TSTP Solution File: KLE022+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 02:28:05 EDT 2022
% Result : Theorem 0.47s 0.64s
% 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('KLE022+2.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE022+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE022+2.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE022+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE022+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE022+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE022+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE022+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE022+2.p',unknown),
[] ).
cnf(21,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE022+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('KLE022+2.p',unknown),
[] ).
cnf(24,axiom,
( ~ leq(skc4,addition(multiplication(skc4,skc3),multiplication(skc4,c(skc3))))
| ~ leq(addition(multiplication(skc5,skc3),multiplication(skc5,c(skc3))),skc5) ),
file('KLE022+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(294,plain,
( ~ complement(u,v)
| equal(multiplication(w,one),addition(multiplication(w,v),multiplication(w,u))) ),
inference(spr,[status(thm),theory(equality)],[16,21]),
[iquote('0:SpR:16.1,21.0')] ).
cnf(306,plain,
( ~ complement(u,v)
| equal(addition(multiplication(w,v),multiplication(w,u)),w) ),
inference(rew,[status(thm),theory(equality)],[4,294]),
[iquote('0:Rew:4.0,294.1')] ).
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(2269,plain,
( ~ complement(c(skc3),skc3)
| ~ leq(skc4,addition(multiplication(skc4,skc3),multiplication(skc4,c(skc3))))
| ~ leq(skc5,skc5) ),
inference(spl,[status(thm),theory(equality)],[306,24]),
[iquote('0:SpL:306.1,24.1')] ).
cnf(2299,plain,
( ~ complement(c(skc3),skc3)
| ~ leq(skc4,skc4)
| ~ leq(skc5,skc5) ),
inference(rew,[status(thm),theory(equality)],[306,2269]),
[iquote('0:Rew:306.1,2269.1')] ).
cnf(2300,plain,
$false,
inference(mrr,[status(thm)],[2299,507,103]),
[iquote('0:MRR:2299.0,2299.1,2299.2,507.0,103.0,103.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 13:42:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.47/0.64
% 0.47/0.64 SPASS V 3.9
% 0.47/0.64 SPASS beiseite: Proof found.
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.64 SPASS derived 1786 clauses, backtracked 0 clauses, performed 0 splits and kept 662 clauses.
% 0.47/0.64 SPASS allocated 99270 KBytes.
% 0.47/0.64 SPASS spent 0:00:00.28 on the problem.
% 0.47/0.64 0:00:00.04 for the input.
% 0.47/0.64 0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.64 0:00:00.01 for inferences.
% 0.47/0.64 0:00:00.00 for the backtracking.
% 0.47/0.64 0:00:00.18 for the reduction.
% 0.47/0.64
% 0.47/0.64
% 0.47/0.64 Here is a proof with depth 3, length 27 :
% 0.47/0.64 % SZS output start Refutation
% See solution above
% 0.47/0.64 Formulae used in the proof : goals additive_idempotence multiplicative_right_identity additive_commutativity order test_2 test_3 right_distributivity
% 0.47/0.64
%------------------------------------------------------------------------------