TSTP Solution File: FLD047-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD047-4 : 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 02:28:29 EDT 2022
% Result : Unsatisfiable 22.19s 22.38s
% Output : Refutation 22.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 22
% Syntax : Number of clauses : 57 ( 20 unt; 5 nHn; 57 RR)
% Number of literals : 128 ( 0 equ; 71 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 : 17 ( 17 usr; 15 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD047-4.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD047-4.p',unknown),
[] ).
cnf(3,axiom,
defined(c),
file('FLD047-4.p',unknown),
[] ).
cnf(4,axiom,
defined(u__dfg),
file('FLD047-4.p',unknown),
[] ).
cnf(6,axiom,
defined(t),
file('FLD047-4.p',unknown),
[] ).
cnf(7,axiom,
~ sum__dfg(additive_identity,b,additive_identity),
file('FLD047-4.p',unknown),
[] ).
cnf(8,axiom,
~ sum__dfg(additive_identity,c,additive_identity),
file('FLD047-4.p',unknown),
[] ).
cnf(9,axiom,
product(a,multiplicative_inverse(b),u__dfg),
file('FLD047-4.p',unknown),
[] ).
cnf(10,axiom,
product(a,c,s),
file('FLD047-4.p',unknown),
[] ).
cnf(11,axiom,
product(b,c,t),
file('FLD047-4.p',unknown),
[] ).
cnf(12,axiom,
~ product(s,multiplicative_inverse(t),u__dfg),
file('FLD047-4.p',unknown),
[] ).
cnf(13,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD047-4.p',unknown),
[] ).
cnf(14,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD047-4.p',unknown),
[] ).
cnf(15,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD047-4.p',unknown),
[] ).
cnf(16,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD047-4.p',unknown),
[] ).
cnf(17,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD047-4.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD047-4.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD047-4.p',unknown),
[] ).
cnf(20,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD047-4.p',unknown),
[] ).
cnf(21,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD047-4.p',unknown),
[] ).
cnf(22,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD047-4.p',unknown),
[] ).
cnf(23,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,v,x1)
| ~ sum__dfg(x,u,z)
| sum__dfg(y,w,x1) ),
file('FLD047-4.p',unknown),
[] ).
cnf(44,plain,
( ~ product(u,c,v)
| ~ product(w,b,u)
| product(w,t,v) ),
inference(res,[status(thm),theory(equality)],[11,18]),
[iquote('0:Res:11.0,18.1')] ).
cnf(67,plain,
( ~ product(a,u,v)
| ~ product(multiplicative_inverse(b),w,u)
| product(u__dfg,w,v) ),
inference(res,[status(thm),theory(equality)],[9,19]),
[iquote('0:Res:9.0,19.0')] ).
cnf(75,plain,
( ~ sum__dfg(u,v,a)
| ~ product(v,multiplicative_inverse(b),w)
| ~ product(u,multiplicative_inverse(b),x)
| sum__dfg(x,w,u__dfg) ),
inference(res,[status(thm),theory(equality)],[9,23]),
[iquote('0:Res:9.0,23.1')] ).
cnf(116,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)],[16,14]),
[iquote('0:Res:16.1,14.0')] ).
cnf(137,plain,
( ~ defined(u)
| ~ sum__dfg(v,u,w)
| ~ sum__dfg(x,v,additive_identity)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[15,13]),
[iquote('0:Res:15.1,13.0')] ).
cnf(178,plain,
( ~ defined(u)
| ~ product(v,u,w)
| ~ product(x,v,multiplicative_identity)
| product(x,w,u) ),
inference(res,[status(thm),theory(equality)],[20,18]),
[iquote('0:Res:20.1,18.0')] ).
cnf(569,plain,
( ~ defined(c)
| ~ product(u,b,multiplicative_identity)
| product(u,t,c) ),
inference(res,[status(thm),theory(equality)],[20,44]),
[iquote('0:Res:20.1,44.0')] ).
cnf(581,plain,
( ~ product(u,b,multiplicative_identity)
| product(u,t,c) ),
inference(ssi,[status(thm)],[569,3]),
[iquote('0:SSi:569.0,3.0')] ).
cnf(687,plain,
( ~ defined(b)
| sum__dfg(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),t,c) ),
inference(res,[status(thm),theory(equality)],[21,581]),
[iquote('0:Res:21.2,581.0')] ).
cnf(688,plain,
( sum__dfg(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),t,c) ),
inference(ssi,[status(thm)],[687,2]),
[iquote('0:SSi:687.0,2.0')] ).
cnf(689,plain,
product(multiplicative_inverse(b),t,c),
inference(mrr,[status(thm)],[688,7]),
[iquote('0:MRR:688.0,7.0')] ).
cnf(693,plain,
product(t,multiplicative_inverse(b),c),
inference(res,[status(thm),theory(equality)],[689,22]),
[iquote('0:Res:689.0,22.0')] ).
cnf(716,plain,
( ~ product(a,c,u)
| product(u__dfg,t,u) ),
inference(res,[status(thm),theory(equality)],[689,67]),
[iquote('0:Res:689.0,67.1')] ).
cnf(931,plain,
product(u__dfg,t,s),
inference(res,[status(thm),theory(equality)],[10,716]),
[iquote('0:Res:10.0,716.0')] ).
cnf(943,plain,
product(t,u__dfg,s),
inference(res,[status(thm),theory(equality)],[931,22]),
[iquote('0:Res:931.0,22.0')] ).
cnf(995,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(v,additive_identity,additive_identity)
| sum__dfg(v,u,u) ),
inference(res,[status(thm),theory(equality)],[15,137]),
[iquote('0:Res:15.1,137.1')] ).
cnf(1006,plain,
( ~ defined(u)
| ~ sum__dfg(v,additive_identity,additive_identity)
| sum__dfg(v,u,u) ),
inference(obv,[status(thm),theory(equality)],[995]),
[iquote('0:Obv:995.0')] ).
cnf(1281,plain,
( ~ defined(u__dfg)
| ~ product(u,t,multiplicative_identity)
| product(u,s,u__dfg) ),
inference(res,[status(thm),theory(equality)],[943,178]),
[iquote('0:Res:943.0,178.1')] ).
cnf(1320,plain,
( ~ product(u,t,multiplicative_identity)
| product(u,s,u__dfg) ),
inference(ssi,[status(thm)],[1281,4]),
[iquote('0:SSi:1281.0,4.0')] ).
cnf(1551,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(u,v,u)
| sum__dfg(additive_identity,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[16,116]),
[iquote('0:Res:16.1,116.2')] ).
cnf(1557,plain,
( ~ defined(u)
| ~ sum__dfg(u,v,u)
| sum__dfg(additive_identity,v,additive_identity) ),
inference(obv,[status(thm),theory(equality)],[1551]),
[iquote('0:Obv:1551.0')] ).
cnf(2463,plain,
( ~ sum__dfg(u,a,a)
| ~ product(u,multiplicative_inverse(b),v)
| sum__dfg(v,u__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[9,75]),
[iquote('0:Res:9.0,75.1')] ).
cnf(4578,plain,
( ~ product(u,t,multiplicative_identity)
| product(s,u,u__dfg) ),
inference(res,[status(thm),theory(equality)],[1320,22]),
[iquote('0:Res:1320.1,22.0')] ).
cnf(16638,plain,
( ~ sum__dfg(t,a,a)
| sum__dfg(c,u__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[693,2463]),
[iquote('0:Res:693.0,2463.1')] ).
cnf(16733,plain,
( ~ sum__dfg(t,a,a)
| sum__dfg(u__dfg,c,u__dfg) ),
inference(res,[status(thm),theory(equality)],[16638,17]),
[iquote('0:Res:16638.1,17.0')] ).
cnf(16819,plain,
( ~ defined(u__dfg)
| ~ sum__dfg(t,a,a)
| sum__dfg(additive_identity,c,additive_identity) ),
inference(res,[status(thm),theory(equality)],[16733,1557]),
[iquote('0:Res:16733.1,1557.1')] ).
cnf(16825,plain,
( ~ sum__dfg(t,a,a)
| sum__dfg(additive_identity,c,additive_identity) ),
inference(ssi,[status(thm)],[16819,4]),
[iquote('0:SSi:16819.0,4.0')] ).
cnf(16826,plain,
~ sum__dfg(t,a,a),
inference(mrr,[status(thm)],[16825,8]),
[iquote('0:MRR:16825.1,8.0')] ).
cnf(20707,plain,
( ~ defined(t)
| sum__dfg(additive_identity,t,additive_identity)
| product(s,multiplicative_inverse(t),u__dfg) ),
inference(res,[status(thm),theory(equality)],[21,4578]),
[iquote('0:Res:21.2,4578.0')] ).
cnf(20714,plain,
( sum__dfg(additive_identity,t,additive_identity)
| product(s,multiplicative_inverse(t),u__dfg) ),
inference(ssi,[status(thm)],[20707,6]),
[iquote('0:SSi:20707.0,6.0')] ).
cnf(20715,plain,
sum__dfg(additive_identity,t,additive_identity),
inference(mrr,[status(thm)],[20714,12]),
[iquote('0:MRR:20714.1,12.0')] ).
cnf(20722,plain,
sum__dfg(t,additive_identity,additive_identity),
inference(res,[status(thm),theory(equality)],[20715,17]),
[iquote('0:Res:20715.0,17.0')] ).
cnf(20793,plain,
( ~ defined(u)
| sum__dfg(t,u,u) ),
inference(res,[status(thm),theory(equality)],[20722,1006]),
[iquote('0:Res:20722.0,1006.1')] ).
cnf(21301,plain,
~ defined(a),
inference(res,[status(thm),theory(equality)],[20793,16826]),
[iquote('0:Res:20793.1,16826.0')] ).
cnf(21302,plain,
$false,
inference(ssi,[status(thm)],[21301,1]),
[iquote('0:SSi:21301.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : FLD047-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.36 % Computer : n017.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 600
% 0.13/0.36 % DateTime : Mon Jun 6 17:32:01 EDT 2022
% 0.13/0.36 % CPUTime :
% 22.19/22.38
% 22.19/22.38 SPASS V 3.9
% 22.19/22.38 SPASS beiseite: Proof found.
% 22.19/22.38 % SZS status Theorem
% 22.19/22.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.19/22.38 SPASS derived 15277 clauses, backtracked 4 clauses, performed 10 splits and kept 12152 clauses.
% 22.19/22.38 SPASS allocated 91158 KBytes.
% 22.19/22.38 SPASS spent 0:0:21.61 on the problem.
% 22.19/22.38 0:00:00.04 for the input.
% 22.19/22.38 0:00:00.00 for the FLOTTER CNF translation.
% 22.19/22.38 0:00:00.17 for inferences.
% 22.19/22.38 0:00:00.93 for the backtracking.
% 22.19/22.38 0:0:20.17 for the reduction.
% 22.19/22.38
% 22.19/22.38
% 22.19/22.38 Here is a proof with depth 12, length 57 :
% 22.19/22.38 % SZS output start Refutation
% See solution above
% 22.19/22.38 Formulae used in the proof : a_is_defined b_is_defined c_is_defined u_is_defined t_is_defined not_sum_7 not_sum_8 product_9 product_10 product_11 not_product_12 associativity_addition_1 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication distributivity_1
% 22.19/22.38
%------------------------------------------------------------------------------