
& program(X0) ) )
& ( ~ halts2(X0,X1)
| ~ program(X0)
| program_halts2(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0,X1] :
( ( ~ program_halts2(X0,X1)
| ( halts2(X0,X1)
& program(X0) ) )
& ( ~ halts2(X0,X1)
| ~ program(X0)
| program_halts2(X0,X1) ) ),
inference(flattening,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ program_not_halts2(X0,X1)
| ( ~ halts2(X0,X1)
& program(X0) ) )
& ( halts2(X0,X1)
| ~ program(X0)
| program_not_halts2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0,X1] :
( ( ~ program_not_halts2(X0,X1)
| ( ~ halts2(X0,X1)
& program(X0) ) )
& ( halts2(X0,X1)
| ~ program(X0)
| program_not_halts2(X0,X1) ) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( ~ halts2_outputs(X0,X1,X2)
| ( outputs(X0,X2)
& halts2(X0,X1) ) )
& ( ~ outputs(X0,X2)
| ~ halts2(X0,X1)
| halts2_outputs(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( ~ halts2_outputs(X0,X1,X2)
| ( outputs(X0,X2)
& halts2(X0,X1) ) )
& ( ~ outputs(X0,X2)
| ~ halts2(X0,X1)
| halts2_outputs(X0,X1,X2) ) ),
inference(flattening,[],[f43]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( ~ program_not_halts2_halts2_outputs(X0,X1,X2)
| ~ program_not_halts2(X1,X1)
| halts2_outputs(X0,X1,X2) )
& ( ( program_not_halts2(X1,X1)
& ~ halts2_outputs(X0,X1,X2) )
| program_not_halts2_halts2_outputs(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( ~ program_not_halts2_halts2_outputs(X0,X1,X2)
| ~ program_not_halts2(X1,X1)
| halts2_outputs(X0,X1,X2) )
& ( ( program_not_halts2(X1,X1)
& ~ halts2_outputs(X0,X1,X2) )
| program_not_halts2_halts2_outputs(X0,X1,X2) ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
( ! [X1] : ~ algorithm_program_decides(X1)
| ? [X0] : program_program_decides(X0) ),
inference(rectify,[],[f26]) ).
fof(f54,plain,
( ! [X1] : ~ algorithm_program_decides(X1)
| program_program_decides(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f53]) ).
fof(f55,plain,
( ! [X2] :
( ? [X3] :
( ~ program_not_halts2_halts3_outputs(X2,X3,X3,bad)
| ~ program_halts2_halts3_outputs(X2,X3,X3,good) )
| ~ program(X2) )
| ? [X0] :
( ! [X1] :
( program_not_halts2_halts2_outputs(X0,X1,bad)
& program_halts2_halts2_outputs(X0,X1,good) )
& program(X0) ) ),
inference(rectify,[],[f28]) ).
fof(f56,plain,
( ! [X2] :
( ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good)
| ~ program(X2) )
| ( ! [X1] :
( program_not_halts2_halts2_outputs(sK3,X1,bad)
& program_halts2_halts2_outputs(sK3,X1,good) )
& program(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X3,sK4(X2))],[f55]) ).
fof(f57,plain,
( ! [X2] :
( ? [X3] :
( ~ program_not_halts2_halts2_outputs(X2,X3,bad)
| ~ program_halts2_halts2_outputs(X2,X3,good) )
| ~ program(X2) )
| ? [X0] :
( ! [X1] :
( program_not_halts2_halts2_outputs(X0,X1,good)
& ( ~ program_halts2(X1,X1)
| ~ halts2(X0,X1) ) )
& program(X0) ) ),
inference(rectify,[],[f29]) ).
fof(f58,plain,
( ! [X2] :
( ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program(X2) )
| ( ! [X1] :
( program_not_halts2_halts2_outputs(sK5,X1,good)
& ( ~ program_halts2(X1,X1)
| ~ halts2(sK5,X1) ) )
& program(sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X3,sK6(X2))],[f57]) ).
fof(f59,plain,
algorithm_program_decides(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f20]) ).
fof(f64,plain,
! [X0] :
( ~ program_program_decides(X0)
| program(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f71,plain,
! [X0,X1] :
( ~ halts2(X0,X1)
| ~ program(X0)
| program_halts2(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f77,plain,
! [X0,X1] :
( halts2(X0,X1)
| ~ program(X0)
| program_not_halts2(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ halts2_outputs(X0,X1,X2)
| halts2(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ program_not_halts2_halts2_outputs(X0,X1,X2)
| ~ program_not_halts2(X1,X1)
| halts2_outputs(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f93,plain,
! [X1] :
( ~ algorithm_program_decides(X1)
| program_program_decides(sK2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ program_program_decides(X0)
| program_not_halts2_halts3_outputs(X0,X1,X2,bad) ),
inference(cnf_transformation,[],[f27]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ program_program_decides(X0)
| program_halts2_halts3_outputs(X0,X1,X2,good) ),
inference(cnf_transformation,[],[f27]) ).
fof(f96,plain,
! [X2,X1] :
( ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good)
| ~ program(X2)
| program_not_halts2_halts2_outputs(sK3,X1,bad) ),
inference(cnf_transformation,[],[f56]) ).
fof(f97,plain,
! [X2,X1] :
( ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good)
| ~ program(X2)
| program_halts2_halts2_outputs(sK3,X1,good) ),
inference(cnf_transformation,[],[f56]) ).
fof(f98,plain,
! [X2] :
( ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good)
| ~ program(X2)
| program(sK3) ),
inference(cnf_transformation,[],[f56]) ).
fof(f99,plain,
! [X2,X1] :
( ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program(X2)
| program_not_halts2_halts2_outputs(sK5,X1,good) ),
inference(cnf_transformation,[],[f58]) ).
fof(f100,plain,
! [X2,X1] :
( ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program(X2)
| ~ program_halts2(X1,X1)
| ~ halts2(sK5,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f101,plain,
! [X2] :
( ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program(X2)
| program(sK5) ),
inference(cnf_transformation,[],[f58]) ).
fof(f102,plain,
algorithm_program_decides(sK7),
inference(cnf_transformation,[],[f59]) ).
tcf(c_53,plain,
! [X0: $i] :
( program(X0)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( program_halts2(X0,X1)
| ~ program(X0)
| ~ halts2(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( program_not_halts2(X0,X1)
| halts2(X0,X1)
| ~ program(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts2(X0,X1)
| ~ halts2_outputs(X0,X1,X2) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( halts2_outputs(X0,X1,X2)
| ~ program_not_halts2(X1,X1)
| ~ program_not_halts2_halts2_outputs(X0,X1,X2) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_82,plain,
! [X0: $i] :
( program_program_decides(sK2)
| ~ algorithm_program_decides(X0) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( program_halts2_halts3_outputs(X0,X1,X2,good)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_85,plain,
! [X0: $i] :
( program(sK3)
| ~ program(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),good) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( program_halts2_halts2_outputs(sK3,X1,good)
| ~ program(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),good) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( program_not_halts2_halts2_outputs(sK3,X1,bad)
| ~ program(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),good) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_88,plain,
! [X0: $i] :
( program(sK5)
| ~ program(X0)
| ~ program_not_halts2_halts2_outputs(X0,sK6(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6(X0),good) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( ~ program(X0)
| ~ halts2(sK5,X1)
| ~ program_halts2(X1,X1)
| ~ program_not_halts2_halts2_outputs(X0,sK6(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6(X0),good) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( program_not_halts2_halts2_outputs(sK5,X1,good)
| ~ program(X0)
| ~ program_not_halts2_halts2_outputs(X0,sK6(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6(X0),good) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_91,negated_conjecture,
algorithm_program_decides(sK7),
inference(cnf_transformation,[],[f102]) ).
tcf(c_354,plain,
program_program_decides(sK2),
inference(resolution,[status(thm)],[c_82,c_91]) ).
tcf(c_1029,plain,
! [X0: $i,X1: $i] :
( program_not_halts2_halts2_outputs(sK3,X1,bad)
| ~ program_program_decides(X0)
| ~ program(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad) ),
inference(resolution,[status(thm)],[c_83,c_87]) ).
tcf(c_1031,plain,
! [X0: $i,X1: $i] :
( program_not_halts2_halts2_outputs(sK3,X1,bad)
| ~ program_program_decides(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad) ),
inference(global_subsumption_just,[status(thm)],[c_1029,c_53,c_1029]) ).
tcf(c_1040,plain,
! [X0: $i,X1: $i] :
( program_not_halts2_halts2_outputs(sK3,X1,bad)
| ~ program_program_decides(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1031,c_84]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i] :
( program_halts2_halts2_outputs(sK3,X1,good)
| ~ program_program_decides(X0)
| ~ program(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad) ),
inference(resolution,[status(thm)],[c_83,c_86]) ).
tcf(c_1046,plain,
! [X0: $i,X1: $i] :
( program_halts2_halts2_outputs(sK3,X1,good)
| ~ program_program_decides(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad) ),
inference(global_subsumption_just,[status(thm)],[c_1044,c_53,c_1044]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i] :
( program_halts2_halts2_outputs(sK3,X1,good)
| ~ program_program_decides(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1046,c_84]) ).
tcf(c_1059,plain,
! [X0: $i] :
( program(sK3)
| ~ program_program_decides(X0)
| ~ program(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad) ),
inference(resolution,[status(thm)],[c_83,c_85]) ).
tcf(c_1061,plain,
! [X0: $i] :
( program(sK3)
| ~ program_program_decides(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad) ),
inference(global_subsumption_just,[status(thm)],[c_1059,c_53,c_1059]) ).
tcf(c_1070,plain,
! [X0: $i] :
( program(sK3)
| ~ program_program_decides(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1061,c_84]) ).
tcf(c_1151,plain,
program(sK3),
inference(resolution,[status(thm)],[c_1070,c_354]) ).
tcf(c_1155,plain,
! [X0: $i] : program_halts2_halts2_outputs(sK3,X0,good),
inference(resolution,[status(thm)],[c_1055,c_354]) ).
tcf(c_1160,plain,
! [X0: $i] : program_not_halts2_halts2_outputs(sK3,X0,bad),
inference(resolution,[status(thm)],[c_1040,c_354]) ).
tcf(c_1655,plain,
! [X0: $i] :
( program_not_halts2_halts2_outputs(sK5,X0,good)
| ~ program(sK3)
| ~ program_not_halts2_halts2_outputs(sK3,sK6(sK3),bad) ),
inference(resolution,[status(thm)],[c_90,c_1155]) ).
tcf(c_1657,plain,
! [X0: $i] :
( program_not_halts2_halts2_outputs(sK5,X0,good)
| ~ program_not_halts2_halts2_outputs(sK3,sK6(sK3),bad) ),
inference(global_subsumption_just,[status(thm)],[c_1655,c_1151,c_1655]) ).
tcf(c_1664,plain,
! [X0: $i] : program_not_halts2_halts2_outputs(sK5,X0,good),
inference(forward_subsumption_resolution,[status(thm)],[c_1657,c_1160]) ).
tcf(c_1667,plain,
! [X0: $i] :
( ~ program(sK3)
| ~ halts2(sK5,X0)
| ~ program_halts2(X0,X0)
| ~ program_not_halts2_halts2_outputs(sK3,sK6(sK3),bad) ),
inference(resolution,[status(thm)],[c_89,c_1155]) ).
tcf(c_1669,plain,
! [X0: $i] :
( ~ program_not_halts2_halts2_outputs(sK3,sK6(sK3),bad)
| ~ program_halts2(X0,X0)
| ~ halts2(sK5,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1667,c_1151,c_1667]) ).
tcf(c_1670,plain,
! [X0: $i] :
( ~ halts2(sK5,X0)
| ~ program_halts2(X0,X0)
| ~ program_not_halts2_halts2_outputs(sK3,sK6(sK3),bad) ),
inference(renaming,[status(thm)],[c_1669]) ).
tcf(c_1678,plain,
! [X0: $i] :
( ~ halts2(sK5,X0)
| ~ program_halts2(X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1670,c_1160]) ).
tcf(c_1682,plain,
( program(sK5)
| ~ program(sK3)
| ~ program_not_halts2_halts2_outputs(sK3,sK6(sK3),bad) ),
inference(resolution,[status(thm)],[c_88,c_1155]) ).
tcf(c_1683,plain,
( program(sK5)
| ~ program_not_halts2_halts2_outputs(sK3,sK6(sK3),bad) ),
inference(global_subsumption_just,[status(thm)],[c_1682,c_1151,c_1682]) ).
tcf(c_1689,plain,
program(sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_1683,c_1160]) ).
tcf(c_1707,plain,
! [X0: $i] :
( halts2_outputs(sK5,X0,good)
| ~ program_not_halts2(X0,X0) ),
inference(resolution,[status(thm)],[c_81,c_1664]) ).
tcf(c_1734,plain,
! [X0: $i] :
( ~ program(X0)
| ~ halts2(sK5,X0)
| ~ halts2(X0,X0) ),
inference(resolution,[status(thm)],[c_58,c_1678]) ).
tcf(c_1781,plain,
! [X0: $i] :
( halts2(X0,X0)
| halts2_outputs(sK5,X0,good)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c_64,c_1707]) ).
tcf(c_1870,plain,
! [X0: $i] :
( halts2(sK5,X0)
| halts2(X0,X0)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c_68,c_1781]) ).
tcf(c_2179,plain,
halts2(sK5,sK5),
inference(resolution,[status(thm)],[c_1870,c_1689]) ).
tcf(c_2187,plain,
~ halts2(sK5,sK5),
inference(resolution,[status(thm)],[c_1734,c_1689]) ).
tcf(c_2188,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2187,c_2179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/15.74 % Computer : n012.cluster.edu
% 0.04/15.74 % Model : x86_64 x86_64
% 0.04/15.74 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.74 % Memory : 8046.5625MB
% 0.04/15.74 % OS : Linux 6.8.0-71-generic
% 0.04/15.74 % CPULimit : 300
% 0.04/15.74 % WCLimit : 300
% 0.04/15.74 % DateTime : Fri Sep 25 07:43:58 UTC 2026
% 0.04/15.74 % CPUTime :
% 0.04/15.74 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/15.76 Running first-order theorem proving
% 0.04/15.76 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
% 0.04/15.77
% 0.04/15.77 % ======== iProver multi-core TPTP/SMT =========
% 0.04/15.77
% 0.04/15.77 % Detected problem language: tptp
% 0.04/15.77 % Proving...
% 1.32/16.50 % SZS status Started for theBenchmark.p
% 1.32/16.50 % SZS status Theorem for theBenchmark.p
% 1.32/16.50
% 1.32/16.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.32/16.50
% 1.32/16.50 % ------ iProver source info
% 1.32/16.50
% 1.32/16.50 % git: date: 2026-07-19 20:42:38 +0200
% 1.32/16.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.32/16.50 % git: non_committed_changes: false
% 1.32/16.50
% 1.32/16.50 % ------ Parsing...
% 1.32/16.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.32/16.50
% 1.32/16.50 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sf_s rm: 7 0s sf_e pe_s pe:1:0s%
% 1.32/16.50
% 1.32/16.50 % SZS status Theorem for theBenchmark.p
% 1.32/16.50
% 1.32/16.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.32/16.50
% 1.32/16.50
%------------------------------------------------------------------------------