TSTP Solution File: RNG004-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG004-2 : 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 : Mon Jul 18 20:41:10 EDT 2022
% Result : Unsatisfiable 4.42s 4.58s
% Output : Refutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 15 unt; 0 nHn; 36 RR)
% Number of literals : 77 ( 0 equ; 45 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 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(u,v,w)
| ~ sum__dfg(u,x,w)
| equal(x,v) ),
file('RNG004-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,w)
| equal(x,u) ),
file('RNG004-2.p',unknown),
[] ).
cnf(3,axiom,
product(a,b,c),
file('RNG004-2.p',unknown),
[] ).
cnf(4,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('RNG004-2.p',unknown),
[] ).
cnf(5,axiom,
~ equal(d,c),
file('RNG004-2.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(additive_identity,u,u),
file('RNG004-2.p',unknown),
[] ).
cnf(8,axiom,
product(u,v,multiply(u,v)),
file('RNG004-2.p',unknown),
[] ).
cnf(10,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG004-2.p',unknown),
[] ).
cnf(11,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG004-2.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('RNG004-2.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('RNG004-2.p',unknown),
[] ).
cnf(26,plain,
( ~ sum__dfg(u,c,v)
| ~ sum__dfg(u,d,v) ),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.2,5.0')] ).
cnf(71,plain,
( ~ sum__dfg(u,v,v)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[6,2]),
[iquote('0:Res:6.0,2.0')] ).
cnf(73,plain,
( ~ sum__dfg(u,v,additive_identity)
| equal(u,additive_inverse(v)) ),
inference(res,[status(thm),theory(equality)],[10,2]),
[iquote('0:Res:10.0,2.0')] ).
cnf(152,plain,
~ sum__dfg(additive_inverse(d),c,additive_identity),
inference(res,[status(thm),theory(equality)],[10,26]),
[iquote('0:Res:10.0,26.1')] ).
cnf(257,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,y)
| ~ product(u,x,z)
| sum__dfg(z,y,multiply(w,x)) ),
inference(res,[status(thm),theory(equality)],[8,19]),
[iquote('0:Res:8.0,19.0')] ).
cnf(267,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)],[8,17]),
[iquote('0:Res:8.0,17.0')] ).
cnf(4331,plain,
( ~ product(u,v,w)
| ~ product(additive_identity,v,x)
| sum__dfg(x,w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[6,257]),
[iquote('0:Res:6.0,257.0')] ).
cnf(4336,plain,
( ~ product(additive_inverse(u),v,w)
| ~ product(u,v,x)
| sum__dfg(x,w,multiply(additive_identity,v)) ),
inference(res,[status(thm),theory(equality)],[11,257]),
[iquote('0:Res:11.0,257.0')] ).
cnf(4479,plain,
( ~ product(u,v,w)
| ~ product(u,additive_identity,x)
| sum__dfg(x,w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[6,267]),
[iquote('0:Res:6.0,267.0')] ).
cnf(4482,plain,
( ~ product(u,v,w)
| ~ product(u,additive_inverse(v),x)
| sum__dfg(x,w,multiply(u,additive_identity)) ),
inference(res,[status(thm),theory(equality)],[10,267]),
[iquote('0:Res:10.0,267.0')] ).
cnf(10452,plain,
( ~ product(u,v,multiply(u,v))
| ~ product(additive_identity,v,w)
| equal(w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[4331,71]),
[iquote('0:Res:4331.2,71.0')] ).
cnf(10515,plain,
( ~ product(additive_identity,u,v)
| equal(v,additive_identity) ),
inference(mrr,[status(thm)],[10452,8]),
[iquote('0:MRR:10452.0,8.0')] ).
cnf(10543,plain,
equal(multiply(additive_identity,u),additive_identity),
inference(res,[status(thm),theory(equality)],[8,10515]),
[iquote('0:Res:8.0,10515.0')] ).
cnf(10574,plain,
( ~ product(additive_inverse(u),v,w)
| ~ product(u,v,x)
| sum__dfg(x,w,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[10543,4336]),
[iquote('0:Rew:10543.0,4336.2')] ).
cnf(10656,plain,
( ~ product(a,additive_inverse(b),u)
| sum__dfg(u,d,additive_identity) ),
inference(res,[status(thm),theory(equality)],[4,10574]),
[iquote('0:Res:4.0,10574.0')] ).
cnf(11082,plain,
( ~ product(u,v,multiply(u,v))
| ~ product(u,additive_identity,w)
| equal(w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[4479,71]),
[iquote('0:Res:4479.2,71.0')] ).
cnf(11145,plain,
( ~ product(u,additive_identity,v)
| equal(v,additive_identity) ),
inference(mrr,[status(thm)],[11082,8]),
[iquote('0:MRR:11082.0,8.0')] ).
cnf(11171,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(res,[status(thm),theory(equality)],[8,11145]),
[iquote('0:Res:8.0,11145.0')] ).
cnf(11186,plain,
( ~ product(u,v,w)
| ~ product(u,additive_inverse(v),x)
| sum__dfg(x,w,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[11171,4482]),
[iquote('0:Rew:11171.0,4482.2')] ).
cnf(11721,plain,
sum__dfg(multiply(a,additive_inverse(b)),d,additive_identity),
inference(res,[status(thm),theory(equality)],[8,10656]),
[iquote('0:Res:8.0,10656.0')] ).
cnf(11753,plain,
equal(multiply(a,additive_inverse(b)),additive_inverse(d)),
inference(res,[status(thm),theory(equality)],[11721,73]),
[iquote('0:Res:11721.0,73.0')] ).
cnf(11853,plain,
product(a,additive_inverse(b),additive_inverse(d)),
inference(spr,[status(thm),theory(equality)],[11753,8]),
[iquote('0:SpR:11753.0,8.0')] ).
cnf(11873,plain,
( ~ product(a,b,u)
| sum__dfg(additive_inverse(d),u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[11853,11186]),
[iquote('0:Res:11853.0,11186.1')] ).
cnf(12353,plain,
~ product(a,b,c),
inference(res,[status(thm),theory(equality)],[11873,152]),
[iquote('0:Res:11873.1,152.0')] ).
cnf(12419,plain,
$false,
inference(mrr,[status(thm)],[12353,3]),
[iquote('0:MRR:12353.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 21:40:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 4.42/4.58
% 4.42/4.58 SPASS V 3.9
% 4.42/4.58 SPASS beiseite: Proof found.
% 4.42/4.58 % SZS status Theorem
% 4.42/4.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.42/4.58 SPASS derived 9720 clauses, backtracked 0 clauses, performed 0 splits and kept 3475 clauses.
% 4.42/4.58 SPASS allocated 70847 KBytes.
% 4.42/4.58 SPASS spent 0:00:04.18 on the problem.
% 4.42/4.58 0:00:00.04 for the input.
% 4.42/4.58 0:00:00.00 for the FLOTTER CNF translation.
% 4.42/4.58 0:00:00.10 for inferences.
% 4.42/4.58 0:00:00.00 for the backtracking.
% 4.42/4.58 0:00:04.00 for the reduction.
% 4.42/4.58
% 4.42/4.58
% 4.42/4.58 Here is a proof with depth 8, length 36 :
% 4.42/4.58 % SZS output start Refutation
% See solution above
% 4.42/4.58 Formulae used in the proof : cancellation1 cancellation2 a_times_b a_inverse_times_b_inverse prove_c_equals_d additive_identity1 closure_of_multiplication left_inverse right_inverse distributivity1 distributivity3
% 4.42/4.58
%------------------------------------------------------------------------------