%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Unsatisfiable 13.49s 2.40s
% Output : CNFRefutation 13.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 8 unt; 0 nHn; 16 RR)
% Number of literals : 40 ( 0 equ; 20 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 51 ( 31 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(program_halts3a,axiom,
( halts2(X0,X1)
| ~ 'program$uhalts2'(X0,X1) ) ).
cnf(program_not_halts3a,axiom,
( ~ halts2(X0,X1)
| ~ 'program$unot$uhalts2'(X0,X1) ) ).
cnf(program_halts2_halts3_outputs1,axiom,
( 'program$uhalts2'(X1,X2)
| ~ 'program$uhalts2$uhalts3$uoutputs'(X0,X1,X2,X3) ) ).
cnf(program_not_halts2_halts3_outputs1,axiom,
( 'program$unot$uhalts2'(X1,X2)
| ~ 'program$unot$uhalts2$uhalts3$uoutputs'(X0,X1,X2,X3) ) ).
cnf(axiom1_1,hypothesis,
( 'program$uprogram$udecides'(c1)
| ~ 'algorithm$uprogram$udecides'(X0) ) ).
cnf(axiom2_1,hypothesis,
( 'program$uhalts2$uhalts3$uoutputs'(X0,X1,X2,good)
| ~ 'program$uprogram$udecides'(X0) ) ).
cnf(axiom2_2,hypothesis,
( 'program$unot$uhalts2$uhalts3$uoutputs'(X0,X1,X2,bad)
| ~ 'program$uprogram$udecides'(X0) ) ).
cnf(prove_algorithm_does_not_exist,negated_conjecture,
'algorithm$uprogram$udecides'(c4) ).
cnf(c10,plain,
( halts2(X0,X1)
| ~ 'program$uhalts2'(X0,X1) ),
inference(clausification,[status(esa)],[program_halts3a]) ).
cnf(c16,plain,
( ~ halts2(X0,X1)
| ~ 'program$unot$uhalts2'(X0,X1) ),
inference(clausification,[status(esa)],[program_not_halts3a]) ).
cnf(c21,plain,
( 'program$uhalts2'(X1,X2)
| ~ 'program$uhalts2$uhalts3$uoutputs'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[program_halts2_halts3_outputs1]) ).
cnf(c24,plain,
( 'program$unot$uhalts2'(X1,X2)
| ~ 'program$unot$uhalts2$uhalts3$uoutputs'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[program_not_halts2_halts3_outputs1]) ).
cnf(c33,plain,
( 'program$uprogram$udecides'(c1)
| ~ 'algorithm$uprogram$udecides'(X0) ),
inference(clausification,[status(esa)],[axiom1_1]) ).
cnf(c34,plain,
( 'program$uhalts2$uhalts3$uoutputs'(X0,X1,X2,good)
| ~ 'program$uprogram$udecides'(X0) ),
inference(clausification,[status(esa)],[axiom2_1]) ).
cnf(c35,plain,
( 'program$unot$uhalts2$uhalts3$uoutputs'(X0,X1,X2,bad)
| ~ 'program$uprogram$udecides'(X0) ),
inference(clausification,[status(esa)],[axiom2_2]) ).
cnf(c42,plain,
'algorithm$uprogram$udecides'(c4),
inference(clausification,[status(esa)],[prove_algorithm_does_not_exist]) ).
cnf(d0,plain,
'program$uprogram$udecides'(c1),
inference(resolution,[status(thm)],[c33,c42]) ).
cnf(d1,plain,
( ~ 'program$uprogram$udecides'(X2)
| 'program$unot$uhalts2'(X0,X1) ),
inference(resolution,[status(thm)],[c24,c35]) ).
cnf(d2,plain,
( ~ 'program$uprogram$udecides'(X2)
| 'program$uhalts2'(X0,X1) ),
inference(resolution,[status(thm)],[c21,c34]) ).
cnf(d3,plain,
'program$uhalts2'(X0,X1),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
halts2(X0,X1),
inference(resolution,[status(thm)],[d3,c10]) ).
cnf(d5,plain,
~ 'program$unot$uhalts2'(X0,X1),
inference(resolution,[status(thm)],[d4,c16]) ).
cnf(d6,plain,
~ 'program$uprogram$udecides'(X0),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 23:25:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.49/2.40 % SZS status Unsatisfiable for theBenchmark.p
% 13.49/2.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------