TSTP Solution File: COM003+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 01:44:12 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of clauses : 39 ( 11 unt; 3 nHn; 39 RR)
% Number of literals : 91 ( 0 equ; 54 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
algorithm_program_decides(skc4),
file('COM003+2.p',unknown),
[] ).
cnf(2,axiom,
program(skc6),
file('COM003+2.p',unknown),
[] ).
cnf(3,axiom,
program(skc7),
file('COM003+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ program_program_decides(u)
| program(u) ),
file('COM003+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ algorithm_program_decides(u)
| program_program_decides(skc5) ),
file('COM003+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ halts2_outputs(u,v,w)
| halts2(u,v) ),
file('COM003+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ program_program_decides(u)
| program_halts2_halts3_outputs(u,v,w,good) ),
file('COM003+2.p',unknown),
[] ).
cnf(23,axiom,
( ~ program_program_decides(u)
| program_not_halts2_halts3_outputs(u,v,w,bad) ),
file('COM003+2.p',unknown),
[] ).
cnf(26,axiom,
( ~ program(u)
| program_not_halts2(u,v)
| halts2(u,v) ),
file('COM003+2.p',unknown),
[] ).
cnf(30,axiom,
( ~ program(u)
| ~ halts2(u,v)
| program_halts2(u,v) ),
file('COM003+2.p',unknown),
[] ).
cnf(36,axiom,
( ~ program_not_halts2(u,u)
| ~ program_not_halts2_halts2_outputs(v,u,w)
| halts2_outputs(v,u,w) ),
file('COM003+2.p',unknown),
[] ).
cnf(40,axiom,
( ~ program(u)
| ~ program_not_halts2_halts2_outputs(u,skf11(u),bad)
| ~ program_halts2_halts2_outputs(u,skf10(u),good)
| program_not_halts2_halts2_outputs(skc7,v,good) ),
file('COM003+2.p',unknown),
[] ).
cnf(41,axiom,
( ~ program(u)
| ~ program_halts2(v,v)
| ~ halts2(skc7,v)
| ~ program_not_halts2_halts2_outputs(u,skf11(u),bad)
| ~ program_halts2_halts2_outputs(u,skf10(u),good) ),
file('COM003+2.p',unknown),
[] ).
cnf(42,axiom,
( ~ program(u)
| ~ program_not_halts2_halts3_outputs(u,skf9(u),skf9(u),bad)
| ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
| program_not_halts2_halts2_outputs(skc6,v,bad) ),
file('COM003+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ program(u)
| ~ program_not_halts2_halts3_outputs(u,skf9(u),skf9(u),bad)
| ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
| program_halts2_halts2_outputs(skc6,v,good) ),
file('COM003+2.p',unknown),
[] ).
cnf(46,plain,
program_program_decides(skc5),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(135,plain,
( ~ program_program_decides(u)
| ~ program(u)
| ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
| program_halts2_halts2_outputs(skc6,v,good) ),
inference(res,[status(thm),theory(equality)],[23,43]),
[iquote('0:Res:23.1,43.1')] ).
cnf(138,plain,
( ~ program_program_decides(u)
| ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
| program_halts2_halts2_outputs(skc6,v,good) ),
inference(ssi,[status(thm)],[135,5]),
[iquote('0:SSi:135.1,5.1')] ).
cnf(139,plain,
( ~ program_program_decides(u)
| program_halts2_halts2_outputs(skc6,v,good) ),
inference(mrr,[status(thm)],[138,22]),
[iquote('0:MRR:138.1,22.1')] ).
cnf(141,plain,
program_halts2_halts2_outputs(skc6,u,good),
inference(ems,[status(thm)],[139,46]),
[iquote('0:EmS:139.0,46.0')] ).
cnf(205,plain,
( ~ program_program_decides(u)
| ~ program(u)
| ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
| program_not_halts2_halts2_outputs(skc6,v,bad) ),
inference(res,[status(thm),theory(equality)],[23,42]),
[iquote('0:Res:23.1,42.1')] ).
cnf(208,plain,
( ~ program_program_decides(u)
| ~ program_halts2_halts3_outputs(u,skf8(u),skf8(u),good)
| program_not_halts2_halts2_outputs(skc6,v,bad) ),
inference(ssi,[status(thm)],[205,5]),
[iquote('0:SSi:205.1,5.1')] ).
cnf(209,plain,
( ~ program_program_decides(u)
| program_not_halts2_halts2_outputs(skc6,v,bad) ),
inference(mrr,[status(thm)],[208,22]),
[iquote('0:MRR:208.1,22.1')] ).
cnf(211,plain,
program_not_halts2_halts2_outputs(skc6,u,bad),
inference(ems,[status(thm)],[209,46]),
[iquote('0:EmS:209.0,46.0')] ).
cnf(379,plain,
( ~ program(skc6)
| ~ program_halts2_halts2_outputs(skc6,skf10(skc6),good)
| program_not_halts2_halts2_outputs(skc7,u,good) ),
inference(res,[status(thm),theory(equality)],[211,40]),
[iquote('0:Res:211.0,40.1')] ).
cnf(385,plain,
( ~ program_halts2_halts2_outputs(skc6,skf10(skc6),good)
| program_not_halts2_halts2_outputs(skc7,u,good) ),
inference(ssi,[status(thm)],[379,2]),
[iquote('0:SSi:379.0,2.0')] ).
cnf(386,plain,
program_not_halts2_halts2_outputs(skc7,u,good),
inference(mrr,[status(thm)],[385,141]),
[iquote('0:MRR:385.0,141.0')] ).
cnf(387,plain,
( ~ program_not_halts2(u,u)
| halts2_outputs(skc7,u,good) ),
inference(res,[status(thm),theory(equality)],[386,36]),
[iquote('0:Res:386.0,36.1')] ).
cnf(393,plain,
( ~ program(skc6)
| ~ program_halts2(u,u)
| ~ halts2(skc7,u)
| ~ program_halts2_halts2_outputs(skc6,skf10(skc6),good) ),
inference(res,[status(thm),theory(equality)],[211,41]),
[iquote('0:Res:211.0,41.3')] ).
cnf(400,plain,
( ~ program_halts2(u,u)
| ~ halts2(skc7,u)
| ~ program_halts2_halts2_outputs(skc6,skf10(skc6),good) ),
inference(ssi,[status(thm)],[393,2]),
[iquote('0:SSi:393.0,2.0')] ).
cnf(401,plain,
( ~ program_halts2(u,u)
| ~ halts2(skc7,u) ),
inference(mrr,[status(thm)],[400,141]),
[iquote('0:MRR:400.2,141.0')] ).
cnf(403,plain,
( ~ program(u)
| halts2(u,u)
| halts2_outputs(skc7,u,good) ),
inference(res,[status(thm),theory(equality)],[26,387]),
[iquote('0:Res:26.1,387.0')] ).
cnf(440,plain,
( ~ program(u)
| halts2(u,u)
| halts2(skc7,u) ),
inference(res,[status(thm),theory(equality)],[403,18]),
[iquote('0:Res:403.2,18.0')] ).
cnf(490,plain,
( ~ program(skc7)
| halts2(skc7,skc7) ),
inference(fac,[status(thm)],[440]),
[iquote('0:Fac:440.1,440.2')] ).
cnf(494,plain,
halts2(skc7,skc7),
inference(ssi,[status(thm)],[490,3]),
[iquote('0:SSi:490.0,3.0')] ).
cnf(498,plain,
( ~ program(skc7)
| program_halts2(skc7,skc7) ),
inference(res,[status(thm),theory(equality)],[494,30]),
[iquote('0:Res:494.0,30.1')] ).
cnf(500,plain,
program_halts2(skc7,skc7),
inference(ssi,[status(thm)],[498,3]),
[iquote('0:SSi:498.0,3.0')] ).
cnf(503,plain,
~ halts2(skc7,skc7),
inference(res,[status(thm),theory(equality)],[500,401]),
[iquote('0:Res:500.0,401.0')] ).
cnf(505,plain,
$false,
inference(mrr,[status(thm)],[503,494]),
[iquote('0:MRR:503.0,494.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 20:11:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 367 clauses, backtracked 89 clauses, performed 8 splits and kept 303 clauses.
% 0.19/0.48 SPASS allocated 97852 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.00 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.02 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 9, length 39 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : prove_this p3 algorithm_program_decides_def p1 program_program_decides_def p4 halts2_outputs_def p2 program_not_halts2_def program_halts2_def program_not_halts2_halts2_outputs_def
% 0.19/0.48
%------------------------------------------------------------------------------