%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% 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 16:45:54 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(f(f(u,v),f(u,w)),f(u,f(v,w))),
file('LDA001-1.p',unknown),
[] ).
cnf(2,axiom,
equal(f(n1,n1),n2),
file('LDA001-1.p',unknown),
[] ).
cnf(3,axiom,
equal(f(n2,n1),n3),
file('LDA001-1.p',unknown),
[] ).
cnf(4,axiom,
equal(f(n2,n2),u__dfg),
file('LDA001-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(f(f(u__dfg,u__dfg),u__dfg),f(f(n3,n2),u__dfg)),
file('LDA001-1.p',unknown),
[] ).
cnf(12,plain,
equal(f(f(n2,u),n3),f(n2,f(u,n1))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(13,plain,
equal(f(f(n2,u),u__dfg),f(n2,f(u,n2))),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(14,plain,
equal(f(f(n1,u),n2),f(n1,f(u,n1))),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(15,plain,
equal(f(n3,f(n2,u)),f(n2,f(n1,u))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(21,plain,
equal(f(n2,f(n1,n1)),f(n3,n3)),
inference(spr,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpR:3.0,12.0')] ).
cnf(23,plain,
equal(f(n3,n3),u__dfg),
inference(rew,[status(thm),theory(equality)],[4,21,2]),
[iquote('0:Rew:4.0,21.0,2.0,21.0')] ).
cnf(30,plain,
equal(f(f(n3,u),u__dfg),f(n3,f(u,n3))),
inference(spr,[status(thm),theory(equality)],[23,1]),
[iquote('0:SpR:23.0,1.0')] ).
cnf(32,plain,
~ equal(f(f(u__dfg,u__dfg),u__dfg),f(n3,f(n2,n3))),
inference(rew,[status(thm),theory(equality)],[30,5]),
[iquote('0:Rew:30.0,5.0')] ).
cnf(33,plain,
~ equal(f(f(u__dfg,u__dfg),u__dfg),f(n2,f(n1,n3))),
inference(rew,[status(thm),theory(equality)],[15,32]),
[iquote('0:Rew:15.0,32.0')] ).
cnf(42,plain,
equal(f(n2,f(n2,n2)),f(u__dfg,u__dfg)),
inference(spr,[status(thm),theory(equality)],[4,13]),
[iquote('0:SpR:4.0,13.0')] ).
cnf(43,plain,
equal(f(u__dfg,u__dfg),f(n2,u__dfg)),
inference(rew,[status(thm),theory(equality)],[4,42]),
[iquote('0:Rew:4.0,42.0')] ).
cnf(44,plain,
~ equal(f(f(n2,u__dfg),u__dfg),f(n2,f(n1,n3))),
inference(rew,[status(thm),theory(equality)],[43,33]),
[iquote('0:Rew:43.0,33.0')] ).
cnf(45,plain,
~ equal(f(n2,f(u__dfg,n2)),f(n2,f(n1,n3))),
inference(rew,[status(thm),theory(equality)],[13,44]),
[iquote('0:Rew:13.0,44.0')] ).
cnf(63,plain,
equal(f(n1,f(n1,n1)),f(n2,n2)),
inference(spr,[status(thm),theory(equality)],[2,14]),
[iquote('0:SpR:2.0,14.0')] ).
cnf(64,plain,
equal(f(n1,n2),u__dfg),
inference(rew,[status(thm),theory(equality)],[2,63,4]),
[iquote('0:Rew:2.0,63.0,4.0,63.0')] ).
cnf(76,plain,
equal(f(n1,f(n2,n1)),f(u__dfg,n2)),
inference(spr,[status(thm),theory(equality)],[64,14]),
[iquote('0:SpR:64.0,14.0')] ).
cnf(80,plain,
equal(f(u__dfg,n2),f(n1,n3)),
inference(rew,[status(thm),theory(equality)],[3,76]),
[iquote('0:Rew:3.0,76.0')] ).
cnf(81,plain,
~ equal(f(n2,f(n1,n3)),f(n2,f(n1,n3))),
inference(rew,[status(thm),theory(equality)],[80,45]),
[iquote('0:Rew:80.0,45.0')] ).
cnf(82,plain,
$false,
inference(obv,[status(thm),theory(equality)],[81]),
[iquote('0:Obv:81.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 02:21:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 51 clauses, backtracked 0 clauses, performed 0 splits and kept 34 clauses.
% 0.19/0.42 SPASS allocated 63192 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 3, length 24 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : a1 clause_2 clause_3 clause_4 prove_equation
% 0.19/0.42
%------------------------------------------------------------------------------