%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG176+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 18:02:49 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 3 unt; 0 nHn; 15 RR)
% Number of literals : 34 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sorti1(skc1),
file('ALG176+1.p',unknown),
[] ).
cnf(2,axiom,
sorti2(skf1(u)),
file('ALG176+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sorti1(u)
| sorti2(h(u)) ),
file('ALG176+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(u)
| sorti1(j(u)) ),
file('ALG176+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ sorti1(u)
| equal(j(h(u)),u) ),
file('ALG176+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ sorti1(u)
| ~ equal(op1(u,skc1),u) ),
file('ALG176+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti2(u)
| equal(op2(skf1(u),u),skf1(u)) ),
file('ALG176+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(u)),j(op2(v,u))) ),
file('ALG176+1.p',unknown),
[] ).
cnf(29,plain,
( ~ sorti1(u)
| ~ sorti2(h(u))
| ~ sorti2(v)
| equal(j(op2(v,h(u))),op1(j(v),u)) ),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.1,12.2')] ).
cnf(33,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| equal(j(op2(v,h(u))),op1(j(v),u)) ),
inference(ssi,[status(thm)],[29,3]),
[iquote('0:SSi:29.1,3.1')] ).
cnf(101,plain,
( ~ sorti2(h(u))
| ~ sorti1(u)
| ~ sorti2(skf1(h(u)))
| equal(op1(j(skf1(h(u))),u),j(skf1(h(u)))) ),
inference(spr,[status(thm),theory(equality)],[10,33]),
[iquote('0:SpR:10.1,33.2')] ).
cnf(108,plain,
( ~ sorti1(u)
| equal(op1(j(skf1(h(u))),u),j(skf1(h(u)))) ),
inference(ssi,[status(thm)],[101,2,3]),
[iquote('0:SSi:101.2,101.0,2.1,3.1,3.0')] ).
cnf(133,plain,
( ~ sorti1(skc1)
| ~ sorti1(j(skf1(h(skc1))))
| ~ equal(j(skf1(h(skc1))),j(skf1(h(skc1)))) ),
inference(spl,[status(thm),theory(equality)],[108,7]),
[iquote('0:SpL:108.1,7.1')] ).
cnf(137,plain,
( ~ sorti1(skc1)
| ~ sorti1(j(skf1(h(skc1)))) ),
inference(obv,[status(thm),theory(equality)],[133]),
[iquote('0:Obv:133.2')] ).
cnf(138,plain,
$false,
inference(ssi,[status(thm)],[137,4,2,3,1]),
[iquote('0:SSi:137.1,137.0,4.0,2.0,3.1,1.0,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG176+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 08:22:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 72 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.19/0.44 SPASS allocated 104019 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.03 for the input.
% 0.19/0.44 0:00:00.02 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.01 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 3, length 15 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : ax3 ax4 co1
% 0.19/0.44
%------------------------------------------------------------------------------