TSTP Solution File: ALG029+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG029+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 18:02:01 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,
sorti2(skc3),
file('ALG029+1.p',unknown),
[] ).
cnf(2,axiom,
sorti2(skc2),
file('ALG029+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(u)
| sorti1(j(u)) ),
file('ALG029+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ sorti2(u)
| equal(h(j(u)),u) ),
file('ALG029+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(op2(skc3,skc2),op2(skc2,skc3)),
file('ALG029+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| sorti2(op2(v,u)) ),
file('ALG029+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op1(v,u),op1(u,v)) ),
file('ALG029+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(u)),j(op2(v,u))) ),
file('ALG029+1.p',unknown),
[] ).
cnf(35,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(v))
| ~ sorti1(j(u))
| equal(op1(j(u),j(v)),j(op2(v,u))) ),
inference(spr,[status(thm),theory(equality)],[12,10]),
[iquote('0:SpR:12.2,10.2')] ).
cnf(42,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti1(j(v))
| ~ sorti1(j(u))
| equal(j(op2(u,v)),j(op2(v,u))) ),
inference(rew,[status(thm),theory(equality)],[12,35]),
[iquote('0:Rew:12.2,35.4')] ).
cnf(43,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(j(op2(u,v)),j(op2(v,u))) ),
inference(ssi,[status(thm)],[42,4]),
[iquote('0:SSi:42.3,42.2,4.1,4.1')] ).
cnf(53,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti2(op2(v,u))
| equal(h(j(op2(u,v))),op2(v,u)) ),
inference(spr,[status(thm),theory(equality)],[43,5]),
[iquote('0:SpR:43.2,5.1')] ).
cnf(61,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(h(j(op2(u,v))),op2(v,u)) ),
inference(ssi,[status(thm)],[53,9]),
[iquote('0:SSi:53.2,9.2')] ).
cnf(66,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ sorti2(op2(u,v))
| equal(op2(v,u),op2(u,v)) ),
inference(spr,[status(thm),theory(equality)],[61,5]),
[iquote('0:SpR:61.2,5.1')] ).
cnf(70,plain,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op2(v,u),op2(u,v)) ),
inference(ssi,[status(thm)],[66,9]),
[iquote('0:SSi:66.2,9.2')] ).
cnf(125,plain,
( ~ sorti2(skc2)
| ~ sorti2(skc3)
| ~ equal(op2(skc2,skc3),op2(skc2,skc3)) ),
inference(spl,[status(thm),theory(equality)],[70,7]),
[iquote('0:SpL:70.2,7.0')] ).
cnf(127,plain,
( ~ sorti2(skc2)
| ~ sorti2(skc3) ),
inference(obv,[status(thm),theory(equality)],[125]),
[iquote('0:Obv:125.2')] ).
cnf(128,plain,
$false,
inference(ssi,[status(thm)],[127,1,2]),
[iquote('0:SSi:127.1,127.0,1.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % 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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 03:36:20 EDT 2022
% 0.12/0.33 % 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 73 clauses, backtracked 0 clauses, performed 0 splits and kept 31 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 : ax4 co1 ax2 ax3
% 0.19/0.44
%------------------------------------------------------------------------------