TSTP Solution File: ALG203+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG203+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Thu Jul 14 18:02:55 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 9 unt; 0 nHn; 24 RR)
% Number of literals : 56 ( 0 equ; 33 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sorti1(skc3),
file('ALG203+1.p',unknown),
[] ).
cnf(2,axiom,
sorti1(skc2),
file('ALG203+1.p',unknown),
[] ).
cnf(3,axiom,
equal(op1(skc2,skc2),skc2),
file('ALG203+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti1(u)
| sorti2(h(u)) ),
file('ALG203+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(op1(skc3,skc3),skc3),
file('ALG203+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ sorti1(u)
| equal(j(h(u)),u) ),
file('ALG203+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| sorti1(op1(v,u)) ),
file('ALG203+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op2(h(v),h(u)),h(op1(v,u))) ),
file('ALG203+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ equal(op2(v,v),v)
| equal(op2(u,u),u) ),
file('ALG203+1.p',unknown),
[] ).
cnf(15,plain,
sorti2(h(skc3)),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.0,4.0')] ).
cnf(17,plain,
equal(j(h(skc3)),skc3),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.0,8.0')] ).
cnf(19,plain,
( ~ sorti1(u)
| equal(op2(h(skc3),h(u)),h(op1(skc3,u))) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(105,plain,
( ~ sorti1(u)
| ~ sorti1(u)
| ~ sorti2(v)
| ~ sorti2(h(u))
| ~ equal(h(op1(u,u)),h(u))
| equal(op2(v,v),v) ),
inference(spl,[status(thm),theory(equality)],[11,13]),
[iquote('0:SpL:11.2,13.2')] ).
cnf(107,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| ~ sorti2(h(u))
| ~ equal(h(op1(u,u)),h(u))
| equal(op2(v,v),v) ),
inference(obv,[status(thm),theory(equality)],[105]),
[iquote('0:Obv:105.0')] ).
cnf(108,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| ~ equal(h(op1(u,u)),h(u))
| equal(op2(v,v),v) ),
inference(ssi,[status(thm)],[107,4]),
[iquote('0:SSi:107.2,4.1')] ).
cnf(415,plain,
( ~ sorti1(skc2)
| ~ sorti2(u)
| ~ equal(h(skc2),h(skc2))
| equal(op2(u,u),u) ),
inference(spl,[status(thm),theory(equality)],[3,108]),
[iquote('0:SpL:3.0,108.2')] ).
cnf(419,plain,
( ~ sorti1(skc2)
| ~ sorti2(u)
| equal(op2(u,u),u) ),
inference(obv,[status(thm),theory(equality)],[415]),
[iquote('0:Obv:415.2')] ).
cnf(420,plain,
( ~ sorti2(u)
| equal(op2(u,u),u) ),
inference(ssi,[status(thm)],[419,2]),
[iquote('0:SSi:419.0,2.0')] ).
cnf(427,plain,
( ~ sorti2(h(skc3))
| ~ sorti1(skc3)
| equal(h(op1(skc3,skc3)),h(skc3)) ),
inference(spr,[status(thm),theory(equality)],[420,19]),
[iquote('0:SpR:420.1,19.1')] ).
cnf(441,plain,
equal(h(op1(skc3,skc3)),h(skc3)),
inference(ssi,[status(thm)],[427,1,15]),
[iquote('0:SSi:427.1,427.0,1.0,15.0')] ).
cnf(453,plain,
( ~ sorti1(op1(skc3,skc3))
| equal(op1(skc3,skc3),j(h(skc3))) ),
inference(spr,[status(thm),theory(equality)],[441,8]),
[iquote('0:SpR:441.0,8.1')] ).
cnf(471,plain,
( ~ sorti1(op1(skc3,skc3))
| equal(op1(skc3,skc3),skc3) ),
inference(rew,[status(thm),theory(equality)],[17,453]),
[iquote('0:Rew:17.0,453.1')] ).
cnf(472,plain,
equal(op1(skc3,skc3),skc3),
inference(ssi,[status(thm)],[471,9,1]),
[iquote('0:SSi:471.0,9.0,1.0,1.2')] ).
cnf(473,plain,
$false,
inference(mrr,[status(thm)],[472,6]),
[iquote('0:MRR:472.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG203+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n018.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 : Thu Jun 9 02:23:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 291 clauses, backtracked 0 clauses, performed 0 splits and kept 126 clauses.
% 0.20/0.48 SPASS allocated 104382 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.03 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 4, length 24 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : ax3 co1 ax1 ax4
% 0.20/0.48
%------------------------------------------------------------------------------