%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 02:28:29 EDT 2022
% Result : Theorem 0.84s 1.06s
% Output : Refutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 22 unt; 0 nHn; 29 RR)
% Number of literals : 36 ( 0 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE093+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE093+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(domain__dfg(star(skc1)),one),
file('KLE093+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(domain__dfg(u),one),one),
file('KLE093+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE093+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE093+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE093+1.p',unknown),
[] ).
cnf(14,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE093+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
file('KLE093+1.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE093+1.p',unknown),
[] ).
cnf(19,axiom,
equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
file('KLE093+1.p',unknown),
[] ).
cnf(24,plain,
equal(addition(one,domain__dfg(u)),one),
inference(rew,[status(thm),theory(equality)],[10,9]),
[iquote('0:Rew:10.0,9.0')] ).
cnf(60,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[11,10]),
[iquote('0:SpR:11.1,10.0')] ).
cnf(192,plain,
equal(addition(one,domain__dfg(one)),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[4,19]),
[iquote('0:SpR:4.0,19.0')] ).
cnf(194,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[24,192]),
[iquote('0:Rew:24.0,192.0')] ).
cnf(200,plain,
equal(addition(one,domain__dfg(u)),domain__dfg(addition(one,u))),
inference(spr,[status(thm),theory(equality)],[194,16]),
[iquote('0:SpR:194.0,16.0')] ).
cnf(207,plain,
equal(domain__dfg(addition(one,u)),one),
inference(rew,[status(thm),theory(equality)],[24,200]),
[iquote('0:Rew:24.0,200.0')] ).
cnf(222,plain,
( ~ leq(one,u)
| equal(domain__dfg(u),one) ),
inference(spr,[status(thm),theory(equality)],[11,207]),
[iquote('0:SpR:11.1,207.0')] ).
cnf(310,plain,
( ~ leq(one,star(skc1))
| ~ equal(one,one) ),
inference(spl,[status(thm),theory(equality)],[222,8]),
[iquote('0:SpL:222.1,8.0')] ).
cnf(313,plain,
~ leq(one,star(skc1)),
inference(obv,[status(thm),theory(equality)],[310]),
[iquote('0:Obv:310.1')] ).
cnf(411,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(901,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[411,12]),
[iquote('0:SpL:411.0,12.0')] ).
cnf(907,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[901]),
[iquote('0:Obv:901.0')] ).
cnf(916,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[10,907]),
[iquote('0:SpR:10.0,907.0')] ).
cnf(938,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[17,916]),
[iquote('0:SpR:17.0,916.0')] ).
cnf(1094,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[10,938]),
[iquote('0:SpR:10.0,938.0')] ).
cnf(1225,plain,
( ~ leq(addition(u,v),w)
| leq(u,w) ),
inference(spr,[status(thm),theory(equality)],[60,1094]),
[iquote('0:SpR:60.1,1094.0')] ).
cnf(6334,plain,
leq(one,star(u)),
inference(res,[status(thm),theory(equality)],[14,1225]),
[iquote('0:Res:14.0,1225.0')] ).
cnf(6351,plain,
$false,
inference(unc,[status(thm)],[6334,313]),
[iquote('0:UnC:6334.0,313.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n007.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Thu Jun 16 12:39:26 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.84/1.06
% 0.84/1.06 SPASS V 3.9
% 0.84/1.06 SPASS beiseite: Proof found.
% 0.84/1.06 % SZS status Theorem
% 0.84/1.06 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.84/1.06 SPASS derived 4738 clauses, backtracked 0 clauses, performed 0 splits and kept 973 clauses.
% 0.84/1.06 SPASS allocated 89821 KBytes.
% 0.84/1.06 SPASS spent 0:00:00.73 on the problem.
% 0.84/1.06 0:00:00.03 for the input.
% 0.84/1.06 0:00:00.02 for the FLOTTER CNF translation.
% 0.84/1.06 0:00:00.04 for inferences.
% 0.84/1.06 0:00:00.00 for the backtracking.
% 0.84/1.06 0:00:00.61 for the reduction.
% 0.84/1.06
% 0.84/1.06
% 0.84/1.06 Here is a proof with depth 7, length 29 :
% 0.84/1.06 % SZS output start Refutation
% See solution above
% 0.84/1.06 Formulae used in the proof : additive_idempotence multiplicative_right_identity goals domain3 additive_commutativity order star_unfold_left domain5 additive_associativity domain1
% 0.84/1.06
%------------------------------------------------------------------------------