TSTP Solution File: RNG037-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG037-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 20:41:17 EDT 2022
% Result : Unsatisfiable 3.40s 3.59s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 11 unt; 0 nHn; 25 RR)
% Number of literals : 53 ( 0 equ; 32 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(a,b,d),
file('RNG037-1.p',unknown),
[] ).
cnf(2,axiom,
product(a,additive_inverse(b),c),
file('RNG037-1.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(c,d,additive_identity),
file('RNG037-1.p',unknown),
[] ).
cnf(4,axiom,
sum__dfg(additive_identity,u,u),
file('RNG037-1.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(u,additive_identity,u),
file('RNG037-1.p',unknown),
[] ).
cnf(6,axiom,
product(u,v,multiply(u,v)),
file('RNG037-1.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG037-1.p',unknown),
[] ).
cnf(9,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG037-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('RNG037-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('RNG037-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG037-1.p',unknown),
[] ).
cnf(25,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,w,additive_identity)
| ~ product(x,v,d)
| ~ product(x,u,c) ),
inference(res,[status(thm),theory(equality)],[15,3]),
[iquote('0:Res:15.4,3.0')] ).
cnf(40,plain,
( ~ sum__dfg(u,additive_inverse(u),v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[9,19]),
[iquote('0:Res:9.0,19.0')] ).
cnf(96,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(w,u,x)
| sum__dfg(x,v,w) ),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.0,11.0')] ).
cnf(246,plain,
( ~ sum__dfg(u,v,b)
| ~ product(a,v,w)
| ~ product(a,u,x)
| sum__dfg(x,w,d) ),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.0')] ).
cnf(305,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(w,additive_inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[9,96]),
[iquote('0:Res:9.0,96.0')] ).
cnf(2851,plain,
( ~ product(a,b,u)
| ~ product(a,additive_identity,v)
| sum__dfg(v,u,d) ),
inference(res,[status(thm),theory(equality)],[4,246]),
[iquote('0:Res:4.0,246.0')] ).
cnf(4285,plain,
( ~ product(u,additive_identity,additive_identity)
| ~ product(u,v,d)
| ~ product(u,additive_inverse(v),c) ),
inference(res,[status(thm),theory(equality)],[8,25]),
[iquote('0:Res:8.0,25.0')] ).
cnf(4501,plain,
( ~ sum__dfg(u,v,v)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[305,40]),
[iquote('0:Res:305.1,40.0')] ).
cnf(9021,plain,
( ~ product(a,b,d)
| ~ product(a,additive_identity,u)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2851,4501]),
[iquote('0:Res:2851.2,4501.0')] ).
cnf(9056,plain,
( ~ product(a,additive_identity,u)
| equal(u,additive_identity) ),
inference(mrr,[status(thm)],[9021,1]),
[iquote('0:MRR:9021.0,1.0')] ).
cnf(9073,plain,
equal(multiply(a,additive_identity),additive_identity),
inference(res,[status(thm),theory(equality)],[6,9056]),
[iquote('0:Res:6.0,9056.0')] ).
cnf(9075,plain,
product(a,additive_identity,additive_identity),
inference(spr,[status(thm),theory(equality)],[9073,6]),
[iquote('0:SpR:9073.0,6.0')] ).
cnf(10968,plain,
( ~ product(a,additive_identity,additive_identity)
| ~ product(a,b,d) ),
inference(res,[status(thm),theory(equality)],[2,4285]),
[iquote('0:Res:2.0,4285.2')] ).
cnf(10969,plain,
$false,
inference(mrr,[status(thm)],[10968,9075,1]),
[iquote('0:MRR:10968.0,10968.1,9075.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG037-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 20:52:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.40/3.59
% 3.40/3.59 SPASS V 3.9
% 3.40/3.59 SPASS beiseite: Proof found.
% 3.40/3.59 % SZS status Theorem
% 3.40/3.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.40/3.59 SPASS derived 8669 clauses, backtracked 0 clauses, performed 0 splits and kept 3071 clauses.
% 3.40/3.59 SPASS allocated 69771 KBytes.
% 3.40/3.59 SPASS spent 0:00:03.21 on the problem.
% 3.40/3.59 0:00:00.04 for the input.
% 3.40/3.59 0:00:00.00 for the FLOTTER CNF translation.
% 3.40/3.59 0:00:00.08 for inferences.
% 3.40/3.59 0:00:00.00 for the backtracking.
% 3.40/3.59 0:00:03.05 for the reduction.
% 3.40/3.59
% 3.40/3.59
% 3.40/3.59 Here is a proof with depth 6, length 25 :
% 3.40/3.59 % SZS output start Refutation
% See solution above
% 3.40/3.59 Formulae used in the proof : a_times_b a_inverse_times_b prove_sum_is_additive_identity additive_identity1 additive_identity2 closure_of_multiplication left_inverse right_inverse associativity_of_addition2 distributivity1 addition_is_well_defined
% 3.40/3.59
%------------------------------------------------------------------------------