TSTP Solution File: RNG001-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Mon Jul 18 20:41:09 EDT 2022
% Result : Unsatisfiable 5.58s 5.75s
% Output : Refutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 8 unt; 0 nHn; 19 RR)
% Number of literals : 41 ( 0 equ; 23 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ product(a,additive_identity,additive_identity),
file('RNG001-1.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(additive_identity,u,u),
file('RNG001-1.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(u,additive_identity,u),
file('RNG001-1.p',unknown),
[] ).
cnf(4,axiom,
product(u,v,multiply(u,v)),
file('RNG001-1.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG001-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('RNG001-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('RNG001-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG001-1.p',unknown),
[] ).
cnf(32,plain,
( ~ sum__dfg(u,additive_inverse(u),v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,17]),
[iquote('0:Res:7.0,17.0')] ).
cnf(72,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(w,u,x)
| sum__dfg(x,v,w) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.0')] ).
cnf(258,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,v,y)
| ~ product(x,u,z)
| sum__dfg(z,y,multiply(x,w)) ),
inference(res,[status(thm),theory(equality)],[4,13]),
[iquote('0:Res:4.0,13.0')] ).
cnf(445,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,additive_inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[7,72]),
[iquote('0:Res:7.0,72.0')] ).
cnf(5005,plain,
( ~ sum__dfg(u,v,v)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[445,32]),
[iquote('0:Res:445.1,32.0')] ).
cnf(5067,plain,
( ~ product(u,v,w)
| ~ product(u,additive_identity,x)
| sum__dfg(x,w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[2,258]),
[iquote('0:Res:2.0,258.0')] ).
cnf(16681,plain,
( ~ product(u,v,multiply(u,v))
| ~ product(u,additive_identity,w)
| equal(w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[5067,5005]),
[iquote('0:Res:5067.2,5005.0')] ).
cnf(16727,plain,
( ~ product(u,additive_identity,v)
| equal(v,additive_identity) ),
inference(mrr,[status(thm)],[16681,4]),
[iquote('0:MRR:16681.0,4.0')] ).
cnf(16760,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(res,[status(thm),theory(equality)],[4,16727]),
[iquote('0:Res:4.0,16727.0')] ).
cnf(16803,plain,
product(u,additive_identity,additive_identity),
inference(spr,[status(thm),theory(equality)],[16760,4]),
[iquote('0:SpR:16760.0,4.0')] ).
cnf(16813,plain,
$false,
inference(unc,[status(thm)],[16803,1]),
[iquote('0:UnC:16803.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n028.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 : Mon May 30 16:10:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 5.58/5.75
% 5.58/5.75 SPASS V 3.9
% 5.58/5.75 SPASS beiseite: Proof found.
% 5.58/5.75 % SZS status Theorem
% 5.58/5.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.58/5.75 SPASS derived 12799 clauses, backtracked 0 clauses, performed 0 splits and kept 3769 clauses.
% 5.58/5.75 SPASS allocated 72487 KBytes.
% 5.58/5.75 SPASS spent 0:00:05.33 on the problem.
% 5.58/5.75 0:00:00.03 for the input.
% 5.58/5.75 0:00:00.00 for the FLOTTER CNF translation.
% 5.58/5.75 0:00:00.10 for inferences.
% 5.58/5.75 0:00:00.00 for the backtracking.
% 5.58/5.75 0:00:05.15 for the reduction.
% 5.58/5.75
% 5.58/5.75
% 5.58/5.75 Here is a proof with depth 6, length 19 :
% 5.58/5.75 % SZS output start Refutation
% See solution above
% 5.58/5.75 Formulae used in the proof : prove_a_times_0_is_0 additive_identity1 additive_identity2 closure_of_multiplication right_inverse associativity_of_addition2 distributivity1 addition_is_well_defined
% 5.58/5.75
%------------------------------------------------------------------------------