TSTP Solution File: BOO016-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO016-1 : TPTP v8.1.0. Released v1.0.0.
% 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 23:49:27 EDT 2022
% Result : Unsatisfiable 1.66s 1.83s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 31 ( 11 unt; 0 nHn; 31 RR)
% Number of literals : 77 ( 0 equ; 51 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(x__dfg,y__dfg,z__dfg),
file('BOO016-1.p',unknown),
[] ).
cnf(2,axiom,
~ sum__dfg(x__dfg,z__dfg,x__dfg),
file('BOO016-1.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(u,v,add(u,v)),
file('BOO016-1.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(additive_identity,u,u),
file('BOO016-1.p',unknown),
[] ).
cnf(9,axiom,
product(multiplicative_identity,u,u),
file('BOO016-1.p',unknown),
[] ).
cnf(10,axiom,
product(u,multiplicative_identity,u),
file('BOO016-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('BOO016-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('BOO016-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,v)
| ~ sum__dfg(u,y,z)
| ~ sum__dfg(u,x,x1)
| product(x1,z,w) ),
file('BOO016-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(x,y,z)
| ~ sum__dfg(y,x1,v)
| ~ sum__dfg(x,x1,u)
| sum__dfg(z,x1,w) ),
file('BOO016-1.p',unknown),
[] ).
cnf(19,axiom,
sum__dfg(inverse(u),u,multiplicative_identity),
file('BOO016-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('BOO016-1.p',unknown),
[] ).
cnf(28,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,w,x__dfg)
| ~ product(x,v,z__dfg)
| ~ product(x,u,x__dfg) ),
inference(res,[status(thm),theory(equality)],[11,2]),
[iquote('0:Res:11.4,2.0')] ).
cnf(46,plain,
( ~ sum__dfg(inverse(u),u,v)
| equal(v,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[19,23]),
[iquote('0:Res:19.0,23.0')] ).
cnf(72,plain,
( ~ product(u,v,w)
| ~ sum__dfg(v,x,y)
| ~ sum__dfg(u,x,multiplicative_identity)
| sum__dfg(w,x,y) ),
inference(res,[status(thm),theory(equality)],[9,18]),
[iquote('0:Res:9.0,18.0')] ).
cnf(124,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,multiplicative_identity,x)
| ~ product(u,multiplicative_identity,y)
| sum__dfg(y,x,w) ),
inference(res,[status(thm),theory(equality)],[10,13]),
[iquote('0:Res:10.0,13.0')] ).
cnf(219,plain,
( ~ product(u,v,w)
| ~ sum__dfg(additive_identity,v,x)
| ~ sum__dfg(additive_identity,u,y)
| product(y,x,w) ),
inference(res,[status(thm),theory(equality)],[7,15]),
[iquote('0:Res:7.0,15.0')] ).
cnf(413,plain,
( ~ product(u,multiplicative_identity,v)
| ~ product(additive_identity,multiplicative_identity,w)
| sum__dfg(w,v,u) ),
inference(res,[status(thm),theory(equality)],[7,124]),
[iquote('0:Res:7.0,124.0')] ).
cnf(531,plain,
( ~ sum__dfg(additive_identity,y__dfg,u)
| ~ sum__dfg(additive_identity,x__dfg,v)
| product(v,u,z__dfg) ),
inference(res,[status(thm),theory(equality)],[1,219]),
[iquote('0:Res:1.0,219.0')] ).
cnf(574,plain,
( ~ sum__dfg(multiplicative_identity,u,v)
| ~ sum__dfg(w,u,multiplicative_identity)
| sum__dfg(w,u,v) ),
inference(res,[status(thm),theory(equality)],[10,72]),
[iquote('0:Res:10.0,72.0')] ).
cnf(653,plain,
( ~ sum__dfg(additive_identity,x__dfg,u)
| product(u,y__dfg,z__dfg) ),
inference(res,[status(thm),theory(equality)],[7,531]),
[iquote('0:Res:7.0,531.0')] ).
cnf(1917,plain,
( ~ product(u,multiplicative_identity,x__dfg)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(u,y__dfg,z__dfg) ),
inference(res,[status(thm),theory(equality)],[413,653]),
[iquote('0:Res:413.2,653.0')] ).
cnf(2005,plain,
( ~ product(u,multiplicative_identity,x__dfg)
| product(u,y__dfg,z__dfg) ),
inference(mrr,[status(thm)],[1917,10]),
[iquote('0:MRR:1917.1,10.0')] ).
cnf(3509,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(u,v,add(multiplicative_identity,v)) ),
inference(res,[status(thm),theory(equality)],[3,574]),
[iquote('0:Res:3.0,574.0')] ).
cnf(3582,plain,
( ~ sum__dfg(inverse(u),u,multiplicative_identity)
| equal(add(multiplicative_identity,u),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[3509,46]),
[iquote('0:Res:3509.1,46.0')] ).
cnf(3600,plain,
equal(add(multiplicative_identity,u),multiplicative_identity),
inference(mrr,[status(thm)],[3582,19]),
[iquote('0:MRR:3582.0,19.0')] ).
cnf(3649,plain,
sum__dfg(multiplicative_identity,u,multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[3600,3]),
[iquote('0:SpR:3600.0,3.0')] ).
cnf(3696,plain,
( ~ product(u,multiplicative_identity,x__dfg)
| ~ product(u,v,z__dfg)
| ~ product(u,multiplicative_identity,x__dfg) ),
inference(res,[status(thm),theory(equality)],[3649,28]),
[iquote('0:Res:3649.0,28.0')] ).
cnf(3732,plain,
( ~ product(u,v,z__dfg)
| ~ product(u,multiplicative_identity,x__dfg) ),
inference(obv,[status(thm),theory(equality)],[3696]),
[iquote('0:Obv:3696.0')] ).
cnf(3733,plain,
~ product(u,multiplicative_identity,x__dfg),
inference(mrr,[status(thm)],[2005,3732]),
[iquote('0:MRR:2005.1,3732.0')] ).
cnf(3734,plain,
$false,
inference(unc,[status(thm)],[3733,10]),
[iquote('0:UnC:3733.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 1 22:37:01 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.66/1.83
% 1.66/1.83 SPASS V 3.9
% 1.66/1.83 SPASS beiseite: Proof found.
% 1.66/1.83 % SZS status Theorem
% 1.66/1.83 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.66/1.83 SPASS derived 3138 clauses, backtracked 0 clauses, performed 0 splits and kept 1860 clauses.
% 1.66/1.83 SPASS allocated 65857 KBytes.
% 1.66/1.83 SPASS spent 0:00:01.46 on the problem.
% 1.66/1.83 0:00:00.04 for the input.
% 1.66/1.83 0:00:00.00 for the FLOTTER CNF translation.
% 1.66/1.83 0:00:00.04 for inferences.
% 1.66/1.83 0:00:00.00 for the backtracking.
% 1.66/1.83 0:00:01.36 for the reduction.
% 1.66/1.83
% 1.66/1.83
% 1.66/1.83 Here is a proof with depth 6, length 31 :
% 1.66/1.83 % SZS output start Refutation
% See solution above
% 1.66/1.83 Formulae used in the proof : x_times_y prove_sum closure_of_addition additive_identity1 multiplicative_identity1 multiplicative_identity2 distributivity1 distributivity3 distributivity5 distributivity8 additive_inverse1 addition_is_well_defined
% 1.66/1.83
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