TSTP Solution File: KLE142+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE142+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 02:28:43 EDT 2022
% Result : Theorem 0.78s 1.01s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of clauses : 65 ( 51 unt; 0 nHn; 65 RR)
% Number of literals : 79 ( 0 equ; 15 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE142+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE142+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE142+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE142+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(zero,u),zero),
file('KLE142+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(strong_iteration(strong_iteration(skc1)),strong_iteration(one)),
file('KLE142+1.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE142+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(one,multiplication(u,star(u))),star(u)),
file('KLE142+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE142+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE142+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE142+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE142+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(star(u),multiplication(strong_iteration(u),zero)),strong_iteration(u)),
file('KLE142+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE142+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE142+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE142+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE142+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ leq(u,addition(multiplication(v,u),w))
| leq(u,multiplication(strong_iteration(v),w)) ),
file('KLE142+1.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.0')] ).
cnf(55,plain,
equal(addition(one,zero),star(zero)),
inference(spr,[status(thm),theory(equality)],[5,8]),
[iquote('0:SpR:5.0,8.0')] ).
cnf(57,plain,
equal(star(zero),one),
inference(rew,[status(thm),theory(equality)],[1,55]),
[iquote('0:Rew:1.0,55.0')] ).
cnf(60,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.1,7.0')] ).
cnf(75,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[2,12]),
[iquote('0:SpL:2.0,12.0')] ).
cnf(85,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[75]),
[iquote('0:Obv:75.0')] ).
cnf(90,plain,
( ~ leq(star(u),multiplication(strong_iteration(u),zero))
| equal(multiplication(strong_iteration(u),zero),strong_iteration(u)) ),
inference(spr,[status(thm),theory(equality)],[13,11]),
[iquote('0:SpR:13.0,11.1')] ).
cnf(135,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,14]),
[iquote('0:SpR:2.0,14.0')] ).
cnf(185,plain,
equal(addition(one,star(u)),star(u)),
inference(spr,[status(thm),theory(equality)],[9,135]),
[iquote('0:SpR:9.0,135.0')] ).
cnf(192,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[135,12]),
[iquote('0:SpL:135.0,12.0')] ).
cnf(197,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[192]),
[iquote('0:Obv:192.0')] ).
cnf(213,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(star(v),v),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[9,17]),
[iquote('0:SpR:9.0,17.0')] ).
cnf(214,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,strong_iteration(v)),u)),multiplication(strong_iteration(v),u)),
inference(spr,[status(thm),theory(equality)],[21,17]),
[iquote('0:SpR:21.0,17.0')] ).
cnf(224,plain,
equal(addition(u,multiplication(star(v),multiplication(v,u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,213,15]),
[iquote('0:Rew:4.0,213.0,15.0,213.0')] ).
cnf(225,plain,
equal(addition(u,multiplication(v,multiplication(strong_iteration(v),u))),multiplication(strong_iteration(v),u)),
inference(rew,[status(thm),theory(equality)],[4,214,15]),
[iquote('0:Rew:4.0,214.0,15.0,214.0')] ).
cnf(233,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[7,197]),
[iquote('0:SpR:7.0,197.0')] ).
cnf(292,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[14,233]),
[iquote('0:SpR:14.0,233.0')] ).
cnf(298,plain,
( ~ leq(star(u),one)
| equal(star(u),one) ),
inference(spr,[status(thm),theory(equality)],[185,60]),
[iquote('0:SpR:185.0,60.1')] ).
cnf(328,plain,
( ~ leq(addition(u,v),u)
| leq(multiplication(star(one),v),u) ),
inference(spl,[status(thm),theory(equality)],[4,18]),
[iquote('0:SpL:4.0,18.0')] ).
cnf(370,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[7,292]),
[iquote('0:SpR:7.0,292.0')] ).
cnf(466,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(487,plain,
leq(u,multiplication(strong_iteration(one),v)),
inference(mrr,[status(thm)],[466,197]),
[iquote('0:MRR:466.0,197.0')] ).
cnf(1287,plain,
( ~ leq(u,u)
| leq(multiplication(star(one),u),u) ),
inference(spl,[status(thm),theory(equality)],[2,328]),
[iquote('0:SpL:2.0,328.0')] ).
cnf(1312,plain,
leq(multiplication(star(one),u),u),
inference(mrr,[status(thm)],[1287,85]),
[iquote('0:MRR:1287.0,85.0')] ).
cnf(1376,plain,
leq(star(one),one),
inference(spr,[status(thm),theory(equality)],[3,1312]),
[iquote('0:SpR:3.0,1312.0')] ).
cnf(1641,plain,
equal(star(one),one),
inference(res,[status(thm),theory(equality)],[1376,298]),
[iquote('0:Res:1376.0,298.0')] ).
cnf(1801,plain,
equal(addition(one,multiplication(strong_iteration(one),zero)),strong_iteration(one)),
inference(spr,[status(thm),theory(equality)],[1641,13]),
[iquote('0:SpR:1641.0,13.0')] ).
cnf(1835,plain,
( ~ leq(one,multiplication(strong_iteration(one),zero))
| equal(multiplication(strong_iteration(one),zero),strong_iteration(one)) ),
inference(spr,[status(thm),theory(equality)],[1801,11]),
[iquote('0:SpR:1801.0,11.1')] ).
cnf(1838,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(strong_iteration(one),zero),u)),multiplication(strong_iteration(one),u)),
inference(spr,[status(thm),theory(equality)],[1801,17]),
[iquote('0:SpR:1801.0,17.0')] ).
cnf(1857,plain,
equal(multiplication(strong_iteration(one),zero),strong_iteration(one)),
inference(mrr,[status(thm)],[1835,487]),
[iquote('0:MRR:1835.0,487.0')] ).
cnf(1863,plain,
equal(addition(u,multiplication(strong_iteration(one),zero)),multiplication(strong_iteration(one),u)),
inference(rew,[status(thm),theory(equality)],[4,1838,5,15]),
[iquote('0:Rew:4.0,1838.0,5.0,1838.0,15.0,1838.0')] ).
cnf(1864,plain,
equal(multiplication(strong_iteration(one),u),addition(u,strong_iteration(one))),
inference(rew,[status(thm),theory(equality)],[1857,1863]),
[iquote('0:Rew:1857.0,1863.0')] ).
cnf(2088,plain,
leq(u,addition(v,multiplication(star(w),u))),
inference(spr,[status(thm),theory(equality)],[224,370]),
[iquote('0:SpR:224.0,370.0')] ).
cnf(2181,plain,
leq(u,addition(v,multiplication(strong_iteration(w),u))),
inference(spr,[status(thm),theory(equality)],[225,370]),
[iquote('0:SpR:225.0,370.0')] ).
cnf(2259,plain,
leq(u,addition(multiplication(star(v),u),w)),
inference(spr,[status(thm),theory(equality)],[7,2088]),
[iquote('0:SpR:7.0,2088.0')] ).
cnf(2352,plain,
leq(u,addition(multiplication(strong_iteration(v),u),w)),
inference(spr,[status(thm),theory(equality)],[7,2181]),
[iquote('0:SpR:7.0,2181.0')] ).
cnf(2389,plain,
leq(u,multiplication(strong_iteration(star(v)),w)),
inference(res,[status(thm),theory(equality)],[2259,20]),
[iquote('0:Res:2259.0,20.0')] ).
cnf(2686,plain,
leq(u,multiplication(strong_iteration(strong_iteration(v)),w)),
inference(res,[status(thm),theory(equality)],[2352,20]),
[iquote('0:Res:2352.0,20.0')] ).
cnf(2769,plain,
leq(u,strong_iteration(strong_iteration(v))),
inference(spr,[status(thm),theory(equality)],[3,2686]),
[iquote('0:SpR:3.0,2686.0')] ).
cnf(4764,plain,
equal(multiplication(strong_iteration(star(u)),zero),strong_iteration(star(u))),
inference(res,[status(thm),theory(equality)],[2389,90]),
[iquote('0:Res:2389.0,90.0')] ).
cnf(4772,plain,
equal(multiplication(strong_iteration(star(u)),multiplication(zero,v)),multiplication(strong_iteration(star(u)),v)),
inference(spr,[status(thm),theory(equality)],[4764,15]),
[iquote('0:SpR:4764.0,15.0')] ).
cnf(4829,plain,
equal(multiplication(strong_iteration(star(u)),v),strong_iteration(star(u))),
inference(rew,[status(thm),theory(equality)],[4764,4772,5]),
[iquote('0:Rew:4764.0,4772.0,5.0,4772.0')] ).
cnf(5014,plain,
equal(multiplication(strong_iteration(one),u),strong_iteration(one)),
inference(spr,[status(thm),theory(equality)],[57,4829]),
[iquote('0:SpR:57.0,4829.0')] ).
cnf(5027,plain,
equal(addition(u,strong_iteration(one)),strong_iteration(one)),
inference(rew,[status(thm),theory(equality)],[1864,5014]),
[iquote('0:Rew:1864.0,5014.0')] ).
cnf(5124,plain,
( ~ leq(strong_iteration(one),u)
| equal(strong_iteration(one),u) ),
inference(spr,[status(thm),theory(equality)],[5027,60]),
[iquote('0:SpR:5027.0,60.1')] ).
cnf(6204,plain,
equal(strong_iteration(strong_iteration(u)),strong_iteration(one)),
inference(res,[status(thm),theory(equality)],[2769,5124]),
[iquote('0:Res:2769.0,5124.0')] ).
cnf(6208,plain,
$false,
inference(unc,[status(thm)],[6204,6]),
[iquote('0:UnC:6204.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE142+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % 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 : Thu Jun 16 15:31:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.78/1.01
% 0.78/1.01 SPASS V 3.9
% 0.78/1.01 SPASS beiseite: Proof found.
% 0.78/1.01 % SZS status Theorem
% 0.78/1.01 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/1.01 SPASS derived 4800 clauses, backtracked 0 clauses, performed 0 splits and kept 1166 clauses.
% 0.78/1.01 SPASS allocated 89742 KBytes.
% 0.78/1.01 SPASS spent 0:00:00.65 on the problem.
% 0.78/1.01 0:00:00.04 for the input.
% 0.78/1.01 0:00:00.03 for the FLOTTER CNF translation.
% 0.78/1.01 0:00:00.03 for inferences.
% 0.78/1.01 0:00:00.00 for the backtracking.
% 0.78/1.01 0:00:00.53 for the reduction.
% 0.78/1.01
% 0.78/1.01
% 0.78/1.01 Here is a proof with depth 13, length 65 :
% 0.78/1.01 % SZS output start Refutation
% See solution above
% 0.78/1.01 Formulae used in the proof : additive_identity idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation goals additive_commutativity star_unfold1 star_unfold2 infty_unfold1 order isolation additive_associativity multiplicative_associativity distributivity2 star_induction1 infty_coinduction
% 0.78/1.01
%------------------------------------------------------------------------------