%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD022-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 02:28:20 EDT 2022
% Result : Unsatisfiable 2.31s 2.52s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 51 ( 17 unt; 0 nHn; 51 RR)
% Number of literals : 105 ( 0 equ; 59 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 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,
defined(a),
file('FLD022-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD022-3.p',unknown),
[] ).
cnf(3,axiom,
defined(c),
file('FLD022-3.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(a,c,u__dfg),
file('FLD022-3.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(b,c,u__dfg),
file('FLD022-3.p',unknown),
[] ).
cnf(7,axiom,
~ sum__dfg(additive_identity,a,b),
file('FLD022-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD022-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD022-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD022-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD022-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD022-3.p',unknown),
[] ).
cnf(22,axiom,
( ~ defined(u)
| defined(additive_inverse(u)) ),
file('FLD022-3.p',unknown),
[] ).
cnf(26,axiom,
( ~ defined(u)
| ~ defined(v)
| sum__dfg(v,u,add(v,u)) ),
file('FLD022-3.p',unknown),
[] ).
cnf(36,plain,
( ~ sum__dfg(u__dfg,u,v)
| ~ sum__dfg(c,u,w)
| sum__dfg(b,w,v) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.0')] ).
cnf(37,plain,
( ~ sum__dfg(b,u,v)
| ~ sum__dfg(c,w,u)
| sum__dfg(u__dfg,w,v) ),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.0,9.0')] ).
cnf(49,plain,
( ~ sum__dfg(a,u,v)
| ~ sum__dfg(c,w,u)
| sum__dfg(u__dfg,w,v) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.0')] ).
cnf(53,plain,
( ~ sum__dfg(u,c,v)
| ~ sum__dfg(w,a,u)
| sum__dfg(w,u__dfg,v) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.1')] ).
cnf(60,plain,
( ~ sum__dfg(u,v,b)
| ~ sum__dfg(w,v,a)
| ~ sum__dfg(additive_identity,w,u) ),
inference(res,[status(thm),theory(equality)],[8,7]),
[iquote('0:Res:8.3,7.0')] ).
cnf(96,plain,
( ~ defined(u)
| sum__dfg(u,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[10,12]),
[iquote('0:Res:10.1,12.0')] ).
cnf(98,plain,
( ~ defined(u)
| sum__dfg(u,additive_inverse(u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[11,12]),
[iquote('0:Res:11.1,12.0')] ).
cnf(108,plain,
( ~ defined(u)
| ~ defined(v)
| sum__dfg(u,v,add(v,u)) ),
inference(res,[status(thm),theory(equality)],[26,12]),
[iquote('0:Res:26.2,12.0')] ).
cnf(136,plain,
( ~ defined(a)
| ~ sum__dfg(c,u,additive_identity)
| sum__dfg(u__dfg,u,a) ),
inference(res,[status(thm),theory(equality)],[96,49]),
[iquote('0:Res:96.1,49.0')] ).
cnf(139,plain,
( ~ sum__dfg(c,u,additive_identity)
| sum__dfg(u__dfg,u,a) ),
inference(ssi,[status(thm)],[136,1]),
[iquote('0:SSi:136.0,1.0')] ).
cnf(144,plain,
( ~ defined(c)
| sum__dfg(u__dfg,additive_inverse(c),a) ),
inference(res,[status(thm),theory(equality)],[98,139]),
[iquote('0:Res:98.1,139.0')] ).
cnf(146,plain,
sum__dfg(u__dfg,additive_inverse(c),a),
inference(ssi,[status(thm)],[144,3]),
[iquote('0:SSi:144.0,3.0')] ).
cnf(156,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)],[11,9]),
[iquote('0:Res:11.1,9.0')] ).
cnf(391,plain,
( ~ defined(b)
| ~ sum__dfg(c,u,additive_identity)
| sum__dfg(u__dfg,u,b) ),
inference(res,[status(thm),theory(equality)],[96,37]),
[iquote('0:Res:96.1,37.0')] ).
cnf(396,plain,
( ~ sum__dfg(c,u,additive_identity)
| sum__dfg(u__dfg,u,b) ),
inference(ssi,[status(thm)],[391,2]),
[iquote('0:SSi:391.0,2.0')] ).
cnf(414,plain,
( ~ defined(c)
| sum__dfg(u__dfg,additive_inverse(c),b) ),
inference(res,[status(thm),theory(equality)],[98,396]),
[iquote('0:Res:98.1,396.0')] ).
cnf(416,plain,
sum__dfg(u__dfg,additive_inverse(c),b),
inference(ssi,[status(thm)],[414,3]),
[iquote('0:SSi:414.0,3.0')] ).
cnf(425,plain,
( ~ sum__dfg(c,additive_inverse(c),u)
| sum__dfg(b,u,a) ),
inference(res,[status(thm),theory(equality)],[146,36]),
[iquote('0:Res:146.0,36.0')] ).
cnf(439,plain,
sum__dfg(additive_inverse(c),u__dfg,b),
inference(res,[status(thm),theory(equality)],[416,12]),
[iquote('0:Res:416.0,12.0')] ).
cnf(496,plain,
( ~ defined(c)
| ~ sum__dfg(u,a,additive_identity)
| sum__dfg(u,u__dfg,c) ),
inference(res,[status(thm),theory(equality)],[10,53]),
[iquote('0:Res:10.1,53.0')] ).
cnf(506,plain,
( ~ sum__dfg(u,a,additive_identity)
| sum__dfg(u,u__dfg,c) ),
inference(ssi,[status(thm)],[496,3]),
[iquote('0:SSi:496.0,3.0')] ).
cnf(557,plain,
( ~ defined(a)
| sum__dfg(additive_inverse(a),u__dfg,c) ),
inference(res,[status(thm),theory(equality)],[11,506]),
[iquote('0:Res:11.1,506.0')] ).
cnf(562,plain,
sum__dfg(additive_inverse(a),u__dfg,c),
inference(ssi,[status(thm)],[557,1]),
[iquote('0:SSi:557.0,1.0')] ).
cnf(566,plain,
sum__dfg(u__dfg,additive_inverse(a),c),
inference(res,[status(thm),theory(equality)],[562,12]),
[iquote('0:Res:562.0,12.0')] ).
cnf(736,plain,
( ~ defined(b)
| ~ sum__dfg(u,b,a)
| ~ sum__dfg(additive_identity,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[10,60]),
[iquote('0:Res:10.1,60.0')] ).
cnf(741,plain,
( ~ sum__dfg(u,b,a)
| ~ sum__dfg(additive_identity,u,additive_identity) ),
inference(ssi,[status(thm)],[736,2]),
[iquote('0:SSi:736.0,2.0')] ).
cnf(1295,plain,
( ~ defined(c)
| ~ sum__dfg(u__dfg,u,c)
| sum__dfg(b,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[439,156]),
[iquote('0:Res:439.0,156.2')] ).
cnf(1307,plain,
( ~ sum__dfg(u__dfg,u,c)
| sum__dfg(b,u,additive_identity) ),
inference(ssi,[status(thm)],[1295,3]),
[iquote('0:SSi:1295.0,3.0')] ).
cnf(1765,plain,
( ~ sum__dfg(u__dfg,u,c)
| sum__dfg(u,b,additive_identity) ),
inference(res,[status(thm),theory(equality)],[1307,12]),
[iquote('0:Res:1307.1,12.0')] ).
cnf(3982,plain,
sum__dfg(additive_inverse(a),b,additive_identity),
inference(res,[status(thm),theory(equality)],[566,1765]),
[iquote('0:Res:566.0,1765.0')] ).
cnf(4000,plain,
( ~ defined(a)
| ~ sum__dfg(b,u,a)
| sum__dfg(additive_identity,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[3982,156]),
[iquote('0:Res:3982.0,156.2')] ).
cnf(4005,plain,
( ~ sum__dfg(b,u,a)
| sum__dfg(additive_identity,u,additive_identity) ),
inference(ssi,[status(thm)],[4000,1]),
[iquote('0:SSi:4000.0,1.0')] ).
cnf(4859,plain,
( ~ defined(c)
| ~ defined(additive_inverse(c))
| sum__dfg(b,add(additive_inverse(c),c),a) ),
inference(res,[status(thm),theory(equality)],[108,425]),
[iquote('0:Res:108.2,425.0')] ).
cnf(4863,plain,
sum__dfg(b,add(additive_inverse(c),c),a),
inference(ssi,[status(thm)],[4859,22,3]),
[iquote('0:SSi:4859.1,4859.0,22.0,3.0,3.1')] ).
cnf(4973,plain,
sum__dfg(add(additive_inverse(c),c),b,a),
inference(res,[status(thm),theory(equality)],[4863,12]),
[iquote('0:Res:4863.0,12.0')] ).
cnf(4974,plain,
sum__dfg(additive_identity,add(additive_inverse(c),c),additive_identity),
inference(res,[status(thm),theory(equality)],[4863,4005]),
[iquote('0:Res:4863.0,4005.0')] ).
cnf(6403,plain,
~ sum__dfg(additive_identity,add(additive_inverse(c),c),additive_identity),
inference(res,[status(thm),theory(equality)],[4973,741]),
[iquote('0:Res:4973.0,741.0')] ).
cnf(6407,plain,
$false,
inference(mrr,[status(thm)],[6403,4974]),
[iquote('0:MRR:6403.0,4974.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD022-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 7 02:39:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.31/2.52
% 2.31/2.52 SPASS V 3.9
% 2.31/2.52 SPASS beiseite: Proof found.
% 2.31/2.52 % SZS status Theorem
% 2.31/2.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.31/2.52 SPASS derived 4989 clauses, backtracked 8 clauses, performed 5 splits and kept 3871 clauses.
% 2.31/2.52 SPASS allocated 80506 KBytes.
% 2.31/2.52 SPASS spent 0:00:02.14 on the problem.
% 2.31/2.52 0:00:00.04 for the input.
% 2.31/2.52 0:00:00.00 for the FLOTTER CNF translation.
% 2.31/2.52 0:00:00.05 for inferences.
% 2.31/2.52 0:00:00.01 for the backtracking.
% 2.31/2.52 0:00:02.00 for the reduction.
% 2.31/2.52
% 2.31/2.52
% 2.31/2.52 Here is a proof with depth 9, length 51 :
% 2.31/2.52 % SZS output start Refutation
% See solution above
% 2.31/2.52 Formulae used in the proof : a_is_defined b_is_defined c_is_defined sum_5 sum_6 not_sum_7 associativity_addition_1 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_inverse totality_of_addition
% 2.31/2.52
%------------------------------------------------------------------------------