TSTP Solution File: BOO017-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO017-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 1.63s 1.90s
% Output : Refutation 1.63s
% 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,
sum__dfg(x__dfg,y__dfg,z__dfg),
file('BOO017-1.p',unknown),
[] ).
cnf(2,axiom,
~ product(x__dfg,z__dfg,x__dfg),
file('BOO017-1.p',unknown),
[] ).
cnf(4,axiom,
product(u,v,multiply(u,v)),
file('BOO017-1.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(additive_identity,u,u),
file('BOO017-1.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(u,additive_identity,u),
file('BOO017-1.p',unknown),
[] ).
cnf(9,axiom,
product(multiplicative_identity,u,u),
file('BOO017-1.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('BOO017-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,z)
| ~ product(y,x1,v)
| ~ product(x,x1,u)
| product(z,x1,w) ),
file('BOO017-1.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('BOO017-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,u)
| ~ sum__dfg(y,v,z)
| ~ sum__dfg(x,v,x1)
| product(x1,z,w) ),
file('BOO017-1.p',unknown),
[] ).
cnf(21,axiom,
product(inverse(u),u,additive_identity),
file('BOO017-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('BOO017-1.p',unknown),
[] ).
cnf(29,plain,
( ~ product(u,v,w)
| ~ sum__dfg(x,w,x__dfg)
| ~ sum__dfg(x,v,z__dfg)
| ~ sum__dfg(x,u,x__dfg) ),
inference(res,[status(thm),theory(equality)],[15,2]),
[iquote('0:Res:15.4,2.0')] ).
cnf(46,plain,
( ~ product(inverse(u),u,v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[21,24]),
[iquote('0:Res:21.0,24.0')] ).
cnf(72,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,y)
| ~ product(u,x,additive_identity)
| product(w,x,y) ),
inference(res,[status(thm),theory(equality)],[7,14]),
[iquote('0:Res:7.0,14.0')] ).
cnf(124,plain,
( ~ product(u,v,w)
| ~ sum__dfg(v,additive_identity,x)
| ~ sum__dfg(u,additive_identity,y)
| product(y,x,w) ),
inference(res,[status(thm),theory(equality)],[8,17]),
[iquote('0:Res:8.0,17.0')] ).
cnf(219,plain,
( ~ sum__dfg(u,v,w)
| ~ product(multiplicative_identity,v,x)
| ~ product(multiplicative_identity,u,y)
| sum__dfg(y,x,w) ),
inference(res,[status(thm),theory(equality)],[9,11]),
[iquote('0:Res:9.0,11.0')] ).
cnf(413,plain,
( ~ sum__dfg(u,additive_identity,v)
| ~ sum__dfg(multiplicative_identity,additive_identity,w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[9,124]),
[iquote('0:Res:9.0,124.0')] ).
cnf(531,plain,
( ~ product(multiplicative_identity,y__dfg,u)
| ~ product(multiplicative_identity,x__dfg,v)
| sum__dfg(v,u,z__dfg) ),
inference(res,[status(thm),theory(equality)],[1,219]),
[iquote('0:Res:1.0,219.0')] ).
cnf(574,plain,
( ~ product(additive_identity,u,v)
| ~ product(w,u,additive_identity)
| product(w,u,v) ),
inference(res,[status(thm),theory(equality)],[8,72]),
[iquote('0:Res:8.0,72.0')] ).
cnf(653,plain,
( ~ product(multiplicative_identity,x__dfg,u)
| sum__dfg(u,y__dfg,z__dfg) ),
inference(res,[status(thm),theory(equality)],[9,531]),
[iquote('0:Res:9.0,531.0')] ).
cnf(1991,plain,
( ~ sum__dfg(u,additive_identity,x__dfg)
| ~ sum__dfg(multiplicative_identity,additive_identity,multiplicative_identity)
| sum__dfg(u,y__dfg,z__dfg) ),
inference(res,[status(thm),theory(equality)],[413,653]),
[iquote('0:Res:413.2,653.0')] ).
cnf(2083,plain,
( ~ sum__dfg(u,additive_identity,x__dfg)
| sum__dfg(u,y__dfg,z__dfg) ),
inference(mrr,[status(thm)],[1991,8]),
[iquote('0:MRR:1991.1,8.0')] ).
cnf(3398,plain,
( ~ product(u,v,additive_identity)
| product(u,v,multiply(additive_identity,v)) ),
inference(res,[status(thm),theory(equality)],[4,574]),
[iquote('0:Res:4.0,574.0')] ).
cnf(3473,plain,
( ~ product(inverse(u),u,additive_identity)
| equal(multiply(additive_identity,u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[3398,46]),
[iquote('0:Res:3398.1,46.0')] ).
cnf(3491,plain,
equal(multiply(additive_identity,u),additive_identity),
inference(mrr,[status(thm)],[3473,21]),
[iquote('0:MRR:3473.0,21.0')] ).
cnf(3541,plain,
product(additive_identity,u,additive_identity),
inference(spr,[status(thm),theory(equality)],[3491,4]),
[iquote('0:SpR:3491.0,4.0')] ).
cnf(3584,plain,
( ~ sum__dfg(u,additive_identity,x__dfg)
| ~ sum__dfg(u,v,z__dfg)
| ~ sum__dfg(u,additive_identity,x__dfg) ),
inference(res,[status(thm),theory(equality)],[3541,29]),
[iquote('0:Res:3541.0,29.0')] ).
cnf(3620,plain,
( ~ sum__dfg(u,v,z__dfg)
| ~ sum__dfg(u,additive_identity,x__dfg) ),
inference(obv,[status(thm),theory(equality)],[3584]),
[iquote('0:Obv:3584.0')] ).
cnf(3621,plain,
~ sum__dfg(u,additive_identity,x__dfg),
inference(mrr,[status(thm)],[2083,3620]),
[iquote('0:MRR:2083.1,3620.0')] ).
cnf(3622,plain,
$false,
inference(unc,[status(thm)],[3621,8]),
[iquote('0:UnC:3621.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO017-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 1 18:07:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.63/1.90
% 1.63/1.90 SPASS V 3.9
% 1.63/1.90 SPASS beiseite: Proof found.
% 1.63/1.90 % SZS status Theorem
% 1.63/1.90 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.63/1.90 SPASS derived 3046 clauses, backtracked 0 clauses, performed 0 splits and kept 1814 clauses.
% 1.63/1.90 SPASS allocated 65784 KBytes.
% 1.63/1.90 SPASS spent 0:00:01.53 on the problem.
% 1.63/1.90 0:00:00.04 for the input.
% 1.63/1.90 0:00:00.00 for the FLOTTER CNF translation.
% 1.63/1.90 0:00:00.04 for inferences.
% 1.63/1.90 0:00:00.00 for the backtracking.
% 1.63/1.90 0:00:01.42 for the reduction.
% 1.63/1.90
% 1.63/1.90
% 1.63/1.90 Here is a proof with depth 6, length 31 :
% 1.63/1.90 % SZS output start Refutation
% See solution above
% 1.63/1.90 Formulae used in the proof : x_plus_y prove_product closure_of_multiplication additive_identity1 additive_identity2 multiplicative_identity1 distributivity1 distributivity4 distributivity5 distributivity7 multiplicative_inverse1 multiplication_is_well_defined
% 1.63/1.90
%------------------------------------------------------------------------------