%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE021+2 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 02:28:03 EDT 2022
% Result : Theorem 0.47s 0.65s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 27 ( 9 unt; 0 nHn; 27 RR)
% Number of literals : 57 ( 0 equ; 33 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
test__dfg(skc3),
file('KLE021+2.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE021+2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE021+2.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE021+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE021+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE021+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE021+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE021+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE021+2.p',unknown),
[] ).
cnf(22,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE021+2.p',unknown),
[] ).
cnf(23,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE021+2.p',unknown),
[] ).
cnf(24,axiom,
( ~ leq(skc4,addition(multiplication(skc3,skc4),multiplication(c(skc3),skc4)))
| ~ leq(addition(multiplication(skc3,skc5),multiplication(c(skc3),skc5)),skc5) ),
file('KLE021+2.p',unknown),
[] ).
cnf(25,plain,
( ~ equal(c(skc3),u)
| complement(skc3,u) ),
inference(res,[status(thm),theory(equality)],[1,19]),
[iquote('0:Res:1.0,19.0')] ).
cnf(57,plain,
( ~ complement(u,v)
| equal(addition(u,v),one) ),
inference(spr,[status(thm),theory(equality)],[16,10]),
[iquote('0:SpR:16.1,10.0')] ).
cnf(68,plain,
complement(skc3,c(skc3)),
inference(eqr,[status(thm),theory(equality)],[25]),
[iquote('0:EqR:25.0')] ).
cnf(96,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpL:3.0,13.0')] ).
cnf(103,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[96]),
[iquote('0:Obv:96.0')] ).
cnf(249,plain,
( ~ complement(u,v)
| equal(multiplication(one,w),addition(multiplication(v,w),multiplication(u,w))) ),
inference(spr,[status(thm),theory(equality)],[16,22]),
[iquote('0:SpR:16.1,22.0')] ).
cnf(261,plain,
( ~ complement(u,v)
| equal(addition(multiplication(v,w),multiplication(u,w)),w) ),
inference(rew,[status(thm),theory(equality)],[5,249]),
[iquote('0:Rew:5.0,249.1')] ).
cnf(319,plain,
( ~ complement(u,v)
| ~ equal(one,one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(spl,[status(thm),theory(equality)],[57,23]),
[iquote('0:SpL:57.1,23.0')] ).
cnf(332,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[319]),
[iquote('0:Obv:319.1')] ).
cnf(333,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[15,332,14]),
[iquote('0:Rew:15.1,332.2,14.1,332.1')] ).
cnf(334,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[333]),
[iquote('0:Obv:333.2')] ).
cnf(507,plain,
complement(c(skc3),skc3),
inference(res,[status(thm),theory(equality)],[68,334]),
[iquote('0:Res:68.0,334.0')] ).
cnf(2126,plain,
( ~ complement(c(skc3),skc3)
| ~ leq(skc4,addition(multiplication(skc3,skc4),multiplication(c(skc3),skc4)))
| ~ leq(skc5,skc5) ),
inference(spl,[status(thm),theory(equality)],[261,24]),
[iquote('0:SpL:261.1,24.1')] ).
cnf(2147,plain,
( ~ complement(c(skc3),skc3)
| ~ leq(skc4,skc4)
| ~ leq(skc5,skc5) ),
inference(rew,[status(thm),theory(equality)],[261,2126]),
[iquote('0:Rew:261.1,2126.1')] ).
cnf(2148,plain,
$false,
inference(mrr,[status(thm)],[2147,507,103]),
[iquote('0:MRR:2147.0,2147.1,2147.2,507.0,103.0,103.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE021+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 13:11:50 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.47/0.65
% 0.47/0.65 SPASS V 3.9
% 0.47/0.65 SPASS beiseite: Proof found.
% 0.47/0.65 % SZS status Theorem
% 0.47/0.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.65 SPASS derived 1681 clauses, backtracked 0 clauses, performed 0 splits and kept 604 clauses.
% 0.47/0.65 SPASS allocated 99133 KBytes.
% 0.47/0.65 SPASS spent 0:00:00.27 on the problem.
% 0.47/0.65 0:00:00.03 for the input.
% 0.47/0.65 0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.65 0:00:00.02 for inferences.
% 0.47/0.65 0:00:00.00 for the backtracking.
% 0.47/0.65 0:00:00.17 for the reduction.
% 0.47/0.65
% 0.47/0.65
% 0.47/0.65 Here is a proof with depth 3, length 27 :
% 0.47/0.65 % SZS output start Refutation
% See solution above
% 0.47/0.65 Formulae used in the proof : goals additive_idempotence multiplicative_left_identity additive_commutativity order test_2 test_3 left_distributivity
% 0.47/0.65
%------------------------------------------------------------------------------