%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG011-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : Thu Jul 14 18:01:56 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 8 unt; 1 nHn; 18 RR)
% Number of literals : 30 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(f(f(u,v),w),f(u,f(v,w))),
file('ALG011-1.p',unknown),
[] ).
cnf(2,axiom,
( d(u)
| c(u) ),
file('ALG011-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ d(u)
| ~ c(u) ),
file('ALG011-1.p',unknown),
[] ).
cnf(4,axiom,
c(a1),
file('ALG011-1.p',unknown),
[] ).
cnf(5,axiom,
d(a2),
file('ALG011-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ c(u)
| ~ c(v)
| d(f(v,u)) ),
file('ALG011-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ d(u)
| ~ d(v)
| c(f(v,u)) ),
file('ALG011-1.p',unknown),
[] ).
cnf(8,plain,
( ~ d(u)
| c(f(a2,u)) ),
inference(res,[status(thm),theory(equality)],[5,7]),
[iquote('0:Res:5.0,7.0')] ).
cnf(9,plain,
( ~ d(u)
| c(f(u,a2)) ),
inference(res,[status(thm),theory(equality)],[5,7]),
[iquote('0:Res:5.0,7.1')] ).
cnf(11,plain,
( ~ c(u)
| d(f(u,a1)) ),
inference(res,[status(thm),theory(equality)],[4,6]),
[iquote('0:Res:4.0,6.1')] ).
cnf(26,plain,
( ~ c(f(u,v))
| d(f(u,f(v,a1))) ),
inference(spr,[status(thm),theory(equality)],[1,11]),
[iquote('0:SpR:1.0,11.1')] ).
cnf(31,plain,
( ~ d(u)
| d(f(u,f(a2,a1))) ),
inference(sor,[status(thm)],[26,9]),
[iquote('0:SoR:26.0,9.1')] ).
cnf(34,plain,
( ~ d(a2)
| ~ d(f(a2,a1)) ),
inference(ems,[status(thm)],[3,31,8]),
[iquote('0:EmS:3.0,3.1,31.1,8.1')] ).
cnf(37,plain,
~ d(f(a2,a1)),
inference(ssi,[status(thm)],[34,5]),
[iquote('0:SSi:34.0,5.0')] ).
cnf(48,plain,
c(f(a2,a1)),
inference(sor,[status(thm)],[37,2]),
[iquote('0:SoR:37.0,2.0')] ).
cnf(52,plain,
d(f(a2,f(a1,a1))),
inference(sor,[status(thm)],[26,48]),
[iquote('0:SoR:26.0,48.0')] ).
cnf(53,plain,
~ d(f(a1,a1)),
inference(ems,[status(thm)],[3,52,8]),
[iquote('0:EmS:3.0,3.1,52.0,8.1')] ).
cnf(56,plain,
$false,
inference(ssi,[status(thm)],[53,6,4]),
[iquote('0:SSi:53.0,6.0,4.0,4.2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG011-1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 8 03:18:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 42 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.21/0.42 SPASS allocated 75649 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.21/0.42 0:00:00.04 for the input.
% 0.21/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.00 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 7, length 18 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : f_is_associative partitions_union partitions_exclusive partition_c_not_empty partition_d_not_empty conjecture_1 conjecture_2
% 0.21/0.42
%------------------------------------------------------------------------------