TSTP Solution File: ALG210+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 18:02:59 EDT 2022
% Result : Theorem 1.99s 2.21s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 32 ( 25 unt; 0 nHn; 32 RR)
% Number of literals : 39 ( 0 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
element(skc3),
file('ALG210+1.p',unknown),
[] ).
cnf(2,axiom,
element(skc2),
file('ALG210+1.p',unknown),
[] ).
cnf(3,axiom,
~ element(times(skc3,skc2)),
file('ALG210+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ element(u)
| equal(times(u,times(u,u)),u) ),
file('ALG210+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(times(u,times(u,u)),u)
| element(u) ),
file('ALG210+1.p',unknown),
[] ).
cnf(6,axiom,
equal(times(times(u,v),w),times(v,times(w,u))),
file('ALG210+1.p',unknown),
[] ).
cnf(7,plain,
equal(times(skc2,times(skc2,skc2)),skc2),
inference(res,[status(thm),theory(equality)],[2,4]),
[iquote('0:Res:2.0,4.0')] ).
cnf(8,plain,
equal(times(skc3,times(skc3,skc3)),skc3),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.0,4.0')] ).
cnf(22,plain,
equal(times(times(u,times(v,w)),x),times(v,times(x,times(w,u)))),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(24,plain,
equal(times(times(skc3,skc3),times(u,skc3)),times(skc3,u)),
inference(spr,[status(thm),theory(equality)],[8,6]),
[iquote('0:SpR:8.0,6.0')] ).
cnf(26,plain,
equal(times(times(skc2,skc2),times(u,skc2)),times(skc2,u)),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(28,plain,
( ~ equal(times(u,times(times(times(v,u),times(v,u)),v)),times(v,u))
| element(times(v,u)) ),
inference(spl,[status(thm),theory(equality)],[6,5]),
[iquote('0:SpL:6.0,5.0')] ).
cnf(29,plain,
equal(times(skc3,times(skc3,times(skc3,u))),times(skc3,u)),
inference(rew,[status(thm),theory(equality)],[6,24]),
[iquote('0:Rew:6.0,24.0,6.0,24.0')] ).
cnf(30,plain,
equal(times(skc2,times(skc2,times(skc2,u))),times(skc2,u)),
inference(rew,[status(thm),theory(equality)],[6,26]),
[iquote('0:Rew:6.0,26.0,6.0,26.0')] ).
cnf(32,plain,
equal(times(u,times(v,times(w,x))),times(w,times(x,times(u,v)))),
inference(rew,[status(thm),theory(equality)],[6,22]),
[iquote('0:Rew:6.0,22.0,6.0,22.0,6.0,22.0')] ).
cnf(33,plain,
( ~ equal(times(u,times(u,times(u,times(v,times(v,v))))),times(v,u))
| element(times(v,u)) ),
inference(rew,[status(thm),theory(equality)],[6,28]),
[iquote('0:Rew:6.0,28.0,6.0,28.0,6.0,28.0,6.0,28.0,6.0,28.0')] ).
cnf(85,plain,
equal(times(skc3,times(u,times(skc3,skc3))),times(skc3,u)),
inference(spr,[status(thm),theory(equality)],[32,29]),
[iquote('0:SpR:32.0,29.0')] ).
cnf(95,plain,
equal(times(skc2,times(u,times(skc2,skc2))),times(skc2,u)),
inference(spr,[status(thm),theory(equality)],[32,30]),
[iquote('0:SpR:32.0,30.0')] ).
cnf(210,plain,
equal(times(u,times(times(skc3,skc3),times(v,skc3))),times(v,times(skc3,u))),
inference(spr,[status(thm),theory(equality)],[85,32]),
[iquote('0:SpR:85.0,32.0')] ).
cnf(219,plain,
equal(times(u,times(skc3,v)),times(v,times(skc3,u))),
inference(rew,[status(thm),theory(equality)],[29,210,6]),
[iquote('0:Rew:29.0,210.0,6.0,210.0,6.0,210.0')] ).
cnf(234,plain,
equal(times(u,times(times(skc2,skc2),times(v,skc2))),times(v,times(skc2,u))),
inference(spr,[status(thm),theory(equality)],[95,32]),
[iquote('0:SpR:95.0,32.0')] ).
cnf(243,plain,
equal(times(u,times(skc2,v)),times(v,times(skc2,u))),
inference(rew,[status(thm),theory(equality)],[30,234,6]),
[iquote('0:Rew:30.0,234.0,6.0,234.0,6.0,234.0')] ).
cnf(252,plain,
( ~ equal(times(u,times(u,times(u,skc3))),times(skc3,u))
| element(times(skc3,u)) ),
inference(spl,[status(thm),theory(equality)],[8,33]),
[iquote('0:SpL:8.0,33.0')] ).
cnf(398,plain,
equal(times(times(skc3,skc3),times(skc3,u)),times(u,skc3)),
inference(spr,[status(thm),theory(equality)],[8,219]),
[iquote('0:SpR:8.0,219.0')] ).
cnf(424,plain,
equal(times(skc3,u),times(u,skc3)),
inference(rew,[status(thm),theory(equality)],[85,398,6]),
[iquote('0:Rew:85.0,398.0,6.0,398.0,6.0,398.0')] ).
cnf(425,plain,
~ element(times(skc2,skc3)),
inference(rew,[status(thm),theory(equality)],[424,3]),
[iquote('0:Rew:424.0,3.0')] ).
cnf(737,plain,
equal(times(times(skc2,skc2),times(skc2,u)),times(u,skc2)),
inference(spr,[status(thm),theory(equality)],[7,243]),
[iquote('0:SpR:7.0,243.0')] ).
cnf(771,plain,
equal(times(skc2,u),times(u,skc2)),
inference(rew,[status(thm),theory(equality)],[95,737,6]),
[iquote('0:Rew:95.0,737.0,6.0,737.0,6.0,737.0')] ).
cnf(8316,plain,
( ~ equal(times(skc3,skc2),times(skc2,skc3))
| element(times(skc3,skc2)) ),
inference(spl,[status(thm),theory(equality)],[30,252]),
[iquote('0:SpL:30.0,252.0')] ).
cnf(8332,plain,
( ~ equal(times(skc2,skc3),times(skc2,skc3))
| element(times(skc2,skc3)) ),
inference(rew,[status(thm),theory(equality)],[771,8316]),
[iquote('0:Rew:771.0,8316.1,771.0,8316.0')] ).
cnf(8333,plain,
element(times(skc2,skc3)),
inference(obv,[status(thm),theory(equality)],[8332]),
[iquote('0:Obv:8332.0')] ).
cnf(8334,plain,
$false,
inference(mrr,[status(thm)],[8333,425]),
[iquote('0:MRR:8333.0,425.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 17:33:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.21
% 1.99/2.21 SPASS V 3.9
% 1.99/2.21 SPASS beiseite: Proof found.
% 1.99/2.21 % SZS status Theorem
% 1.99/2.21 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.99/2.21 SPASS derived 5319 clauses, backtracked 0 clauses, performed 0 splits and kept 527 clauses.
% 1.99/2.21 SPASS allocated 103778 KBytes.
% 1.99/2.21 SPASS spent 0:00:01.80 on the problem.
% 1.99/2.21 0:00:00.04 for the input.
% 1.99/2.21 0:00:00.03 for the FLOTTER CNF translation.
% 1.99/2.21 0:00:00.05 for inferences.
% 1.99/2.21 0:00:00.00 for the backtracking.
% 1.99/2.21 0:00:01.66 for the reduction.
% 1.99/2.21
% 1.99/2.21
% 1.99/2.21 Here is a proof with depth 5, length 32 :
% 1.99/2.21 % SZS output start Refutation
% See solution above
% 1.99/2.21 Formulae used in the proof : conjecture_1 axiom_2 axiom_1
% 1.99/2.21
%------------------------------------------------------------------------------