TSTP Solution File: LCL456+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 14:37:09 EDT 2022
% Result : Theorem 0.52s 0.72s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 41 ( 28 unt; 0 nHn; 41 RR)
% Number of literals : 57 ( 0 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 9 usr; 8 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('LCL456+1.p',unknown),
[] ).
cnf(2,axiom,
op_and,
file('LCL456+1.p',unknown),
[] ).
cnf(4,axiom,
op_or,
file('LCL456+1.p',unknown),
[] ).
cnf(5,axiom,
op_implies_and,
file('LCL456+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL456+1.p',unknown),
[] ).
cnf(8,axiom,
modus_tollens,
file('LCL456+1.p',unknown),
[] ).
cnf(22,axiom,
~ r3,
file('LCL456+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc103,skc102),or__dfg(skc102,skc103)))
| r3 ),
file('LCL456+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL456+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL456+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL456+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('LCL456+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL456+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL456+1.p',unknown),
[] ).
cnf(90,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(91,plain,
~ is_a_theorem(implies__dfg(or__dfg(skc103,skc102),or__dfg(skc102,skc103))),
inference(mrr,[status(thm)],[58,22]),
[iquote('0:MRR:58.1,22.0')] ).
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)],[90,67]),
[iquote('0:Rew:90.0,67.1')] ).
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(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(157,plain,
equal(implies__dfg(and__dfg(u,not__dfg(v)),w),or__dfg(implies__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[96,90]),
[iquote('0:SpR:96.0,90.0')] ).
cnf(158,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(173,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[98,90]),
[iquote('0:SpR:98.0,90.0')] ).
cnf(185,plain,
equal(not__dfg(or__dfg(u,not__dfg(v))),and__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[100,98]),
[iquote('0:SpR:100.0,98.0')] ).
cnf(201,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[90,108]),
[iquote('0:SpR:90.0,108.0')] ).
cnf(202,plain,
is_a_theorem(or__dfg(and__dfg(u,v),implies__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[173,201]),
[iquote('0:Rew:173.0,201.0')] ).
cnf(218,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(325,plain,
is_a_theorem(or__dfg(and__dfg(u,not__dfg(v)),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[100,202]),
[iquote('0:SpR:100.0,202.0')] ).
cnf(327,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[158,325]),
[iquote('0:Rew:158.0,325.0')] ).
cnf(342,plain,
is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,not__dfg(not__dfg(u))))),
inference(spr,[status(thm),theory(equality)],[100,327]),
[iquote('0:SpR:100.0,327.0')] ).
cnf(343,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(or__dfg(v,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[327,109]),
[iquote('0:Res:327.0,109.1')] ).
cnf(381,plain,
equal(or__dfg(or__dfg(u,not__dfg(v)),w),implies__dfg(and__dfg(not__dfg(u),v),w)),
inference(spr,[status(thm),theory(equality)],[185,100]),
[iquote('0:SpR:185.0,100.0')] ).
cnf(1397,plain,
is_a_theorem(or__dfg(or__dfg(u,not__dfg(not__dfg(v))),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[343,342]),
[iquote('0:SoR:343.0,342.0')] ).
cnf(1458,plain,
is_a_theorem(implies__dfg(and__dfg(not__dfg(u),not__dfg(v)),not__dfg(or__dfg(v,u)))),
inference(rew,[status(thm),theory(equality)],[381,1397]),
[iquote('0:Rew:381.0,1397.0')] ).
cnf(1459,plain,
is_a_theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(rew,[status(thm),theory(equality)],[100,1458,157]),
[iquote('0:Rew:100.0,1458.0,157.0,1458.0')] ).
cnf(2126,plain,
is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(sor,[status(thm)],[218,1459]),
[iquote('0:SoR:218.0,1459.0')] ).
cnf(2134,plain,
$false,
inference(unc,[status(thm)],[2126,91]),
[iquote('0:UnC:2126.0,91.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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 : Sun Jul 3 19:17:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.52/0.72
% 0.52/0.72 SPASS V 3.9
% 0.52/0.72 SPASS beiseite: Proof found.
% 0.52/0.72 % SZS status Theorem
% 0.52/0.72 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.72 SPASS derived 1345 clauses, backtracked 0 clauses, performed 0 splits and kept 771 clauses.
% 0.52/0.72 SPASS allocated 100736 KBytes.
% 0.52/0.72 SPASS spent 0:00:00.35 on the problem.
% 0.52/0.72 0:00:00.04 for the input.
% 0.52/0.72 0:00:00.04 for the FLOTTER CNF translation.
% 0.52/0.72 0:00:00.02 for inferences.
% 0.52/0.72 0:00:00.00 for the backtracking.
% 0.52/0.72 0:00:00.22 for the reduction.
% 0.52/0.72
% 0.52/0.72
% 0.52/0.72 Here is a proof with depth 5, length 41 :
% 0.52/0.72 % SZS output start Refutation
% See solution above
% 0.52/0.72 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 principia_r3 r3 op_implies_or op_implies_and modus_ponens hilbert_implies_1 implies_1 hilbert_implies_2 implies_2 hilbert_and_3 and_3 modus_tollens op_or op_and
% 0.52/0.72
%------------------------------------------------------------------------------