TSTP Solution File: FLD008-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD008-4 : 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 02:28:14 EDT 2022
% Result : Unsatisfiable 2.28s 2.48s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 33 ( 13 unt; 0 nHn; 33 RR)
% Number of literals : 66 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD008-4.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD008-4.p',unknown),
[] ).
cnf(3,axiom,
defined(c),
file('FLD008-4.p',unknown),
[] ).
cnf(4,axiom,
defined(d),
file('FLD008-4.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(a,b,c),
file('FLD008-4.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(additive_inverse(a),additive_inverse(b),d),
file('FLD008-4.p',unknown),
[] ).
cnf(7,axiom,
~ sum__dfg(additive_identity,additive_inverse(c),d),
file('FLD008-4.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('FLD008-4.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('FLD008-4.p',unknown),
[] ).
cnf(10,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD008-4.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD008-4.p',unknown),
[] ).
cnf(12,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD008-4.p',unknown),
[] ).
cnf(37,plain,
( ~ sum__dfg(a,u,v)
| ~ sum__dfg(b,w,u)
| sum__dfg(c,w,v) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.0')] ).
cnf(49,plain,
( ~ sum__dfg(u,v,d)
| ~ sum__dfg(u,w,additive_identity)
| ~ sum__dfg(w,additive_inverse(c),v) ),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.3,7.0')] ).
cnf(54,plain,
( ~ sum__dfg(additive_inverse(a),u,v)
| ~ sum__dfg(additive_inverse(b),w,u)
| sum__dfg(d,w,v) ),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.0,9.0')] ).
cnf(90,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(94,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(132,plain,
( ~ defined(a)
| ~ sum__dfg(b,u,additive_identity)
| sum__dfg(c,u,a) ),
inference(res,[status(thm),theory(equality)],[90,37]),
[iquote('0:Res:90.1,37.0')] ).
cnf(135,plain,
( ~ sum__dfg(b,u,additive_identity)
| sum__dfg(c,u,a) ),
inference(ssi,[status(thm)],[132,1]),
[iquote('0:SSi:132.0,1.0')] ).
cnf(140,plain,
( ~ defined(b)
| sum__dfg(c,additive_inverse(b),a) ),
inference(res,[status(thm),theory(equality)],[94,135]),
[iquote('0:Res:94.1,135.0')] ).
cnf(142,plain,
sum__dfg(c,additive_inverse(b),a),
inference(ssi,[status(thm)],[140,2]),
[iquote('0:SSi:140.0,2.0')] ).
cnf(159,plain,
sum__dfg(additive_inverse(b),c,a),
inference(res,[status(thm),theory(equality)],[142,12]),
[iquote('0:Res:142.0,12.0')] ).
cnf(168,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)],[10,8]),
[iquote('0:Res:10.1,8.0')] ).
cnf(546,plain,
( ~ defined(a)
| ~ sum__dfg(additive_inverse(b),u,a)
| sum__dfg(d,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[11,54]),
[iquote('0:Res:11.1,54.0')] ).
cnf(555,plain,
( ~ sum__dfg(additive_inverse(b),u,a)
| sum__dfg(d,u,additive_identity) ),
inference(ssi,[status(thm)],[546,1]),
[iquote('0:SSi:546.0,1.0')] ).
cnf(744,plain,
( ~ defined(c)
| ~ sum__dfg(u,additive_identity,d)
| ~ sum__dfg(u,c,additive_identity) ),
inference(res,[status(thm),theory(equality)],[94,49]),
[iquote('0:Res:94.1,49.2')] ).
cnf(748,plain,
( ~ sum__dfg(u,additive_identity,d)
| ~ sum__dfg(u,c,additive_identity) ),
inference(ssi,[status(thm)],[744,3]),
[iquote('0:SSi:744.0,3.0')] ).
cnf(5878,plain,
sum__dfg(d,c,additive_identity),
inference(res,[status(thm),theory(equality)],[159,555]),
[iquote('0:Res:159.0,555.0')] ).
cnf(5889,plain,
sum__dfg(c,d,additive_identity),
inference(res,[status(thm),theory(equality)],[5878,12]),
[iquote('0:Res:5878.0,12.0')] ).
cnf(5921,plain,
( ~ defined(d)
| ~ sum__dfg(u,c,additive_identity)
| sum__dfg(u,additive_identity,d) ),
inference(res,[status(thm),theory(equality)],[5889,168]),
[iquote('0:Res:5889.0,168.1')] ).
cnf(5933,plain,
( ~ sum__dfg(u,c,additive_identity)
| sum__dfg(u,additive_identity,d) ),
inference(ssi,[status(thm)],[5921,4]),
[iquote('0:SSi:5921.0,4.0')] ).
cnf(5934,plain,
~ sum__dfg(u,c,additive_identity),
inference(mrr,[status(thm)],[5933,748]),
[iquote('0:MRR:5933.1,748.0')] ).
cnf(5935,plain,
$false,
inference(unc,[status(thm)],[5934,5878]),
[iquote('0:UnC:5934.0,5878.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : FLD008-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.14/0.15 % Command : run_spass %d %s
% 0.16/0.37 % Computer : n017.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Tue Jun 7 00:57:47 EDT 2022
% 0.16/0.37 % CPUTime :
% 2.28/2.48
% 2.28/2.48 SPASS V 3.9
% 2.28/2.48 SPASS beiseite: Proof found.
% 2.28/2.48 % SZS status Theorem
% 2.28/2.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.28/2.48 SPASS derived 4430 clauses, backtracked 8 clauses, performed 5 splits and kept 3347 clauses.
% 2.28/2.48 SPASS allocated 80299 KBytes.
% 2.28/2.48 SPASS spent 0:00:02.07 on the problem.
% 2.28/2.48 0:00:00.04 for the input.
% 2.28/2.48 0:00:00.00 for the FLOTTER CNF translation.
% 2.28/2.48 0:00:00.05 for inferences.
% 2.28/2.48 0:00:00.08 for the backtracking.
% 2.28/2.48 0:00:01.86 for the reduction.
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Here is a proof with depth 7, length 33 :
% 2.28/2.48 % SZS output start Refutation
% See solution above
% 2.28/2.48 Formulae used in the proof : a_is_defined b_is_defined c_is_defined d_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
% 2.28/2.48
%------------------------------------------------------------------------------