TSTP Solution File: ALG178+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG178+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 18:02:49 EDT 2022
% Result : Theorem 0.18s 0.45s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 4 unt; 0 nHn; 25 RR)
% Number of literals : 76 ( 0 equ; 54 neg)
% Maximal clause size : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 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,
sorti2(skc3),
file('ALG178+1.p',unknown),
[] ).
cnf(2,axiom,
sorti2(skc2),
file('ALG178+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(u)
| sorti1(j(u)) ),
file('ALG178+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ sorti2(u)
| equal(h(j(u)),u) ),
file('ALG178+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(op2(skc2,op2(skc2,skc3)),skc3),
file('ALG178+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| sorti2(op2(v,u)) ),
file('ALG178+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op1(v,op1(v,u)),u) ),
file('ALG178+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op2(h(v),h(u)),h(op1(v,u))) ),
file('ALG178+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(u)),j(op2(v,u))) ),
file('ALG178+1.p',unknown),
[] ).
cnf(29,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(u))
| ~ sorti1(j(v))
| equal(op1(j(v),j(op2(v,u))),j(u)) ),
inference(spr,[status(thm),theory(equality)],[12,10]),
[iquote('0:SpR:12.2,10.2')] ).
cnf(36,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(op2(v,u))),j(u)) ),
inference(ssi,[status(thm)],[29,4]),
[iquote('0:SSi:29.3,29.2,4.1,4.1')] ).
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(208,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti2(v)
| ~ sorti1(j(u))
| equal(op2(v,h(j(u))),h(j(op2(v,u)))) ),
inference(spr,[status(thm),theory(equality)],[12,43]),
[iquote('0:SpR:12.2,43.2')] ).
cnf(209,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti2(v)
| ~ sorti1(j(op2(v,u)))
| equal(op2(v,h(j(op2(v,u)))),h(j(u))) ),
inference(spr,[status(thm),theory(equality)],[36,43]),
[iquote('0:SpR:36.2,43.2')] ).
cnf(214,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(u))
| equal(op2(v,h(j(u))),h(j(op2(v,u)))) ),
inference(obv,[status(thm),theory(equality)],[208]),
[iquote('0:Obv:208.1')] ).
cnf(215,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(u))
| equal(h(j(op2(v,u))),op2(v,u)) ),
inference(rew,[status(thm),theory(equality)],[5,214]),
[iquote('0:Rew:5.1,214.3')] ).
cnf(216,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(h(j(op2(v,u))),op2(v,u)) ),
inference(ssi,[status(thm)],[215,4]),
[iquote('0:SSi:215.2,4.1')] ).
cnf(219,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(op2(v,u)))
| equal(op2(v,h(j(op2(v,u)))),h(j(u))) ),
inference(obv,[status(thm),theory(equality)],[209]),
[iquote('0:Obv:209.1')] ).
cnf(220,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(op2(v,u)))
| equal(op2(v,h(j(op2(v,u)))),u) ),
inference(rew,[status(thm),theory(equality)],[5,219]),
[iquote('0:Rew:5.1,219.3')] ).
cnf(221,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(op2(v,u)))
| equal(op2(v,op2(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[216,220]),
[iquote('0:Rew:216.2,220.3')] ).
cnf(222,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op2(v,op2(v,u)),u) ),
inference(ssi,[status(thm)],[221,4,9]),
[iquote('0:SSi:221.2,4.2,9.1')] ).
cnf(244,plain,
( ~ sorti2(skc3)
| ~ sorti2(skc2)
| ~ equal(skc3,skc3) ),
inference(spl,[status(thm),theory(equality)],[222,7]),
[iquote('0:SpL:222.2,7.0')] ).
cnf(245,plain,
( ~ sorti2(skc3)
| ~ sorti2(skc2) ),
inference(obv,[status(thm),theory(equality)],[244]),
[iquote('0:Obv:244.2')] ).
cnf(246,plain,
$false,
inference(ssi,[status(thm)],[245,2,1]),
[iquote('0:SSi:245.1,245.0,2.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG178+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 14:27:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.45
% 0.18/0.45 SPASS V 3.9
% 0.18/0.45 SPASS beiseite: Proof found.
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 SPASS derived 133 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.18/0.45 SPASS allocated 104162 KBytes.
% 0.18/0.45 SPASS spent 0:00:00.11 on the problem.
% 0.18/0.45 0:00:00.03 for the input.
% 0.18/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.45 0:00:00.00 for inferences.
% 0.18/0.45 0:00:00.00 for the backtracking.
% 0.18/0.45 0:00:00.02 for the reduction.
% 0.18/0.45
% 0.18/0.45
% 0.18/0.45 Here is a proof with depth 3, length 25 :
% 0.18/0.45 % SZS output start Refutation
% See solution above
% 0.18/0.45 Formulae used in the proof : ax4 co1 ax2 ax3
% 0.18/0.45
%------------------------------------------------------------------------------