TSTP Solution File: LCL454+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL454+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 : Sun Jul 17 14:37:08 EDT 2022
% Result : Theorem 0.38s 0.57s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of clauses : 51 ( 32 unt; 0 nHn; 51 RR)
% Number of literals : 73 ( 0 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_implies_or,
file('LCL454+1.p',unknown),
[] ).
cnf(2,axiom,
op_and,
file('LCL454+1.p',unknown),
[] ).
cnf(4,axiom,
op_or,
file('LCL454+1.p',unknown),
[] ).
cnf(5,axiom,
op_implies_and,
file('LCL454+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL454+1.p',unknown),
[] ).
cnf(8,axiom,
modus_tollens,
file('LCL454+1.p',unknown),
[] ).
cnf(10,axiom,
implies_2,
file('LCL454+1.p',unknown),
[] ).
cnf(14,axiom,
and_3,
file('LCL454+1.p',unknown),
[] ).
cnf(22,axiom,
~ r1,
file('LCL454+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ kn1
| is_a_theorem(implies__dfg(u,and__dfg(u,u))) ),
file('LCL454+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
| kn1 ),
file('LCL454+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc99,skc99),skc99))
| r1 ),
file('LCL454+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL454+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL454+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL454+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL454+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ modus_tollens
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))) ),
file('LCL454+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL454+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL454+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL454+1.p',unknown),
[] ).
cnf(83,plain,
~ is_a_theorem(implies__dfg(or__dfg(skc99,skc99),skc99)),
inference(mrr,[status(thm)],[43,22]),
[iquote('0:MRR:43.1,22.0')] ).
cnf(91,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(mrr,[status(thm)],[59,1]),
[iquote('0:MRR:59.0,1.0')] ).
cnf(94,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[51,14]),
[iquote('0:MRR:51.0,14.0')] ).
cnf(96,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[60,5]),
[iquote('0:MRR:60.0,5.0')] ).
cnf(97,plain,
( ~ op_and
| equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[91,67]),
[iquote('0:Rew:91.0,67.1')] ).
cnf(98,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(mrr,[status(thm)],[97,2]),
[iquote('0:MRR:97.0,2.0')] ).
cnf(99,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[96,66]),
[iquote('0:Rew:96.0,66.1')] ).
cnf(100,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[99,4]),
[iquote('0:MRR:99.0,4.0')] ).
cnf(106,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[64,10]),
[iquote('0:MRR:64.0,10.0')] ).
cnf(107,plain,
( ~ modus_tollens
| is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))) ),
inference(rew,[status(thm),theory(equality)],[100,62]),
[iquote('0:Rew:100.0,62.1')] ).
cnf(108,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(mrr,[status(thm)],[107,8]),
[iquote('0:MRR:107.0,8.0')] ).
cnf(109,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[61,7]),
[iquote('0:MRR:61.1,7.0')] ).
cnf(151,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),w),implies__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[96,100]),
[iquote('0:SpR:96.0,100.0')] ).
cnf(168,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[98,91]),
[iquote('0:SpR:98.0,91.0')] ).
cnf(190,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[91,108]),
[iquote('0:SpR:91.0,108.0')] ).
cnf(191,plain,
is_a_theorem(or__dfg(and__dfg(u,v),implies__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[168,190]),
[iquote('0:Rew:168.0,190.0')] ).
cnf(218,plain,
is_a_theorem(or__dfg(and__dfg(u,not__dfg(v)),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[100,191]),
[iquote('0:SpR:100.0,191.0')] ).
cnf(219,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[151,218]),
[iquote('0:Rew:151.0,218.0')] ).
cnf(265,plain,
( ~ is_a_theorem(or__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[108,109]),
[iquote('0:Res:108.0,109.1')] ).
cnf(271,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(or__dfg(v,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[219,109]),
[iquote('0:Res:219.0,109.1')] ).
cnf(277,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[106,109]),
[iquote('0:Res:106.0,109.1')] ).
cnf(558,plain,
( ~ kn1
| is_a_theorem(or__dfg(and__dfg(u,u),not__dfg(u))) ),
inference(sor,[status(thm)],[271,38]),
[iquote('0:SoR:271.0,38.1')] ).
cnf(757,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(sor,[status(thm)],[277,94]),
[iquote('0:SoR:277.0,94.0')] ).
cnf(762,plain,
kn1,
inference(mrr,[status(thm)],[39,757]),
[iquote('0:MRR:39.0,757.0')] ).
cnf(767,plain,
is_a_theorem(or__dfg(and__dfg(u,u),not__dfg(u))),
inference(mrr,[status(thm)],[558,762]),
[iquote('0:MRR:558.0,762.0')] ).
cnf(1070,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[151,767]),
[iquote('0:SpR:151.0,767.0')] ).
cnf(1075,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),not__dfg(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[100,1070]),
[iquote('0:Rew:100.0,1070.0')] ).
cnf(1117,plain,
is_a_theorem(or__dfg(not__dfg(not__dfg(u)),not__dfg(or__dfg(u,u)))),
inference(sor,[status(thm)],[271,1075]),
[iquote('0:SoR:271.0,1075.0')] ).
cnf(1124,plain,
is_a_theorem(or__dfg(u,not__dfg(or__dfg(u,u)))),
inference(rew,[status(thm),theory(equality)],[100,1117,91]),
[iquote('0:Rew:100.0,1117.0,91.0,1117.0')] ).
cnf(1133,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),u)),
inference(sor,[status(thm)],[265,1124]),
[iquote('0:SoR:265.0,1124.0')] ).
cnf(1139,plain,
$false,
inference(unc,[status(thm)],[1133,83]),
[iquote('0:UnC:1133.0,83.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL454+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 06:03:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.38/0.57
% 0.38/0.57 SPASS V 3.9
% 0.38/0.57 SPASS beiseite: Proof found.
% 0.38/0.57 % SZS status Theorem
% 0.38/0.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.57 SPASS derived 740 clauses, backtracked 0 clauses, performed 0 splits and kept 418 clauses.
% 0.38/0.57 SPASS allocated 99208 KBytes.
% 0.38/0.57 SPASS spent 0:00:00.20 on the problem.
% 0.38/0.57 0:00:00.04 for the input.
% 0.38/0.57 0:00:00.05 for the FLOTTER CNF translation.
% 0.38/0.57 0:00:00.01 for inferences.
% 0.38/0.57 0:00:00.00 for the backtracking.
% 0.38/0.57 0:00:00.08 for the reduction.
% 0.38/0.57
% 0.38/0.57
% 0.38/0.57 Here is a proof with depth 7, length 51 :
% 0.38/0.57 % SZS output start Refutation
% See solution above
% 0.38/0.57 Formulae used in the proof : principia_op_implies_or principia_op_and hilbert_op_or hilbert_op_implies_and hilbert_modus_ponens hilbert_modus_tollens hilbert_implies_2 hilbert_and_3 principia_r1 kn1 r1 and_3 op_implies_or op_implies_and modus_ponens hilbert_implies_1 implies_1 implies_2 modus_tollens op_or op_and
% 0.38/0.57
%------------------------------------------------------------------------------