%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG030+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 18:02:02 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 4 unt; 0 nHn; 18 RR)
% Number of literals : 49 ( 0 equ; 34 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sorti1(skc3),
file('ALG030+1.p',unknown),
[] ).
cnf(2,axiom,
sorti1(skc2),
file('ALG030+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sorti1(u)
| sorti2(h(u)) ),
file('ALG030+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ sorti1(u)
| equal(j(h(u)),u) ),
file('ALG030+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(op1(skc3,skc2),op1(skc2,skc3)),
file('ALG030+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| sorti1(op1(v,u)) ),
file('ALG030+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op2(v,u),op2(u,v)) ),
file('ALG030+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op2(h(v),h(u)),h(op1(v,u))) ),
file('ALG030+1.p',unknown),
[] ).
cnf(47,plain,
( ~ sorti1(u)
| ~ sorti1(v)
| ~ sorti2(h(v))
| ~ sorti2(h(u))
| equal(op2(h(u),h(v)),h(op1(v,u))) ),
inference(spr,[status(thm),theory(equality)],[11,10]),
[iquote('0:SpR:11.2,10.2')] ).
cnf(55,plain,
( ~ sorti1(u)
| ~ sorti1(v)
| ~ sorti2(h(v))
| ~ sorti2(h(u))
| equal(h(op1(u,v)),h(op1(v,u))) ),
inference(rew,[status(thm),theory(equality)],[11,47]),
[iquote('0:Rew:11.2,47.4')] ).
cnf(56,plain,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(h(op1(u,v)),h(op1(v,u))) ),
inference(ssi,[status(thm)],[55,3]),
[iquote('0:SSi:55.3,55.2,3.1,3.1')] ).
cnf(68,plain,
( ~ sorti1(u)
| ~ sorti1(v)
| ~ sorti1(op1(v,u))
| equal(j(h(op1(u,v))),op1(v,u)) ),
inference(spr,[status(thm),theory(equality)],[56,6]),
[iquote('0:SpR:56.2,6.1')] ).
cnf(78,plain,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(j(h(op1(u,v))),op1(v,u)) ),
inference(ssi,[status(thm)],[68,8]),
[iquote('0:SSi:68.2,8.2')] ).
cnf(95,plain,
( ~ sorti1(u)
| ~ sorti1(v)
| ~ sorti1(op1(u,v))
| equal(op1(v,u),op1(u,v)) ),
inference(spr,[status(thm),theory(equality)],[78,6]),
[iquote('0:SpR:78.2,6.1')] ).
cnf(101,plain,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op1(v,u),op1(u,v)) ),
inference(ssi,[status(thm)],[95,8]),
[iquote('0:SSi:95.2,8.2')] ).
cnf(126,plain,
( ~ sorti1(skc2)
| ~ sorti1(skc3)
| ~ equal(op1(skc2,skc3),op1(skc2,skc3)) ),
inference(spl,[status(thm),theory(equality)],[101,7]),
[iquote('0:SpL:101.2,7.0')] ).
cnf(128,plain,
( ~ sorti1(skc2)
| ~ sorti1(skc3) ),
inference(obv,[status(thm),theory(equality)],[126]),
[iquote('0:Obv:126.2')] ).
cnf(129,plain,
$false,
inference(ssi,[status(thm)],[128,1,2]),
[iquote('0:SSi:128.1,128.0,1.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG030+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 00:39:06 EDT 2022
% 0.13/0.33 % 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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 74 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.19/0.44 SPASS allocated 103991 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 0:00:00.03 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 4, length 18 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : ax3 co1 ax1 ax4
% 0.19/0.44
%------------------------------------------------------------------------------