TSTP Solution File: ALG071+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG071+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 0.88s 1.05s
% Output : Refutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of clauses : 40 ( 9 unt; 0 nHn; 40 RR)
% Number of literals : 92 ( 0 equ; 55 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sorti2(skc1),
file('ALG071+1.p',unknown),
[] ).
cnf(2,axiom,
sorti1(skf1(u)),
file('ALG071+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sorti1(u)
| sorti2(h(u)) ),
file('ALG071+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(u)
| sorti1(j(u)) ),
file('ALG071+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ sorti2(u)
| equal(h(j(u)),u) ),
file('ALG071+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ sorti1(u)
| equal(j(h(u)),u) ),
file('ALG071+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| sorti1(op1(v,u)) ),
file('ALG071+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| sorti2(op2(v,u)) ),
file('ALG071+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sorti1(u)
| equal(op1(u,op1(skf1(u),u)),skf1(u)) ),
file('ALG071+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti1(u)
| ~ equal(op1(skf1(u),op1(skf1(u),u)),u) ),
file('ALG071+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op2(h(v),h(u)),h(op1(v,u))) ),
file('ALG071+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(u)),j(op2(v,u))) ),
file('ALG071+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ sorti2(u)
| ~ equal(op2(skc1,op2(u,skc1)),u)
| equal(op2(u,op2(u,skc1)),skc1) ),
file('ALG071+1.p',unknown),
[] ).
cnf(14,plain,
sorti1(j(skc1)),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.0,4.0')] ).
cnf(17,plain,
equal(h(j(skc1)),skc1),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.0,5.0')] ).
cnf(19,plain,
( ~ sorti2(u)
| equal(op1(j(u),j(skc1)),j(op2(u,skc1))) ),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.1')] ).
cnf(54,plain,
( ~ sorti1(u)
| ~ sorti2(h(u))
| equal(j(op2(h(u),skc1)),op1(u,j(skc1))) ),
inference(spr,[status(thm),theory(equality)],[6,19]),
[iquote('0:SpR:6.1,19.1')] ).
cnf(56,plain,
( ~ sorti1(u)
| equal(j(op2(h(u),skc1)),op1(u,j(skc1))) ),
inference(ssi,[status(thm)],[54,3]),
[iquote('0:SSi:54.1,3.1')] ).
cnf(88,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| ~ sorti2(h(u))
| equal(j(op2(h(u),v)),op1(u,j(v))) ),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.1,12.2')] ).
cnf(91,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| equal(j(op2(h(u),v)),op1(u,j(v))) ),
inference(ssi,[status(thm)],[88,3]),
[iquote('0:SSi:88.2,3.1')] ).
cnf(97,plain,
( ~ sorti1(u)
| ~ sorti2(op2(h(u),skc1))
| equal(h(op1(u,j(skc1))),op2(h(u),skc1)) ),
inference(spr,[status(thm),theory(equality)],[56,5]),
[iquote('0:SpR:56.1,5.1')] ).
cnf(108,plain,
( ~ sorti1(u)
| equal(h(op1(u,j(skc1))),op2(h(u),skc1)) ),
inference(ssi,[status(thm)],[97,8,3,1]),
[iquote('0:SSi:97.1,8.0,3.1,1.2')] ).
cnf(123,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(125,plain,
( ~ sorti2(u)
| ~ sorti1(v)
| equal(h(op1(j(u),v)),op2(u,h(v))) ),
inference(ssi,[status(thm)],[123,4]),
[iquote('0:SSi:123.2,4.1')] ).
cnf(322,plain,
( ~ sorti1(j(u))
| ~ sorti2(u)
| ~ sorti1(op1(skf1(j(u)),j(u)))
| equal(op2(u,h(op1(skf1(j(u)),j(u)))),h(skf1(j(u)))) ),
inference(spr,[status(thm),theory(equality)],[9,125]),
[iquote('0:SpR:9.1,125.2')] ).
cnf(342,plain,
( ~ sorti2(u)
| equal(op2(u,h(op1(skf1(j(u)),j(u)))),h(skf1(j(u)))) ),
inference(ssi,[status(thm)],[322,7,2,4]),
[iquote('0:SSi:322.2,322.0,7.1,2.1,4.1,4.0,4.2')] ).
cnf(643,plain,
( ~ sorti1(u)
| ~ sorti2(h(u))
| equal(op2(h(u),h(op1(skf1(u),u))),h(skf1(u))) ),
inference(spr,[status(thm),theory(equality)],[6,342]),
[iquote('0:SpR:6.1,342.1')] ).
cnf(664,plain,
( ~ sorti1(u)
| equal(op2(h(u),h(op1(skf1(u),u))),h(skf1(u))) ),
inference(ssi,[status(thm)],[643,3]),
[iquote('0:SSi:643.1,3.1')] ).
cnf(2389,plain,
( ~ sorti1(skf1(j(skc1)))
| ~ sorti1(j(skc1))
| equal(op2(h(j(skc1)),op2(h(skf1(j(skc1))),skc1)),h(skf1(j(skc1)))) ),
inference(spr,[status(thm),theory(equality)],[108,664]),
[iquote('0:SpR:108.1,664.1')] ).
cnf(2407,plain,
( ~ sorti1(skf1(j(skc1)))
| ~ sorti1(j(skc1))
| equal(op2(skc1,op2(h(skf1(j(skc1))),skc1)),h(skf1(j(skc1)))) ),
inference(rew,[status(thm),theory(equality)],[17,2389]),
[iquote('0:Rew:17.0,2389.2')] ).
cnf(2408,plain,
equal(op2(skc1,op2(h(skf1(j(skc1))),skc1)),h(skf1(j(skc1)))),
inference(ssi,[status(thm)],[2407,14,2]),
[iquote('0:SSi:2407.1,2407.0,14.0,2.0,14.0')] ).
cnf(2607,plain,
( ~ sorti2(h(skf1(j(skc1))))
| ~ equal(h(skf1(j(skc1))),h(skf1(j(skc1))))
| equal(op2(h(skf1(j(skc1))),op2(h(skf1(j(skc1))),skc1)),skc1) ),
inference(spl,[status(thm),theory(equality)],[2408,13]),
[iquote('0:SpL:2408.0,13.1')] ).
cnf(2608,plain,
( ~ sorti2(h(skf1(j(skc1))))
| equal(op2(h(skf1(j(skc1))),op2(h(skf1(j(skc1))),skc1)),skc1) ),
inference(obv,[status(thm),theory(equality)],[2607]),
[iquote('0:Obv:2607.1')] ).
cnf(2609,plain,
equal(op2(h(skf1(j(skc1))),op2(h(skf1(j(skc1))),skc1)),skc1),
inference(ssi,[status(thm)],[2608,3,2,14]),
[iquote('0:SSi:2608.0,3.0,2.0,14.1')] ).
cnf(2617,plain,
( ~ sorti1(skf1(j(skc1)))
| ~ sorti2(op2(h(skf1(j(skc1))),skc1))
| equal(op1(skf1(j(skc1)),j(op2(h(skf1(j(skc1))),skc1))),j(skc1)) ),
inference(spr,[status(thm),theory(equality)],[2609,91]),
[iquote('0:SpR:2609.0,91.2')] ).
cnf(2628,plain,
( ~ sorti1(skf1(j(skc1)))
| ~ sorti2(op2(h(skf1(j(skc1))),skc1))
| equal(op1(skf1(j(skc1)),op1(skf1(j(skc1)),j(skc1))),j(skc1)) ),
inference(rew,[status(thm),theory(equality)],[56,2617]),
[iquote('0:Rew:56.1,2617.2')] ).
cnf(2629,plain,
equal(op1(skf1(j(skc1)),op1(skf1(j(skc1)),j(skc1))),j(skc1)),
inference(ssi,[status(thm)],[2628,8,3,2,14,1]),
[iquote('0:SSi:2628.1,2628.0,8.0,3.0,2.0,14.0,1.0,2.1,14.2')] ).
cnf(2645,plain,
( ~ sorti1(j(skc1))
| ~ equal(j(skc1),j(skc1)) ),
inference(spl,[status(thm),theory(equality)],[2629,10]),
[iquote('0:SpL:2629.0,10.1')] ).
cnf(2646,plain,
~ sorti1(j(skc1)),
inference(obv,[status(thm),theory(equality)],[2645]),
[iquote('0:Obv:2645.1')] ).
cnf(2647,plain,
$false,
inference(ssi,[status(thm)],[2646,14]),
[iquote('0:SSi:2646.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG071+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Wed Jun 8 05:16:10 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.88/1.05
% 0.88/1.05 SPASS V 3.9
% 0.88/1.05 SPASS beiseite: Proof found.
% 0.88/1.05 % SZS status Theorem
% 0.88/1.05 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.88/1.05 SPASS derived 1449 clauses, backtracked 0 clauses, performed 0 splits and kept 689 clauses.
% 0.88/1.05 SPASS allocated 107943 KBytes.
% 0.88/1.05 SPASS spent 0:00:00.66 on the problem.
% 0.88/1.05 0:00:00.04 for the input.
% 0.88/1.05 0:00:00.03 for the FLOTTER CNF translation.
% 0.88/1.05 0:00:00.03 for inferences.
% 0.88/1.05 0:00:00.00 for the backtracking.
% 0.88/1.05 0:00:00.54 for the reduction.
% 0.88/1.05
% 0.88/1.05
% 0.88/1.05 Here is a proof with depth 7, length 40 :
% 0.88/1.05 % SZS output start Refutation
% See solution above
% 0.88/1.05 Formulae used in the proof : ax4 ax3 co1 ax1 ax2
% 0.88/1.05
%------------------------------------------------------------------------------