TSTP Solution File: FLD040-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD040-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : Sat Jul 16 02:28:26 EDT 2022
% Result : Unsatisfiable 3.44s 3.63s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 44 ( 14 unt; 1 nHn; 44 RR)
% Number of literals : 105 ( 0 equ; 62 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 : 12 ( 12 usr; 10 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD040-3.p',unknown),
[] ).
cnf(2,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD040-3.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(additive_identity,additive_identity,multiplicative_inverse(a)),
file('FLD040-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD040-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD040-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD040-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD040-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD040-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD040-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD040-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD040-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,v,x1)
| ~ sum__dfg(x,u,z)
| sum__dfg(y,w,x1) ),
file('FLD040-3.p',unknown),
[] ).
cnf(20,axiom,
defined(multiplicative_identity),
file('FLD040-3.p',unknown),
[] ).
cnf(29,axiom,
~ sum__dfg(additive_identity,additive_identity,multiplicative_identity),
file('FLD040-3.p',unknown),
[] ).
cnf(42,plain,
( ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[12,2]),
[iquote('0:Res:12.2,2.0')] ).
cnf(50,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(mrr,[status(thm)],[42,1]),
[iquote('0:MRR:42.0,1.0')] ).
cnf(77,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[50,13]),
[iquote('0:Res:50.0,13.0')] ).
cnf(80,plain,
( ~ defined(u)
| sum__dfg(u,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.1,8.0')] ).
cnf(138,plain,
( ~ defined(u)
| ~ product(v,u,w)
| ~ product(x,v,multiplicative_identity)
| product(x,w,u) ),
inference(res,[status(thm),theory(equality)],[11,9]),
[iquote('0:Res:11.1,9.0')] ).
cnf(153,plain,
( ~ defined(u)
| ~ sum__dfg(v,w,u)
| ~ sum__dfg(additive_identity,v,x)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[6,5]),
[iquote('0:Res:6.1,5.0')] ).
cnf(154,plain,
( ~ defined(u)
| ~ sum__dfg(v,w,u)
| ~ sum__dfg(additive_inverse(u),v,x)
| sum__dfg(x,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.1,5.0')] ).
cnf(360,plain,
( ~ defined(u)
| ~ product(v,u,w)
| ~ product(x,u,y)
| ~ sum__dfg(v,multiplicative_identity,x)
| sum__dfg(w,u,y) ),
inference(res,[status(thm),theory(equality)],[11,14]),
[iquote('0:Res:11.1,14.0')] ).
cnf(885,plain,
( ~ defined(a)
| ~ product(u,multiplicative_inverse(a),multiplicative_identity)
| product(u,multiplicative_identity,a) ),
inference(res,[status(thm),theory(equality)],[50,138]),
[iquote('0:Res:50.0,138.1')] ).
cnf(895,plain,
( ~ product(u,multiplicative_inverse(a),multiplicative_identity)
| product(u,multiplicative_identity,a) ),
inference(ssi,[status(thm)],[885,1]),
[iquote('0:SSi:885.0,1.0')] ).
cnf(942,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(additive_identity,additive_identity,v)
| sum__dfg(v,u,u) ),
inference(res,[status(thm),theory(equality)],[6,153]),
[iquote('0:Res:6.1,153.1')] ).
cnf(978,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(additive_identity,u,v)
| sum__dfg(v,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[80,153]),
[iquote('0:Res:80.1,153.1')] ).
cnf(1005,plain,
( ~ defined(u)
| ~ sum__dfg(additive_identity,additive_identity,v)
| sum__dfg(v,u,u) ),
inference(obv,[status(thm),theory(equality)],[942]),
[iquote('0:Obv:942.0')] ).
cnf(1014,plain,
( ~ defined(u)
| ~ sum__dfg(additive_identity,u,v)
| sum__dfg(v,additive_identity,u) ),
inference(obv,[status(thm),theory(equality)],[978]),
[iquote('0:Obv:978.0')] ).
cnf(1196,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(u,v,u)
| sum__dfg(additive_identity,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,154]),
[iquote('0:Res:7.1,154.2')] ).
cnf(1214,plain,
( ~ defined(u)
| ~ sum__dfg(u,v,u)
| sum__dfg(additive_identity,v,additive_identity) ),
inference(obv,[status(thm),theory(equality)],[1196]),
[iquote('0:Obv:1196.0')] ).
cnf(1230,plain,
product(a,multiplicative_identity,a),
inference(res,[status(thm),theory(equality)],[77,895]),
[iquote('0:Res:77.0,895.0')] ).
cnf(1238,plain,
product(multiplicative_identity,a,a),
inference(res,[status(thm),theory(equality)],[1230,13]),
[iquote('0:Res:1230.0,13.0')] ).
cnf(3060,plain,
( ~ defined(a)
| ~ product(u,a,v)
| ~ sum__dfg(multiplicative_inverse(a),multiplicative_identity,u)
| sum__dfg(multiplicative_identity,a,v) ),
inference(res,[status(thm),theory(equality)],[50,360]),
[iquote('0:Res:50.0,360.1')] ).
cnf(3096,plain,
( ~ product(u,a,v)
| ~ sum__dfg(multiplicative_inverse(a),multiplicative_identity,u)
| sum__dfg(multiplicative_identity,a,v) ),
inference(ssi,[status(thm)],[3060,1]),
[iquote('0:SSi:3060.0,1.0')] ).
cnf(5502,plain,
( ~ defined(u)
| sum__dfg(multiplicative_inverse(a),u,u) ),
inference(res,[status(thm),theory(equality)],[3,1005]),
[iquote('0:Res:3.0,1005.1')] ).
cnf(8844,plain,
( ~ defined(multiplicative_identity)
| ~ product(multiplicative_identity,a,u)
| sum__dfg(multiplicative_identity,a,u) ),
inference(res,[status(thm),theory(equality)],[5502,3096]),
[iquote('0:Res:5502.1,3096.1')] ).
cnf(8845,plain,
( ~ product(multiplicative_identity,a,u)
| sum__dfg(multiplicative_identity,a,u) ),
inference(ssi,[status(thm)],[8844,20]),
[iquote('0:SSi:8844.0,20.0')] ).
cnf(8852,plain,
sum__dfg(multiplicative_identity,a,a),
inference(res,[status(thm),theory(equality)],[1238,8845]),
[iquote('0:Res:1238.0,8845.0')] ).
cnf(8861,plain,
sum__dfg(a,multiplicative_identity,a),
inference(res,[status(thm),theory(equality)],[8852,8]),
[iquote('0:Res:8852.0,8.0')] ).
cnf(8885,plain,
( ~ defined(a)
| sum__dfg(additive_identity,multiplicative_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[8861,1214]),
[iquote('0:Res:8861.0,1214.1')] ).
cnf(8889,plain,
sum__dfg(additive_identity,multiplicative_identity,additive_identity),
inference(ssi,[status(thm)],[8885,1]),
[iquote('0:SSi:8885.0,1.0')] ).
cnf(8898,plain,
( ~ defined(multiplicative_identity)
| sum__dfg(additive_identity,additive_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[8889,1014]),
[iquote('0:Res:8889.0,1014.1')] ).
cnf(8920,plain,
sum__dfg(additive_identity,additive_identity,multiplicative_identity),
inference(ssi,[status(thm)],[8898,20]),
[iquote('0:SSi:8898.0,20.0')] ).
cnf(8921,plain,
$false,
inference(mrr,[status(thm)],[8920,29]),
[iquote('0:MRR:8920.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : FLD040-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 6 12:22:31 EDT 2022
% 0.14/0.36 % CPUTime :
% 3.44/3.63
% 3.44/3.63 SPASS V 3.9
% 3.44/3.63 SPASS beiseite: Proof found.
% 3.44/3.63 % SZS status Theorem
% 3.44/3.63 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/3.63 SPASS derived 7030 clauses, backtracked 0 clauses, performed 1 splits and kept 3898 clauses.
% 3.44/3.63 SPASS allocated 81653 KBytes.
% 3.44/3.63 SPASS spent 0:00:03.19 on the problem.
% 3.44/3.63 0:00:00.04 for the input.
% 3.44/3.63 0:00:00.00 for the FLOTTER CNF translation.
% 3.44/3.63 0:00:00.07 for inferences.
% 3.44/3.63 0:00:00.00 for the backtracking.
% 3.44/3.63 0:00:03.02 for the reduction.
% 3.44/3.63
% 3.44/3.63
% 3.44/3.63 Here is a proof with depth 8, length 44 :
% 3.44/3.63 % SZS output start Refutation
% See solution above
% 3.44/3.63 Formulae used in the proof : a_is_defined not_sum_2 sum_3 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition associativity_multiplication_1 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication distributivity_1 well_definedness_of_multiplicative_identity different_identities
% 3.44/3.63
%------------------------------------------------------------------------------