TSTP Solution File: KLE090-10 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 02:28:27 EDT 2022
% Result : Unsatisfiable 0.61s 0.79s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 37 RR)
% Number of literals : 37 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 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(3,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE090-10.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE090-10.p',unknown),
[] ).
cnf(5,axiom,
equal(addition(u,zero),u),
file('KLE090-10.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,u),u),
file('KLE090-10.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(u,one),u),
file('KLE090-10.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(one,u),u),
file('KLE090-10.p',unknown),
[] ).
cnf(10,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE090-10.p',unknown),
[] ).
cnf(11,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE090-10.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE090-10.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE090-10.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE090-10.p',unknown),
[] ).
cnf(24,axiom,
equal(addition(sK2_goals_X0,sK1_goals_X1),sK1_goals_X1),
file('KLE090-10.p',unknown),
[] ).
cnf(25,axiom,
~ equal(addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),antidomain(sK2_goals_X0)),
file('KLE090-10.p',unknown),
[] ).
cnf(27,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[3,18]),
[iquote('0:Rew:3.0,18.0')] ).
cnf(28,plain,
~ equal(addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)),antidomain(sK2_goals_X0)),
inference(rew,[status(thm),theory(equality)],[3,25]),
[iquote('0:Rew:3.0,25.0')] ).
cnf(43,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[16,8]),
[iquote('0:SpR:16.0,8.0')] ).
cnf(53,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(78,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[43,27]),
[iquote('0:SpR:43.0,27.0')] ).
cnf(80,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[53,78]),
[iquote('0:Rew:53.0,78.0')] ).
cnf(244,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(418,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[27,244]),
[iquote('0:SpR:27.0,244.0')] ).
cnf(421,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[3,418]),
[iquote('0:Rew:3.0,418.0')] ).
cnf(439,plain,
equal(addition(multiplication(u,sK2_goals_X0),multiplication(u,sK1_goals_X1)),multiplication(u,sK1_goals_X1)),
inference(spr,[status(thm),theory(equality)],[24,10]),
[iquote('0:SpR:24.0,10.0')] ).
cnf(449,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[27,10]),
[iquote('0:SpR:27.0,10.0')] ).
cnf(460,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[8,449]),
[iquote('0:Rew:8.0,449.0')] ).
cnf(486,plain,
equal(addition(multiplication(one,u),multiplication(antidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[421,11]),
[iquote('0:SpR:421.0,11.0')] ).
cnf(493,plain,
equal(addition(u,multiplication(antidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[9,486]),
[iquote('0:Rew:9.0,486.0')] ).
cnf(1236,plain,
equal(addition(multiplication(antidomain(sK1_goals_X1),sK2_goals_X0),zero),zero),
inference(spr,[status(thm),theory(equality)],[16,439]),
[iquote('0:SpR:16.0,439.0')] ).
cnf(1248,plain,
equal(multiplication(antidomain(sK1_goals_X1),sK2_goals_X0),zero),
inference(rew,[status(thm),theory(equality)],[53,1236,3]),
[iquote('0:Rew:53.0,1236.0,3.0,1236.0')] ).
cnf(1263,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))),
inference(spr,[status(thm),theory(equality)],[1248,17]),
[iquote('0:SpR:1248.0,17.0')] ).
cnf(1271,plain,
equal(antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),one),
inference(rew,[status(thm),theory(equality)],[421,1263,80]),
[iquote('0:Rew:421.0,1263.0,80.0,1263.0')] ).
cnf(1395,plain,
equal(multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),zero),
inference(spr,[status(thm),theory(equality)],[1271,16]),
[iquote('0:SpR:1271.0,16.0')] ).
cnf(1416,plain,
equal(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))),zero),
inference(rew,[status(thm),theory(equality)],[9,1395]),
[iquote('0:Rew:9.0,1395.0')] ).
cnf(3430,plain,
equal(addition(multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),zero),antidomain(sK1_goals_X1)),
inference(spr,[status(thm),theory(equality)],[1416,460]),
[iquote('0:SpR:1416.0,460.0')] ).
cnf(3457,plain,
equal(multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),antidomain(sK1_goals_X1)),
inference(rew,[status(thm),theory(equality)],[53,3430,3]),
[iquote('0:Rew:53.0,3430.0,3.0,3430.0')] ).
cnf(3636,plain,
equal(addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)),antidomain(sK2_goals_X0)),
inference(spr,[status(thm),theory(equality)],[3457,493]),
[iquote('0:SpR:3457.0,493.0')] ).
cnf(3648,plain,
$false,
inference(mrr,[status(thm)],[3636,28]),
[iquote('0:MRR:3636.0,28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n027.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 14:14:35 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.61/0.79
% 0.61/0.79 SPASS V 3.9
% 0.61/0.79 SPASS beiseite: Proof found.
% 0.61/0.79 % SZS status Theorem
% 0.61/0.79 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.79 SPASS derived 2522 clauses, backtracked 0 clauses, performed 0 splits and kept 573 clauses.
% 0.61/0.79 SPASS allocated 66667 KBytes.
% 0.61/0.79 SPASS spent 0:00:00.41 on the problem.
% 0.61/0.79 0:00:00.03 for the input.
% 0.61/0.79 0:00:00.00 for the FLOTTER CNF translation.
% 0.61/0.79 0:00:00.03 for inferences.
% 0.61/0.79 0:00:00.00 for the backtracking.
% 0.61/0.79 0:00:00.32 for the reduction.
% 0.61/0.79
% 0.61/0.79
% 0.61/0.79 Here is a proof with depth 6, length 37 :
% 0.61/0.79 % SZS output start Refutation
% See solution above
% 0.61/0.79 Formulae used in the proof : additive_commutativity additive_associativity additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity right_distributivity left_distributivity domain1 domain2 domain3 goals goals_1
% 0.61/0.79
%------------------------------------------------------------------------------