TSTP Solution File: ALG070+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 18:02:13 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 4 unt; 0 nHn; 26 RR)
% Number of literals : 72 ( 0 equ; 49 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sorti2(skc1),
file('ALG070+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sorti1(u)
| sorti2(h(u)) ),
file('ALG070+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(u)
| sorti1(j(u)) ),
file('ALG070+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ sorti2(u)
| equal(h(j(u)),u) ),
file('ALG070+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ sorti1(u)
| equal(j(h(u)),u) ),
file('ALG070+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(op2(skc1,op2(skc1,skc1)),skc1),
file('ALG070+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| sorti2(op2(v,u)) ),
file('ALG070+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti1(u)
| ~ sorti1(op1(u,u))
| equal(op1(u,op1(u,u)),u) ),
file('ALG070+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op2(h(v),h(u)),h(op1(v,u))) ),
file('ALG070+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(u)),j(op2(v,u))) ),
file('ALG070+1.p',unknown),
[] ).
cnf(30,plain,
( ~ sorti1(u)
| ~ sorti2(h(u))
| ~ sorti2(v)
| equal(j(op2(v,h(u))),op1(j(v),u)) ),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.1,12.2')] ).
cnf(34,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| equal(j(op2(v,h(u))),op1(j(v),u)) ),
inference(ssi,[status(thm)],[30,3]),
[iquote('0:SSi:30.1,3.1')] ).
cnf(41,plain,
( ~ sorti2(u)
| ~ sorti1(v)
| ~ sorti1(j(u))
| equal(h(op1(j(u),v)),op2(u,h(v))) ),
inference(spr,[status(thm),theory(equality)],[5,11]),
[iquote('0:SpR:5.1,11.2')] ).
cnf(43,plain,
( ~ sorti2(u)
| ~ sorti1(v)
| equal(h(op1(j(u),v)),op2(u,h(v))) ),
inference(ssi,[status(thm)],[41,4]),
[iquote('0:SSi:41.2,4.1')] ).
cnf(96,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| ~ sorti2(op2(v,h(u)))
| sorti1(op1(j(v),u)) ),
inference(spr,[status(thm),theory(equality)],[34,4]),
[iquote('0:SpR:34.2,4.1')] ).
cnf(107,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| sorti1(op1(j(v),u)) ),
inference(ssi,[status(thm)],[96,9,3]),
[iquote('0:SSi:96.2,9.1,3.2')] ).
cnf(145,plain,
( ~ sorti1(j(u))
| ~ sorti2(u)
| ~ sorti1(op1(j(u),j(u)))
| ~ sorti1(op1(j(u),j(u)))
| equal(op2(u,h(op1(j(u),j(u)))),h(j(u))) ),
inference(spr,[status(thm),theory(equality)],[10,43]),
[iquote('0:SpR:10.2,43.2')] ).
cnf(159,plain,
( ~ sorti1(j(u))
| ~ sorti2(u)
| ~ sorti1(op1(j(u),j(u)))
| equal(op2(u,h(op1(j(u),j(u)))),h(j(u))) ),
inference(obv,[status(thm),theory(equality)],[145]),
[iquote('0:Obv:145.2')] ).
cnf(160,plain,
( ~ sorti1(j(u))
| ~ sorti2(u)
| ~ sorti1(op1(j(u),j(u)))
| equal(op2(u,op2(u,u)),u) ),
inference(rew,[status(thm),theory(equality)],[5,159,43]),
[iquote('0:Rew:5.1,159.3,43.2,159.3,5.1,159.3')] ).
cnf(161,plain,
( ~ sorti2(u)
| ~ sorti1(op1(j(u),j(u)))
| equal(op2(u,op2(u,u)),u) ),
inference(ssi,[status(thm)],[160,4]),
[iquote('0:SSi:160.0,4.1')] ).
cnf(320,plain,
( ~ sorti1(j(u))
| ~ sorti2(u)
| ~ sorti2(u)
| equal(op2(u,op2(u,u)),u) ),
inference(res,[status(thm),theory(equality)],[107,161]),
[iquote('0:Res:107.2,161.1')] ).
cnf(323,plain,
( ~ sorti1(j(u))
| ~ sorti2(u)
| equal(op2(u,op2(u,u)),u) ),
inference(obv,[status(thm),theory(equality)],[320]),
[iquote('0:Obv:320.1')] ).
cnf(324,plain,
( ~ sorti2(u)
| equal(op2(u,op2(u,u)),u) ),
inference(ssi,[status(thm)],[323,4]),
[iquote('0:SSi:323.0,4.1')] ).
cnf(340,plain,
( ~ sorti2(skc1)
| ~ equal(skc1,skc1) ),
inference(spl,[status(thm),theory(equality)],[324,7]),
[iquote('0:SpL:324.1,7.0')] ).
cnf(341,plain,
~ sorti2(skc1),
inference(obv,[status(thm),theory(equality)],[340]),
[iquote('0:Obv:340.1')] ).
cnf(342,plain,
$false,
inference(ssi,[status(thm)],[341,1]),
[iquote('0:SSi:341.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 7 22:03:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 193 clauses, backtracked 0 clauses, performed 0 splits and kept 79 clauses.
% 0.20/0.47 SPASS allocated 104331 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.03 for the input.
% 0.20/0.47 0:00:00.02 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.04 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 4, length 26 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : ax4 co1 ax2 ax3
% 0.20/0.47
%------------------------------------------------------------------------------