TSTP Solution File: KLE142+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 : Sun Jul 17 02:28:43 EDT 2022
% Result : Theorem 0.46s 0.68s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 24 unt; 0 nHn; 29 RR)
% Number of literals : 34 ( 0 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE142+2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE142+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE142+2.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE142+2.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE142+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE142+2.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE142+2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE142+2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE142+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(skc3)))
| ~ leq(strong_iteration(strong_iteration(skc2)),strong_iteration(one)) ),
file('KLE142+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ leq(u,addition(multiplication(v,u),w))
| leq(u,multiplication(strong_iteration(v),w)) ),
file('KLE142+2.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[6,9]),
[iquote('0:Rew:6.0,9.0')] ).
cnf(150,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,13]),
[iquote('0:SpR:2.0,13.0')] ).
cnf(192,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[150,11]),
[iquote('0:SpL:150.0,11.0')] ).
cnf(197,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[192]),
[iquote('0:Obv:192.0')] ).
cnf(203,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[6,197]),
[iquote('0:SpR:6.0,197.0')] ).
cnf(227,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,strong_iteration(v)),u)),multiplication(strong_iteration(v),u)),
inference(spr,[status(thm),theory(equality)],[21,16]),
[iquote('0:SpR:21.0,16.0')] ).
cnf(238,plain,
equal(addition(u,multiplication(v,multiplication(strong_iteration(v),u))),multiplication(strong_iteration(v),u)),
inference(rew,[status(thm),theory(equality)],[4,227,14]),
[iquote('0:Rew:4.0,227.0,14.0,227.0')] ).
cnf(260,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[13,203]),
[iquote('0:SpR:13.0,203.0')] ).
cnf(352,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[6,260]),
[iquote('0:SpR:6.0,260.0')] ).
cnf(526,plain,
( ~ leq(u,addition(u,v))
| leq(u,multiplication(strong_iteration(one),v)) ),
inference(spl,[status(thm),theory(equality)],[4,20]),
[iquote('0:SpL:4.0,20.0')] ).
cnf(548,plain,
leq(u,multiplication(strong_iteration(one),v)),
inference(mrr,[status(thm)],[526,197]),
[iquote('0:MRR:526.0,197.0')] ).
cnf(552,plain,
leq(u,strong_iteration(one)),
inference(spr,[status(thm),theory(equality)],[3,548]),
[iquote('0:SpR:3.0,548.0')] ).
cnf(557,plain,
~ leq(strong_iteration(one),strong_iteration(strong_iteration(skc3))),
inference(mrr,[status(thm)],[17,552]),
[iquote('0:MRR:17.1,552.0')] ).
cnf(2179,plain,
leq(u,addition(v,multiplication(strong_iteration(w),u))),
inference(spr,[status(thm),theory(equality)],[238,352]),
[iquote('0:SpR:238.0,352.0')] ).
cnf(2354,plain,
leq(u,addition(multiplication(strong_iteration(v),u),w)),
inference(spr,[status(thm),theory(equality)],[6,2179]),
[iquote('0:SpR:6.0,2179.0')] ).
cnf(2760,plain,
leq(u,multiplication(strong_iteration(strong_iteration(v)),w)),
inference(res,[status(thm),theory(equality)],[2354,20]),
[iquote('0:Res:2354.0,20.0')] ).
cnf(2769,plain,
leq(u,strong_iteration(strong_iteration(v))),
inference(spr,[status(thm),theory(equality)],[3,2760]),
[iquote('0:SpR:3.0,2760.0')] ).
cnf(2778,plain,
$false,
inference(unc,[status(thm)],[2769,557]),
[iquote('0:UnC:2769.0,557.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 : Thu Jun 16 09:21:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/0.68
% 0.46/0.68 SPASS V 3.9
% 0.46/0.68 SPASS beiseite: Proof found.
% 0.46/0.68 % SZS status Theorem
% 0.46/0.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.68 SPASS derived 2074 clauses, backtracked 0 clauses, performed 0 splits and kept 641 clauses.
% 0.46/0.68 SPASS allocated 87475 KBytes.
% 0.46/0.68 SPASS spent 0:00:00.32 on the problem.
% 0.46/0.68 0:00:00.04 for the input.
% 0.46/0.68 0:00:00.03 for the FLOTTER CNF translation.
% 0.46/0.68 0:00:00.02 for inferences.
% 0.46/0.68 0:00:00.00 for the backtracking.
% 0.46/0.68 0:00:00.22 for the reduction.
% 0.46/0.68
% 0.46/0.68
% 0.46/0.68 Here is a proof with depth 9, length 29 :
% 0.46/0.68 % SZS output start Refutation
% See solution above
% 0.46/0.68 Formulae used in the proof : idempotence multiplicative_right_identity multiplicative_left_identity additive_commutativity infty_unfold1 order additive_associativity multiplicative_associativity distributivity2 goals infty_coinduction
% 0.46/0.68
%------------------------------------------------------------------------------