TSTP Solution File: RNG005-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 20:41:10 EDT 2022
% Result : Unsatisfiable 3.43s 3.70s
% Output : Refutation 3.43s
% 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('RNG005-1.p',unknown),
[] ).
cnf(2,axiom,
product(additive_inverse(a),b,c),
file('RNG005-1.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(c,d,additive_identity),
file('RNG005-1.p',unknown),
[] ).
cnf(4,axiom,
sum__dfg(additive_identity,u,u),
file('RNG005-1.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(u,additive_identity,u),
file('RNG005-1.p',unknown),
[] ).
cnf(6,axiom,
product(u,v,multiply(u,v)),
file('RNG005-1.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG005-1.p',unknown),
[] ).
cnf(9,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG005-1.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('RNG005-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('RNG005-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG005-1.p',unknown),
[] ).
cnf(24,plain,
( ~ sum__dfg(u,v,w)
| ~ product(w,x,additive_identity)
| ~ product(v,x,d)
| ~ product(u,x,c) ),
inference(res,[status(thm),theory(equality)],[17,3]),
[iquote('0:Res:17.4,3.0')] ).
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(187,plain,
( ~ sum__dfg(u,v,a)
| ~ product(v,b,w)
| ~ product(u,b,x)
| sum__dfg(x,w,d) ),
inference(res,[status(thm),theory(equality)],[1,17]),
[iquote('0:Res:1.0,17.0')] ).
cnf(296,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(2572,plain,
( ~ product(a,b,u)
| ~ product(additive_identity,b,v)
| sum__dfg(v,u,d) ),
inference(res,[status(thm),theory(equality)],[4,187]),
[iquote('0:Res:4.0,187.0')] ).
cnf(3999,plain,
( ~ product(additive_identity,u,additive_identity)
| ~ product(v,u,d)
| ~ product(additive_inverse(v),u,c) ),
inference(res,[status(thm),theory(equality)],[8,24]),
[iquote('0:Res:8.0,24.0')] ).
cnf(4520,plain,
( ~ sum__dfg(u,v,v)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[296,40]),
[iquote('0:Res:296.1,40.0')] ).
cnf(8755,plain,
( ~ product(a,b,d)
| ~ product(additive_identity,b,u)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2572,4520]),
[iquote('0:Res:2572.2,4520.0')] ).
cnf(8790,plain,
( ~ product(additive_identity,b,u)
| equal(u,additive_identity) ),
inference(mrr,[status(thm)],[8755,1]),
[iquote('0:MRR:8755.0,1.0')] ).
cnf(8809,plain,
equal(multiply(additive_identity,b),additive_identity),
inference(res,[status(thm),theory(equality)],[6,8790]),
[iquote('0:Res:6.0,8790.0')] ).
cnf(8811,plain,
product(additive_identity,b,additive_identity),
inference(spr,[status(thm),theory(equality)],[8809,6]),
[iquote('0:SpR:8809.0,6.0')] ).
cnf(10732,plain,
( ~ product(additive_identity,b,additive_identity)
| ~ product(a,b,d) ),
inference(res,[status(thm),theory(equality)],[2,3999]),
[iquote('0:Res:2.0,3999.2')] ).
cnf(10733,plain,
$false,
inference(mrr,[status(thm)],[10732,8811,1]),
[iquote('0:MRR:10732.0,10732.1,8811.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 06:05:01 EDT 2022
% 0.14/0.34 % CPUTime :
% 3.43/3.70
% 3.43/3.70 SPASS V 3.9
% 3.43/3.70 SPASS beiseite: Proof found.
% 3.43/3.70 % SZS status Theorem
% 3.43/3.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.43/3.70 SPASS derived 8511 clauses, backtracked 0 clauses, performed 0 splits and kept 3071 clauses.
% 3.43/3.70 SPASS allocated 69676 KBytes.
% 3.43/3.70 SPASS spent 0:00:03.31 on the problem.
% 3.43/3.70 0:00:00.04 for the input.
% 3.43/3.70 0:00:00.00 for the FLOTTER CNF translation.
% 3.43/3.70 0:00:00.08 for inferences.
% 3.43/3.70 0:00:00.00 for the backtracking.
% 3.43/3.70 0:00:03.15 for the reduction.
% 3.43/3.70
% 3.43/3.70
% 3.43/3.70 Here is a proof with depth 6, length 25 :
% 3.43/3.70 % SZS output start Refutation
% See solution above
% 3.43/3.70 Formulae used in the proof : a_times_b a_inverse_times_b prove_sum_is_additive_id additive_identity1 additive_identity2 closure_of_multiplication left_inverse right_inverse associativity_of_addition2 distributivity3 addition_is_well_defined
% 3.43/3.70
%------------------------------------------------------------------------------