TSTP Solution File: RNG039-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG039-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 20:41:18 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 47 ( 33 unt; 0 nHn; 47 RR)
% Number of literals : 66 ( 0 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sum__dfg(u,add(u,v),v),
file('RNG039-1.p',unknown),
[] ).
cnf(5,axiom,
equal(add(u,u),additive_identity),
file('RNG039-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(u,u),u),
file('RNG039-1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(b,a),d),
file('RNG039-1.p',unknown),
[] ).
cnf(15,axiom,
product(a,multiply(b,u),multiply(v,u)),
file('RNG039-1.p',unknown),
[] ).
cnf(37,axiom,
product(add(b,a),b,add(b,c)),
file('RNG039-1.p',unknown),
[] ).
cnf(38,axiom,
product(add(b,a),a,add(d,a)),
file('RNG039-1.p',unknown),
[] ).
cnf(40,axiom,
product(u,u,u),
file('RNG039-1.p',unknown),
[] ).
cnf(41,axiom,
product(a,b,c),
file('RNG039-1.p',unknown),
[] ).
cnf(42,axiom,
product(b,a,d),
file('RNG039-1.p',unknown),
[] ).
cnf(43,axiom,
~ equal(d,c),
file('RNG039-1.p',unknown),
[] ).
cnf(44,axiom,
sum__dfg(additive_identity,u,u),
file('RNG039-1.p',unknown),
[] ).
cnf(46,axiom,
product(u,v,multiply(u,v)),
file('RNG039-1.p',unknown),
[] ).
cnf(54,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('RNG039-1.p',unknown),
[] ).
cnf(59,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG039-1.p',unknown),
[] ).
cnf(60,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('RNG039-1.p',unknown),
[] ).
cnf(71,plain,
( ~ product(b,a,u)
| equal(d,u) ),
inference(res,[status(thm),theory(equality)],[42,60]),
[iquote('0:Res:42.0,60.0')] ).
cnf(76,plain,
( ~ product(u,d,v)
| ~ product(u,b,w)
| product(w,a,v) ),
inference(res,[status(thm),theory(equality)],[42,54]),
[iquote('0:Res:42.0,54.1')] ).
cnf(89,plain,
( ~ product(a,b,u)
| equal(c,u) ),
inference(res,[status(thm),theory(equality)],[41,60]),
[iquote('0:Res:41.0,60.0')] ).
cnf(106,plain,
( ~ product(a,d,u)
| product(c,a,u) ),
inference(res,[status(thm),theory(equality)],[41,76]),
[iquote('0:Res:41.0,76.0')] ).
cnf(168,plain,
product(a,d,multiply(u,a)),
inference(spr,[status(thm),theory(equality)],[8,15]),
[iquote('0:SpR:8.0,15.0')] ).
cnf(169,plain,
product(a,b,multiply(u,b)),
inference(spr,[status(thm),theory(equality)],[6,15]),
[iquote('0:SpR:6.0,15.0')] ).
cnf(188,plain,
product(a,d,a),
inference(spr,[status(thm),theory(equality)],[6,168]),
[iquote('0:SpR:6.0,168.0')] ).
cnf(191,plain,
product(a,b,b),
inference(spr,[status(thm),theory(equality)],[6,169]),
[iquote('0:SpR:6.0,169.0')] ).
cnf(192,plain,
equal(multiply(u,b),c),
inference(res,[status(thm),theory(equality)],[169,89]),
[iquote('0:Res:169.0,89.0')] ).
cnf(197,plain,
equal(c,b),
inference(res,[status(thm),theory(equality)],[191,89]),
[iquote('0:Res:191.0,89.0')] ).
cnf(201,plain,
~ equal(d,b),
inference(rew,[status(thm),theory(equality)],[197,43]),
[iquote('0:Rew:197.0,43.0')] ).
cnf(204,plain,
product(add(b,a),b,add(b,b)),
inference(rew,[status(thm),theory(equality)],[197,37]),
[iquote('0:Rew:197.0,37.0')] ).
cnf(213,plain,
( ~ product(a,d,u)
| product(b,a,u) ),
inference(rew,[status(thm),theory(equality)],[197,106]),
[iquote('0:Rew:197.0,106.1')] ).
cnf(244,plain,
equal(multiply(u,b),b),
inference(rew,[status(thm),theory(equality)],[197,192]),
[iquote('0:Rew:197.0,192.0')] ).
cnf(251,plain,
product(add(b,a),b,additive_identity),
inference(rew,[status(thm),theory(equality)],[5,204]),
[iquote('0:Rew:5.0,204.0')] ).
cnf(256,plain,
product(u,b,b),
inference(spr,[status(thm),theory(equality)],[244,46]),
[iquote('0:SpR:244.0,46.0')] ).
cnf(312,plain,
( ~ product(a,d,u)
| equal(d,u) ),
inference(res,[status(thm),theory(equality)],[213,71]),
[iquote('0:Res:213.1,71.0')] ).
cnf(316,plain,
equal(d,a),
inference(res,[status(thm),theory(equality)],[188,312]),
[iquote('0:Res:188.0,312.0')] ).
cnf(322,plain,
product(add(b,a),a,add(a,a)),
inference(rew,[status(thm),theory(equality)],[316,38]),
[iquote('0:Rew:316.0,38.0')] ).
cnf(328,plain,
~ equal(b,a),
inference(rew,[status(thm),theory(equality)],[316,201]),
[iquote('0:Rew:316.0,201.0')] ).
cnf(360,plain,
product(add(b,a),a,additive_identity),
inference(rew,[status(thm),theory(equality)],[5,322]),
[iquote('0:Rew:5.0,322.0')] ).
cnf(398,plain,
( ~ sum__dfg(additive_identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[44,59]),
[iquote('0:Res:44.0,59.0')] ).
cnf(413,plain,
equal(add(additive_identity,u),u),
inference(res,[status(thm),theory(equality)],[1,398]),
[iquote('0:Res:1.0,398.0')] ).
cnf(438,plain,
( ~ product(u,b,v)
| equal(v,b) ),
inference(res,[status(thm),theory(equality)],[256,60]),
[iquote('0:Res:256.0,60.0')] ).
cnf(451,plain,
( ~ product(add(b,a),a,u)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[360,60]),
[iquote('0:Res:360.0,60.0')] ).
cnf(458,plain,
equal(b,additive_identity),
inference(res,[status(thm),theory(equality)],[251,438]),
[iquote('0:Res:251.0,438.0')] ).
cnf(471,plain,
~ equal(a,additive_identity),
inference(rew,[status(thm),theory(equality)],[458,328]),
[iquote('0:Rew:458.0,328.0')] ).
cnf(525,plain,
( ~ product(add(additive_identity,a),a,u)
| equal(u,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[458,451]),
[iquote('0:Rew:458.0,451.0')] ).
cnf(545,plain,
( ~ product(a,a,u)
| equal(u,additive_identity) ),
inference(rew,[status(thm),theory(equality)],[413,525]),
[iquote('0:Rew:413.0,525.0')] ).
cnf(608,plain,
equal(a,additive_identity),
inference(res,[status(thm),theory(equality)],[40,545]),
[iquote('0:Res:40.0,545.0')] ).
cnf(612,plain,
$false,
inference(mrr,[status(thm)],[608,471]),
[iquote('0:MRR:608.0,471.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n025.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 11:23:12 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 472 clauses, backtracked 0 clauses, performed 0 splits and kept 304 clauses.
% 0.20/0.47 SPASS allocated 63497 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.04 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 5, length 47 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : absorbtion1 clause34 clause35 clause37 clause44 clause68 clause69 clause71 a_times_b b_times_a prove_c_equals_d additive_identity1 closure_of_multiplication associativity_of_multiplication2 addition_is_well_defined multiplication_is_well_defined
% 0.20/0.47
%------------------------------------------------------------------------------