%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE004+1 : 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 02:27:56 EDT 2022
% Result : Theorem 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 27 ( 10 unt; 1 nHn; 27 RR)
% Number of literals : 51 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(c(zero),one),
file('KLE004+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE004+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE004+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(u,zero),zero),
file('KLE004+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(zero,u),zero),
file('KLE004+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ complement(u,v)
| test__dfg(v) ),
file('KLE004+1.p',unknown),
[] ).
cnf(9,axiom,
( test__dfg(u)
| equal(c(u),zero) ),
file('KLE004+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE004+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE004+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE004+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE004+1.p',unknown),
[] ).
cnf(53,plain,
( ~ complement(zero,u)
| equal(one,u) ),
inference(spr,[status(thm),theory(equality)],[16,2]),
[iquote('0:SpR:16.1,2.0')] ).
cnf(62,plain,
( ~ complement(one,u)
| equal(zero,u) ),
inference(spr,[status(thm),theory(equality)],[15,5]),
[iquote('0:SpR:15.1,5.0')] ).
cnf(134,plain,
( ~ test__dfg(u)
| complement(u,c(u)) ),
inference(eqr,[status(thm),theory(equality)],[19]),
[iquote('0:EqR:19.1')] ).
cnf(140,plain,
( ~ test__dfg(u)
| test__dfg(c(u)) ),
inference(res,[status(thm),theory(equality)],[134,8]),
[iquote('0:Res:134.1,8.0')] ).
cnf(141,plain,
( ~ test__dfg(zero)
| equal(c(zero),one) ),
inference(res,[status(thm),theory(equality)],[134,53]),
[iquote('0:Res:134.1,53.0')] ).
cnf(142,plain,
( ~ test__dfg(one)
| equal(c(one),zero) ),
inference(res,[status(thm),theory(equality)],[134,62]),
[iquote('0:Res:134.1,62.0')] ).
cnf(143,plain,
~ test__dfg(zero),
inference(mrr,[status(thm)],[141,1]),
[iquote('0:MRR:141.1,1.0')] ).
cnf(145,plain,
equal(c(one),zero),
inference(mrr,[status(thm)],[142,9]),
[iquote('0:MRR:142.0,9.0')] ).
cnf(171,plain,
( ~ test__dfg(one)
| test__dfg(zero) ),
inference(spr,[status(thm),theory(equality)],[145,140]),
[iquote('0:SpR:145.0,140.1')] ).
cnf(172,plain,
~ test__dfg(one),
inference(mrr,[status(thm)],[171,143]),
[iquote('0:MRR:171.1,143.0')] ).
cnf(374,plain,
( ~ equal(u,one)
| ~ equal(multiplication(zero,u),zero)
| ~ equal(multiplication(u,zero),zero)
| complement(zero,u) ),
inference(spl,[status(thm),theory(equality)],[2,23]),
[iquote('0:SpL:2.0,23.0')] ).
cnf(385,plain,
( ~ equal(u,one)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(zero,u) ),
inference(rew,[status(thm),theory(equality)],[6,374,7]),
[iquote('0:Rew:6.0,374.2,7.0,374.1')] ).
cnf(386,plain,
( ~ equal(u,one)
| complement(zero,u) ),
inference(obv,[status(thm),theory(equality)],[385]),
[iquote('0:Obv:385.2')] ).
cnf(399,plain,
( ~ equal(u,one)
| test__dfg(u) ),
inference(res,[status(thm),theory(equality)],[386,8]),
[iquote('0:Res:386.1,8.0')] ).
cnf(410,plain,
~ equal(one,one),
inference(sor,[status(thm)],[172,399]),
[iquote('0:SoR:172.0,399.1')] ).
cnf(411,plain,
$false,
inference(obv,[status(thm),theory(equality)],[410]),
[iquote('0:Obv:410.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE004+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 09:36:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.47
% 0.22/0.47 SPASS V 3.9
% 0.22/0.47 SPASS beiseite: Proof found.
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.47 SPASS derived 318 clauses, backtracked 0 clauses, performed 0 splits and kept 142 clauses.
% 0.22/0.47 SPASS allocated 97893 KBytes.
% 0.22/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.22/0.47 0:00:00.03 for the input.
% 0.22/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.47 0:00:00.00 for inferences.
% 0.22/0.47 0:00:00.00 for the backtracking.
% 0.22/0.47 0:00:00.02 for the reduction.
% 0.22/0.47
% 0.22/0.47
% 0.22/0.47 Here is a proof with depth 4, length 27 :
% 0.22/0.47 % SZS output start Refutation
% See solution above
% 0.22/0.47 Formulae used in the proof : goals additive_identity multiplicative_left_identity right_annihilation left_annihilation test_1 test_4 test_2 test_3
% 0.22/0.47
%------------------------------------------------------------------------------