TSTP Solution File: LCL096-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:34:34 EDT 2022
% Result : Unsatisfiable 34.24s 34.43s
% Output : Refutation 34.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 23 RR)
% Number of literals : 23 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq(u,u,v,w),v),
file('LCL096-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ifeq(is_a_theorem(equivalent(u,v)),true__dfg,ifeq(is_a_theorem(u),true__dfg,is_a_theorem(v),true__dfg),true__dfg),true__dfg),
file('LCL096-10.p',unknown),
[] ).
cnf(3,axiom,
equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x)),true__dfg),
file('LCL096-10.p',unknown),
[] ).
cnf(4,axiom,
equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y),y)),true__dfg),
file('LCL096-10.p',unknown),
[] ).
cnf(5,axiom,
equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),x),equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x)))),true__dfg),
file('LCL096-10.p',unknown),
[] ).
cnf(6,axiom,
~ equal(is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),true__dfg),
file('LCL096-10.p',unknown),
[] ).
cnf(12,plain,
equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x),y)),true__dfg,ifeq(true__dfg,true__dfg,is_a_theorem(y),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(14,plain,
equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x),y)),true__dfg,is_a_theorem(y),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,12]),
[iquote('0:Rew:1.0,12.0')] ).
cnf(18,plain,
equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y),y),z)),true__dfg,ifeq(true__dfg,true__dfg,is_a_theorem(z),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(20,plain,
equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y),y),z)),true__dfg,is_a_theorem(z),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,18]),
[iquote('0:Rew:1.0,18.0')] ).
cnf(28,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(is_a_theorem(equivalent(equivalent(equivalent(u,v),w),x)),true__dfg,is_a_theorem(equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x))),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(33,plain,
equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(u,v),w),x)),true__dfg,is_a_theorem(equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x))),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,28]),
[iquote('0:Rew:1.0,28.0')] ).
cnf(68,plain,
equal(ifeq(true__dfg,true__dfg,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),equivalent(equivalent(equivalent(v,w),x),y))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[5,14]),
[iquote('0:SpR:5.0,14.0')] ).
cnf(72,plain,
equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),equivalent(equivalent(equivalent(v,w),x),y))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,68]),
[iquote('0:Rew:1.0,68.0')] ).
cnf(250,plain,
equal(ifeq(true__dfg,true__dfg,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),z),equivalent(equivalent(equivalent(equivalent(v,w),x),y),z))),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[4,33]),
[iquote('0:SpR:4.0,33.0')] ).
cnf(265,plain,
equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),z),equivalent(equivalent(equivalent(equivalent(v,w),x),y),z))),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,250]),
[iquote('0:Rew:1.0,250.0')] ).
cnf(1683,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y)),true__dfg,is_a_theorem(equivalent(equivalent(equivalent(v,w),x),y)),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[72,2]),
[iquote('0:SpR:72.0,2.0')] ).
cnf(1727,plain,
equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y)),true__dfg,is_a_theorem(equivalent(equivalent(equivalent(v,w),x),y)),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,1683]),
[iquote('0:Rew:1.0,1683.0')] ).
cnf(3129,plain,
equal(ifeq(true__dfg,true__dfg,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w))),y),y)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[265,20]),
[iquote('0:SpR:265.0,20.0')] ).
cnf(3175,plain,
equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w))),y),y)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,3129]),
[iquote('0:Rew:1.0,3129.0')] ).
cnf(24317,plain,
equal(ifeq(true__dfg,true__dfg,is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,v),u)),w),w)),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[3175,1727]),
[iquote('0:SpR:3175.0,1727.0')] ).
cnf(24453,plain,
equal(is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,v),u)),w),w)),true__dfg),
inference(rew,[status(thm),theory(equality)],[1,24317]),
[iquote('0:Rew:1.0,24317.0')] ).
cnf(24454,plain,
$false,
inference(unc,[status(thm)],[24453,6]),
[iquote('0:UnC:24453.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 4 05:22:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 34.24/34.43
% 34.24/34.43 SPASS V 3.9
% 34.24/34.43 SPASS beiseite: Proof found.
% 34.24/34.43 % SZS status Theorem
% 34.24/34.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.24/34.43 SPASS derived 16079 clauses, backtracked 0 clauses, performed 0 splits and kept 5564 clauses.
% 34.24/34.43 SPASS allocated 99755 KBytes.
% 34.24/34.43 SPASS spent 0:0:32.94 on the problem.
% 34.24/34.43 0:00:00.04 for the input.
% 34.24/34.43 0:00:00.00 for the FLOTTER CNF translation.
% 34.24/34.43 0:00:00.35 for inferences.
% 34.24/34.43 0:00:00.00 for the backtracking.
% 34.24/34.43 0:0:32.48 for the reduction.
% 34.24/34.43
% 34.24/34.43
% 34.24/34.43 Here is a proof with depth 4, length 23 :
% 34.24/34.43 % SZS output start Refutation
% See solution above
% 34.24/34.43 Formulae used in the proof : ifeq_axiom condensed_detachment lg_2 lg_3 lg_4 prove_lg_1
% 34.24/34.43
%------------------------------------------------------------------------------