%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 06:59:26 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.51s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 62 ( 29 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom2_2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( program_not_halts2_halts3_outputs(VAR_0,VAR_1,VAR_2,bad)
| ~ program_program_decides(VAR_0) ),
file('theBenchmark.p',axiom2_2) ).
cnf(c_13,plain,
( program_not_halts2_halts3_outputs(A,B,C,bad)
| ~ program_program_decides(A) ),
inference(clausify,[status(thm)],[axiom2_2]) ).
fof(axiom2_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( program_halts2_halts3_outputs(VAR_0,VAR_1,VAR_2,good)
| ~ program_program_decides(VAR_0) ),
file('theBenchmark.p',axiom2_1) ).
cnf(c_14,plain,
( program_halts2_halts3_outputs(A,B,C,good)
| ~ program_program_decides(A) ),
inference(clausify,[status(thm)],[axiom2_1]) ).
fof(axiom1_1,axiom,
! [VAR_0] :
( program_program_decides(c1)
| ~ algorithm_program_decides(VAR_0) ),
file('theBenchmark.p',axiom1_1) ).
cnf(c_15,plain,
( program_program_decides(c1)
| ~ algorithm_program_decides(A) ),
inference(clausify,[status(thm)],[axiom1_1]) ).
fof(prove_algorithm_does_not_exist,axiom,
algorithm_program_decides(c4),
file('theBenchmark.p',prove_algorithm_does_not_exist) ).
cnf(c_23,plain,
algorithm_program_decides(c4),
inference(clausify,[status(thm)],[prove_algorithm_does_not_exist]) ).
cnf(c_28,plain,
( program_halts2_halts3_outputs(c1,B,C,good)
| ~ algorithm_program_decides(A) ),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_29,plain,
( program_not_halts2_halts3_outputs(c1,B,C,bad)
| ~ algorithm_program_decides(A) ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
fof(program_halts3a,axiom,
! [VAR_0,VAR_1] :
( halts2(VAR_0,VAR_1)
| ~ program_halts2(VAR_0,VAR_1) ),
file('theBenchmark.p',program_halts3a) ).
cnf(c_33,plain,
( halts2(A,B)
| ~ program_halts2(A,B) ),
inference(clausify,[status(thm)],[program_halts3a]) ).
fof(program_halts2_halts3_outputs1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( program_halts2(VAR_1,VAR_2)
| ~ program_halts2_halts3_outputs(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',program_halts2_halts3_outputs1) ).
cnf(c_35,plain,
( program_halts2(B,C)
| ~ program_halts2_halts3_outputs(A,B,C,D) ),
inference(clausify,[status(thm)],[program_halts2_halts3_outputs1]) ).
fof(program_not_halts3a,axiom,
! [VAR_0,VAR_1] :
( ~ halts2(VAR_0,VAR_1)
| ~ program_not_halts2(VAR_0,VAR_1) ),
file('theBenchmark.p',program_not_halts3a) ).
cnf(c_68,plain,
( ~ halts2(A,B)
| ~ program_not_halts2(A,B) ),
inference(clausify,[status(thm)],[program_not_halts3a]) ).
fof(program_not_halts2_halts3_outputs1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( program_not_halts2(VAR_1,VAR_2)
| ~ program_not_halts2_halts3_outputs(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',program_not_halts2_halts3_outputs1) ).
cnf(c_77,plain,
( program_not_halts2(B,C)
| ~ program_not_halts2_halts3_outputs(A,B,C,D) ),
inference(clausify,[status(thm)],[program_not_halts2_halts3_outputs1]) ).
cnf(c_97,plain,
( ~ halts2(B,C)
| ~ program_not_halts2_halts3_outputs(A,B,C,D) ),
inference(resolve,[status(thm)],[c_77,c_68]) ).
cnf(c_110,plain,
( halts2(B,C)
| ~ program_halts2_halts3_outputs(A,B,C,D) ),
inference(resolve,[status(thm)],[c_35,c_33]) ).
cnf(c_128,plain,
program_halts2_halts3_outputs(c1,A,B,good),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_129,plain,
program_not_halts2_halts3_outputs(c1,A,B,bad),
inference(resolve,[status(thm)],[c_29,c_23]) ).
cnf(c_160,plain,
halts2(A,B),
inference(resolve,[status(thm)],[c_128,c_110]) ).
cnf(c_169,plain,
~ program_not_halts2_halts3_outputs(A,B,C,D),
inference(resolve,[status(thm)],[c_160,c_97]) ).
cnf(c_170,plain,
$false,
inference(resolve,[status(thm)],[c_169,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42 % Computer : n008.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Sat Sep 26 23:20:11 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.10/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.43 % Process 616996 was started by sandbox on n008,
% 0.10/0.43 % Sat Sep 26 23:20:11 2026
% 0.10/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.44
% 0.10/0.44 % From the command line: assign(max_seconds, 300).
% 0.10/0.51
% 0.10/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.51
% 0.10/0.51 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.51 % Length of proof is 17.
% 0.10/0.51 % Level of proof is 5.
% 0.10/0.51 % Maximum clause weight is 8.000.
% 0.10/0.51 % Given clauses 43.
% 0.10/0.51
% 0.10/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------