%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 : Sun Sep 27 06:58:30 AM UTC 2026
% Result : Theorem 13.26s 2.11s
% Output : CNFRefutation 13.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 82 ( 13 unt; 0 def)
% Number of atoms : 217 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 236 ( 101 ~; 109 |; 13 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% 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 : 123 ( 39 sgn 21 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(program_program_decides_def,axiom,
! [X0] :
( 'program$uprogram$udecides'(X0)
<=> ( 'program$udecides'(X0)
& program(X0) ) ) ).
fof(program_halts2_def,axiom,
! [X0,X1] :
( 'program$uhalts2'(X0,X1)
<=> ( halts2(X0,X1)
& program(X0) ) ) ).
fof(program_not_halts2_def,axiom,
! [X0,X1] :
( 'program$unot$uhalts2'(X0,X1)
<=> ( ~ halts2(X0,X1)
& program(X0) ) ) ).
fof(halts2_outputs_def,axiom,
! [X0,X1,X2] :
( 'halts2$uoutputs'(X0,X1,X2)
<=> ( outputs(X0,X2)
& halts2(X0,X1) ) ) ).
fof(program_halts2_halts2_outputs_def,axiom,
! [X0,X1,X2] :
( 'program$uhalts2$uhalts2$uoutputs'(X0,X1,X2)
<=> ( 'program$uhalts2'(X1,X1)
=> 'halts2$uoutputs'(X0,X1,X2) ) ) ).
fof(program_not_halts2_halts2_outputs_def,axiom,
! [X0,X1,X2] :
( 'program$unot$uhalts2$uhalts2$uoutputs'(X0,X1,X2)
<=> ( 'program$unot$uhalts2'(X1,X1)
=> 'halts2$uoutputs'(X0,X1,X2) ) ) ).
fof(p1,axiom,
( ? [X0] : 'algorithm$uprogram$udecides'(X0)
=> ? [X1] : 'program$uprogram$udecides'(X1) ) ).
fof(p2,axiom,
! [X0] :
( 'program$uprogram$udecides'(X0)
=> ! [X1,X2] :
( 'program$unot$uhalts2$uhalts3$uoutputs'(X0,X1,X2,bad)
& 'program$uhalts2$uhalts3$uoutputs'(X0,X1,X2,good) ) ) ).
fof(p3,axiom,
( ? [X0] :
( ! [X1] :
( 'program$unot$uhalts2$uhalts3$uoutputs'(X0,X1,X1,bad)
& 'program$uhalts2$uhalts3$uoutputs'(X0,X1,X1,good) )
& program(X0) )
=> ? [X2] :
( ! [X1] :
( 'program$unot$uhalts2$uhalts2$uoutputs'(X2,X1,bad)
& 'program$uhalts2$uhalts2$uoutputs'(X2,X1,good) )
& program(X2) ) ) ).
fof(p4,axiom,
( ? [X0] :
( ! [X1] :
( 'program$unot$uhalts2$uhalts2$uoutputs'(X0,X1,bad)
& 'program$uhalts2$uhalts2$uoutputs'(X0,X1,good) )
& program(X0) )
=> ? [X2] :
( ! [X1] :
( 'program$unot$uhalts2$uhalts2$uoutputs'(X2,X1,good)
& ( 'program$uhalts2'(X1,X1)
=> ~ halts2(X2,X1) ) )
& program(X2) ) ) ).
fof(prove_this,conjecture,
~ ? [X0] : 'algorithm$uprogram$udecides'(X0) ).
fof(negated_conjecture,negated_conjecture,
~ ~ ? [X0] : 'algorithm$uprogram$udecides'(X0),
inference(negate_conjecture,[status(cth)],[prove_this]) ).
cnf(c3,plain,
( program(X0)
| ~ 'program$uprogram$udecides'(X0) ),
inference(clausification,[status(esa)],[program_program_decides_def]) ).
cnf(c10,plain,
( halts2(X0,X1)
| ~ 'program$uhalts2'(X0,X1) ),
inference(clausification,[status(esa)],[program_halts2_def]) ).
cnf(c11,plain,
( ~ halts2(X0,X1)
| ~ program(X0)
| 'program$uhalts2'(X0,X1) ),
inference(clausification,[status(esa)],[program_halts2_def]) ).
cnf(c16,plain,
( ~ halts2(X0,X1)
| ~ 'program$unot$uhalts2'(X0,X1) ),
inference(clausification,[status(esa)],[program_not_halts2_def]) ).
cnf(c17,plain,
( halts2(X0,X1)
| ~ program(X0)
| 'program$unot$uhalts2'(X0,X1) ),
inference(clausification,[status(esa)],[program_not_halts2_def]) ).
cnf(c18,plain,
( halts2(X0,X1)
| ~ 'halts2$uoutputs'(X0,X1,X2) ),
inference(clausification,[status(esa)],[halts2_outputs_def]) ).
cnf(c19,plain,
( outputs(X0,X2)
| ~ 'halts2$uoutputs'(X0,X1,X2) ),
inference(clausification,[status(esa)],[halts2_outputs_def]) ).
cnf(c20,plain,
( ~ outputs(X0,X2)
| ~ halts2(X0,X1)
| 'halts2$uoutputs'(X0,X1,X2) ),
inference(clausification,[status(esa)],[halts2_outputs_def]) ).
cnf(c28,plain,
( 'program$uhalts2'(X1,X1)
| 'program$uhalts2$uhalts2$uoutputs'(X0,X1,X2) ),
inference(clausification,[status(esa)],[program_halts2_halts2_outputs_def]) ).
cnf(c30,plain,
( 'halts2$uoutputs'(X0,X1,X2)
| ~ 'program$unot$uhalts2'(X1,X1)
| ~ 'program$unot$uhalts2$uhalts2$uoutputs'(X0,X1,X2) ),
inference(clausification,[status(esa)],[program_not_halts2_halts2_outputs_def]) ).
cnf(c31,plain,
( 'program$unot$uhalts2'(X1,X1)
| 'program$unot$uhalts2$uhalts2$uoutputs'(X0,X1,X2) ),
inference(clausification,[status(esa)],[program_not_halts2_halts2_outputs_def]) ).
cnf(c32,plain,
( ~ 'halts2$uoutputs'(X0,X1,X2)
| 'program$unot$uhalts2$uhalts2$uoutputs'(X0,X1,X2) ),
inference(clausification,[status(esa)],[program_not_halts2_halts2_outputs_def]) ).
cnf(c33,plain,
( 'program$uprogram$udecides'(sK33)
| ~ 'algorithm$uprogram$udecides'(X0) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c34,plain,
( 'program$uhalts2$uhalts3$uoutputs'(X0,X1,X2,good)
| ~ 'program$uprogram$udecides'(X0) ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c35,plain,
( 'program$unot$uhalts2$uhalts3$uoutputs'(X0,X1,X2,bad)
| ~ 'program$uprogram$udecides'(X0) ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c36,plain,
( program(sK39)
| ~ 'program$unot$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),bad)
| ~ 'program$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),good)
| ~ program(X0) ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c37,plain,
( 'program$uhalts2$uhalts2$uoutputs'(sK39,X1,good)
| ~ 'program$unot$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),bad)
| ~ 'program$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),good)
| ~ program(X0) ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c38,plain,
( 'program$unot$uhalts2$uhalts2$uoutputs'(sK39,X1,bad)
| ~ 'program$unot$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),bad)
| ~ 'program$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),good)
| ~ program(X0) ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c39,plain,
( program(sK43)
| ~ 'program$unot$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),bad)
| ~ 'program$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),good)
| ~ program(X0) ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c40,plain,
( ~ 'program$unot$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),bad)
| ~ 'program$uhalts2'(X1,X1)
| ~ program(X0)
| ~ halts2(sK43,X1)
| ~ 'program$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),good) ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c41,plain,
( 'program$unot$uhalts2$uhalts2$uoutputs'(sK43,X1,good)
| ~ 'program$unot$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),bad)
| ~ 'program$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),good)
| ~ program(X0) ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c42,plain,
'algorithm$uprogram$udecides'(sK45),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'program$uprogram$udecides'(sK33),
inference(resolution,[status(thm)],[c33,c42]) ).
cnf(d1,plain,
( ~ 'program$uprogram$udecides'(X0)
| 'program$unot$uhalts2$uhalts2$uoutputs'(sK39,X1,bad)
| ~ 'program$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),good)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c38,c35]) ).
cnf(d2,plain,
( ~ 'program$uprogram$udecides'(X0)
| 'program$unot$uhalts2$uhalts2$uoutputs'(sK39,X1,bad)
| ~ 'program$uprogram$udecides'(X0)
| ~ program(X0) ),
inference(resolution,[status(thm)],[d1,c34]) ).
cnf(d3,plain,
( 'program$unot$uhalts2$uhalts2$uoutputs'(sK39,X0,bad)
| ~ program(sK33) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
program(sK33),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d5,plain,
'program$unot$uhalts2$uhalts2$uoutputs'(sK39,X0,bad),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'program$unot$uhalts2$uhalts2$uoutputs'(sK43,X0,good)
| ~ 'program$uhalts2$uhalts2$uoutputs'(sK39,sK42(sK39),good)
| ~ program(sK39) ),
inference(resolution,[status(thm)],[d5,c41]) ).
cnf(d7,plain,
( ~ 'program$uprogram$udecides'(X0)
| ~ 'program$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),good)
| program(sK39)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c36,c35]) ).
cnf(d8,plain,
( ~ 'program$uprogram$udecides'(X0)
| ~ 'program$uprogram$udecides'(X0)
| program(sK39)
| ~ program(X0) ),
inference(resolution,[status(thm)],[d7,c34]) ).
cnf(d9,plain,
( program(sK39)
| ~ program(sK33) ),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
program(sK39),
inference(resolution,[status(thm)],[d4,d9]) ).
cnf(d11,plain,
( 'program$unot$uhalts2$uhalts2$uoutputs'(sK43,X0,good)
| ~ 'program$uhalts2$uhalts2$uoutputs'(sK39,sK42(sK39),good) ),
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ 'program$uprogram$udecides'(X0)
| 'program$uhalts2$uhalts2$uoutputs'(sK39,X1,good)
| ~ 'program$uhalts2$uhalts3$uoutputs'(X0,sK38(X0),sK38(X0),good)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c37,c35]) ).
cnf(d13,plain,
( ~ 'program$uprogram$udecides'(X0)
| 'program$uhalts2$uhalts2$uoutputs'(sK39,X1,good)
| ~ 'program$uprogram$udecides'(X0)
| ~ program(X0) ),
inference(resolution,[status(thm)],[d12,c34]) ).
cnf(d14,plain,
( 'program$uhalts2$uhalts2$uoutputs'(sK39,X0,good)
| ~ program(sK33) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
'program$uhalts2$uhalts2$uoutputs'(sK39,X0,good),
inference(resolution,[status(thm)],[d4,d14]) ).
cnf(d16,plain,
'program$unot$uhalts2$uhalts2$uoutputs'(sK43,X0,good),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( 'halts2$uoutputs'(sK43,X0,good)
| ~ 'program$unot$uhalts2'(X0,X0) ),
inference(resolution,[status(thm)],[d16,c30]) ).
cnf(d18,plain,
( halts2(X0,X0)
| ~ program(X0)
| 'halts2$uoutputs'(sK43,X0,good) ),
inference(resolution,[status(thm)],[d17,c17]) ).
cnf(d19,plain,
( halts2(sK43,X0)
| halts2(X0,X0)
| ~ program(X0) ),
inference(resolution,[status(thm)],[d18,c18]) ).
cnf(d20,plain,
( halts2(sK43,sK43)
| ~ program(sK43) ),
inference(factoring,[status(thm)],[d19]) ).
cnf(d21,plain,
( 'program$unot$uhalts2'(sK42(X0),sK42(X0))
| ~ 'program$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),good)
| program(sK43)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c39,c31]) ).
cnf(d22,plain,
( 'program$unot$uhalts2'(sK42(sK39),sK42(sK39))
| program(sK43)
| ~ program(sK39) ),
inference(resolution,[status(thm)],[d21,d15]) ).
cnf(d23,plain,
( 'program$unot$uhalts2'(sK42(sK39),sK42(sK39))
| program(sK43) ),
inference(resolution,[status(thm)],[d10,d22]) ).
cnf(d24,plain,
( 'halts2$uoutputs'(sK39,X0,bad)
| ~ 'program$unot$uhalts2'(X0,X0) ),
inference(resolution,[status(thm)],[d5,c30]) ).
cnf(d25,plain,
( program(sK43)
| 'halts2$uoutputs'(sK39,sK42(sK39),bad) ),
inference(resolution,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
( outputs(sK39,bad)
| program(sK43) ),
inference(resolution,[status(thm)],[d25,c19]) ).
cnf(d27,plain,
( halts2(X1,X1)
| 'program$uhalts2$uhalts2$uoutputs'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c28,c10]) ).
cnf(d28,plain,
( ~ halts2(X1,X1)
| 'program$unot$uhalts2$uhalts2$uoutputs'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c31,c16]) ).
cnf(d29,plain,
( 'program$uhalts2$uhalts2$uoutputs'(X3,X1,X4)
| 'program$unot$uhalts2$uhalts2$uoutputs'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
( 'program$uhalts2$uhalts2$uoutputs'(X1,sK42(X0),X2)
| ~ 'program$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),good)
| program(sK43)
| ~ program(X0) ),
inference(resolution,[status(thm)],[c39,d29]) ).
cnf(d31,plain,
( 'program$uhalts2$uhalts2$uoutputs'(X0,sK42(sK39),X1)
| program(sK43)
| ~ program(sK39) ),
inference(resolution,[status(thm)],[d30,d15]) ).
cnf(d32,plain,
( 'program$uhalts2$uhalts2$uoutputs'(X0,sK42(sK39),X1)
| program(sK43) ),
inference(resolution,[status(thm)],[d10,d31]) ).
cnf(d33,plain,
( ~ outputs(X0,X2)
| ~ halts2(X0,X1)
| 'program$unot$uhalts2$uhalts2$uoutputs'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c32,c20]) ).
cnf(d34,plain,
( ~ 'program$uhalts2$uhalts2$uoutputs'(X0,sK42(X0),good)
| program(sK43)
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ halts2(X0,sK42(X0)) ),
inference(resolution,[status(thm)],[d33,c39]) ).
cnf(d35,plain,
( program(sK43)
| ~ outputs(sK39,bad)
| ~ halts2(sK39,sK42(sK39))
| program(sK43)
| ~ program(sK39) ),
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
( ~ outputs(sK39,bad)
| ~ halts2(sK39,sK42(sK39))
| program(sK43) ),
inference(resolution,[status(thm)],[d10,d35]) ).
cnf(d37,plain,
( halts2(sK39,sK42(sK39))
| program(sK43) ),
inference(resolution,[status(thm)],[d25,c18]) ).
cnf(d38,plain,
( ~ outputs(sK39,bad)
| program(sK43)
| program(sK43) ),
inference(resolution,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
( program(sK43)
| program(sK43) ),
inference(resolution,[status(thm)],[d38,d26]) ).
cnf(d40,plain,
halts2(sK43,sK43),
inference(resolution,[status(thm)],[d39,d20]) ).
cnf(d41,plain,
( ~ 'program$uhalts2$uhalts2$uoutputs'(sK39,sK42(sK39),good)
| ~ halts2(sK43,X0)
| ~ 'program$uhalts2'(X0,X0)
| ~ program(sK39) ),
inference(resolution,[status(thm)],[d5,c40]) ).
cnf(d42,plain,
( ~ 'program$uhalts2$uhalts2$uoutputs'(sK39,sK42(sK39),good)
| ~ halts2(sK43,X0)
| ~ 'program$uhalts2'(X0,X0) ),
inference(resolution,[status(thm)],[d10,d41]) ).
cnf(d43,plain,
( ~ halts2(sK43,X0)
| ~ 'program$uhalts2'(X0,X0) ),
inference(resolution,[status(thm)],[d15,d42]) ).
cnf(d44,plain,
~ 'program$uhalts2'(sK43,sK43),
inference(resolution,[status(thm)],[d43,d40]) ).
cnf(d45,plain,
( 'program$uhalts2'(sK43,sK43)
| ~ program(sK43) ),
inference(resolution,[status(thm)],[d40,c11]) ).
cnf(d46,plain,
'program$uhalts2'(sK43,sK43),
inference(resolution,[status(thm)],[d39,d45]) ).
cnf(d47,plain,
$false,
inference(resolution,[status(thm)],[d46,d44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:19:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.26/2.11 % SZS status Theorem for theBenchmark.p
% 13.26/2.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------