%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE009+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 02:27:58 EDT 2022
% Result : Theorem 0.47s 0.67s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 32 ( 15 unt; 0 nHn; 32 RR)
% Number of literals : 59 ( 0 equ; 34 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
test__dfg(skc3),
file('KLE009+1.p',unknown),
[] ).
cnf(2,axiom,
test__dfg(skc2),
file('KLE009+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE009+1.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE009+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE009+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE009+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE009+1.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE009+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE009+1.p',unknown),
[] ).
cnf(22,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE009+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE009+1.p',unknown),
[] ).
cnf(25,axiom,
~ equal(addition(addition(addition(multiplication(skc3,skc2),multiplication(skc3,c(skc2))),multiplication(c(skc3),skc2)),multiplication(c(skc3),c(skc2))),one),
file('KLE009+1.p',unknown),
[] ).
cnf(26,plain,
~ equal(addition(multiplication(skc3,skc2),addition(multiplication(skc3,c(skc2)),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2))))),one),
inference(rew,[status(thm),theory(equality)],[18,25]),
[iquote('0:Rew:18.0,25.0,18.0,25.0,18.0,25.0')] ).
cnf(27,plain,
( ~ equal(c(skc2),u)
| complement(skc2,u) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.0')] ).
cnf(30,plain,
( ~ equal(c(skc3),u)
| complement(skc3,u) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).
cnf(59,plain,
( ~ complement(u,v)
| equal(addition(u,v),one) ),
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.1,11.0')] ).
cnf(81,plain,
complement(skc3,c(skc3)),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.0')] ).
cnf(94,plain,
complement(skc2,c(skc2)),
inference(eqr,[status(thm),theory(equality)],[27]),
[iquote('0:EqR:27.0')] ).
cnf(186,plain,
equal(addition(u,addition(v,w)),addition(w,addition(u,v))),
inference(spr,[status(thm),theory(equality)],[18,11]),
[iquote('0:SpR:18.0,11.0')] ).
cnf(307,plain,
( ~ complement(u,v)
| equal(multiplication(w,one),addition(multiplication(w,v),multiplication(w,u))) ),
inference(spr,[status(thm),theory(equality)],[17,22]),
[iquote('0:SpR:17.1,22.0')] ).
cnf(319,plain,
( ~ complement(u,v)
| equal(addition(multiplication(w,v),multiplication(w,u)),w) ),
inference(rew,[status(thm),theory(equality)],[5,307]),
[iquote('0:Rew:5.0,307.1')] ).
cnf(333,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)],[59,24]),
[iquote('0:SpL:59.1,24.0')] ).
cnf(347,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[333]),
[iquote('0:Obv:333.1')] ).
cnf(348,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[16,347,15]),
[iquote('0:Rew:16.1,347.2,15.1,347.1')] ).
cnf(349,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[348]),
[iquote('0:Obv:348.2')] ).
cnf(554,plain,
complement(c(skc2),skc2),
inference(res,[status(thm),theory(equality)],[94,349]),
[iquote('0:Res:94.0,349.0')] ).
cnf(2314,plain,
( ~ complement(c(skc2),skc2)
| ~ equal(addition(multiplication(skc3,skc2),addition(multiplication(skc3,c(skc2)),c(skc3))),one) ),
inference(spl,[status(thm),theory(equality)],[319,26]),
[iquote('0:SpL:319.1,26.0')] ).
cnf(2344,plain,
( ~ complement(c(skc2),skc2)
| ~ equal(addition(skc3,c(skc3)),one) ),
inference(rew,[status(thm),theory(equality)],[11,2314,319,186]),
[iquote('0:Rew:11.0,2314.1,319.1,2314.1,186.0,2314.1')] ).
cnf(2345,plain,
~ equal(addition(skc3,c(skc3)),one),
inference(mrr,[status(thm)],[2344,554]),
[iquote('0:MRR:2344.0,554.0')] ).
cnf(2358,plain,
( ~ complement(skc3,c(skc3))
| ~ equal(one,one) ),
inference(spl,[status(thm),theory(equality)],[59,2345]),
[iquote('0:SpL:59.1,2345.0')] ).
cnf(2362,plain,
~ complement(skc3,c(skc3)),
inference(obv,[status(thm),theory(equality)],[2358]),
[iquote('0:Obv:2358.1')] ).
cnf(2363,plain,
$false,
inference(mrr,[status(thm)],[2362,81]),
[iquote('0:MRR:2362.0,81.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE009+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 08:32:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.47/0.67
% 0.47/0.67 SPASS V 3.9
% 0.47/0.67 SPASS beiseite: Proof found.
% 0.47/0.67 % SZS status Theorem
% 0.47/0.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.67 SPASS derived 1829 clauses, backtracked 0 clauses, performed 0 splits and kept 694 clauses.
% 0.47/0.67 SPASS allocated 99323 KBytes.
% 0.47/0.67 SPASS spent 0:00:00.32 on the problem.
% 0.47/0.67 0:00:00.03 for the input.
% 0.47/0.67 0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.67 0:00:00.02 for inferences.
% 0.47/0.67 0:00:00.00 for the backtracking.
% 0.47/0.67 0:00:00.21 for the reduction.
% 0.47/0.67
% 0.47/0.67
% 0.47/0.67 Here is a proof with depth 3, length 32 :
% 0.47/0.67 % SZS output start Refutation
% See solution above
% 0.47/0.67 Formulae used in the proof : goals multiplicative_right_identity additive_commutativity test_2 additive_associativity test_3 right_distributivity
% 0.47/0.67
%------------------------------------------------------------------------------