TSTP Solution File: FLD013-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD013-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 02:28:16 EDT 2022
% Result : Unsatisfiable 2.41s 2.66s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 55 ( 23 unt; 0 nHn; 55 RR)
% Number of literals : 108 ( 0 equ; 58 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 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('FLD013-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD013-3.p',unknown),
[] ).
cnf(3,axiom,
defined(c),
file('FLD013-3.p',unknown),
[] ).
cnf(4,axiom,
defined(d),
file('FLD013-3.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(additive_identity,a,b),
file('FLD013-3.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(additive_identity,c,d),
file('FLD013-3.p',unknown),
[] ).
cnf(7,axiom,
~ sum__dfg(a,c,add(d,b)),
file('FLD013-3.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('FLD013-3.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('FLD013-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD013-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD013-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD013-3.p',unknown),
[] ).
cnf(21,axiom,
defined(additive_identity),
file('FLD013-3.p',unknown),
[] ).
cnf(26,axiom,
( ~ defined(u)
| ~ defined(v)
| sum__dfg(v,u,add(v,u)) ),
file('FLD013-3.p',unknown),
[] ).
cnf(39,plain,
( ~ sum__dfg(u,c,v)
| ~ sum__dfg(w,additive_identity,u)
| sum__dfg(w,d,v) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.1')] ).
cnf(49,plain,
( ~ sum__dfg(additive_identity,u,v)
| ~ sum__dfg(a,w,u)
| sum__dfg(b,w,v) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.0')] ).
cnf(52,plain,
( ~ sum__dfg(u,b,v)
| ~ sum__dfg(u,additive_identity,w)
| sum__dfg(w,a,v) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.1')] ).
cnf(54,plain,
( ~ sum__dfg(u,v,a)
| ~ sum__dfg(additive_identity,u,w)
| sum__dfg(w,v,b) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.2')] ).
cnf(60,plain,
( ~ sum__dfg(u,v,c)
| ~ sum__dfg(w,v,add(d,b))
| ~ sum__dfg(a,u,w) ),
inference(res,[status(thm),theory(equality)],[8,7]),
[iquote('0:Res:8.3,7.0')] ).
cnf(62,plain,
( ~ sum__dfg(a,u,a)
| sum__dfg(b,u,b) ),
inference(res,[status(thm),theory(equality)],[5,54]),
[iquote('0:Res:5.0,54.0')] ).
cnf(89,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(92,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(95,plain,
( ~ defined(a)
| sum__dfg(b,additive_identity,b) ),
inference(res,[status(thm),theory(equality)],[89,62]),
[iquote('0:Res:89.1,62.0')] ).
cnf(97,plain,
sum__dfg(b,additive_identity,b),
inference(ssi,[status(thm)],[95,1]),
[iquote('0:SSi:95.0,1.0')] ).
cnf(98,plain,
sum__dfg(additive_identity,b,b),
inference(res,[status(thm),theory(equality)],[97,12]),
[iquote('0:Res:97.0,12.0')] ).
cnf(115,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(146,plain,
( ~ defined(u)
| ~ sum__dfg(a,v,u)
| sum__dfg(b,v,u) ),
inference(res,[status(thm),theory(equality)],[10,49]),
[iquote('0:Res:10.1,49.0')] ).
cnf(170,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(190,plain,
( ~ defined(a)
| ~ defined(a)
| sum__dfg(b,additive_identity,a) ),
inference(res,[status(thm),theory(equality)],[89,146]),
[iquote('0:Res:89.1,146.1')] ).
cnf(191,plain,
( ~ defined(a)
| ~ defined(additive_identity)
| sum__dfg(b,additive_inverse(a),additive_identity) ),
inference(res,[status(thm),theory(equality)],[92,146]),
[iquote('0:Res:92.1,146.1')] ).
cnf(192,plain,
( ~ defined(a)
| sum__dfg(b,additive_identity,a) ),
inference(obv,[status(thm),theory(equality)],[190]),
[iquote('0:Obv:190.0')] ).
cnf(193,plain,
sum__dfg(b,additive_identity,a),
inference(ssi,[status(thm)],[192,1]),
[iquote('0:SSi:192.0,1.0')] ).
cnf(194,plain,
sum__dfg(b,additive_inverse(a),additive_identity),
inference(ssi,[status(thm)],[191,21,1]),
[iquote('0:SSi:191.1,191.0,21.0,1.0')] ).
cnf(220,plain,
sum__dfg(additive_identity,b,a),
inference(res,[status(thm),theory(equality)],[193,12]),
[iquote('0:Res:193.0,12.0')] ).
cnf(221,plain,
( ~ sum__dfg(a,u,b)
| sum__dfg(b,u,a) ),
inference(res,[status(thm),theory(equality)],[220,49]),
[iquote('0:Res:220.0,49.0')] ).
cnf(227,plain,
sum__dfg(additive_inverse(a),b,additive_identity),
inference(res,[status(thm),theory(equality)],[194,12]),
[iquote('0:Res:194.0,12.0')] ).
cnf(532,plain,
( ~ sum__dfg(additive_identity,additive_identity,u)
| sum__dfg(u,a,b) ),
inference(res,[status(thm),theory(equality)],[98,52]),
[iquote('0:Res:98.0,52.0')] ).
cnf(656,plain,
( ~ defined(c)
| ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,d,c) ),
inference(res,[status(thm),theory(equality)],[10,39]),
[iquote('0:Res:10.1,39.0')] ).
cnf(669,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,d,c) ),
inference(ssi,[status(thm)],[656,3]),
[iquote('0:SSi:656.0,3.0')] ).
cnf(686,plain,
( ~ defined(additive_identity)
| ~ defined(additive_identity)
| sum__dfg(add(additive_identity,additive_identity),a,b) ),
inference(res,[status(thm),theory(equality)],[26,532]),
[iquote('0:Res:26.2,532.0')] ).
cnf(690,plain,
( ~ defined(additive_identity)
| sum__dfg(add(additive_identity,additive_identity),a,b) ),
inference(obv,[status(thm),theory(equality)],[686]),
[iquote('0:Obv:686.0')] ).
cnf(691,plain,
sum__dfg(add(additive_identity,additive_identity),a,b),
inference(ssi,[status(thm)],[690,21]),
[iquote('0:SSi:690.0,21.0')] ).
cnf(696,plain,
sum__dfg(a,add(additive_identity,additive_identity),b),
inference(res,[status(thm),theory(equality)],[691,12]),
[iquote('0:Res:691.0,12.0')] ).
cnf(712,plain,
sum__dfg(b,add(additive_identity,additive_identity),a),
inference(res,[status(thm),theory(equality)],[696,221]),
[iquote('0:Res:696.0,221.0')] ).
cnf(838,plain,
( ~ defined(b)
| ~ defined(d)
| ~ sum__dfg(u,d,c)
| ~ sum__dfg(a,u,b) ),
inference(res,[status(thm),theory(equality)],[115,60]),
[iquote('0:Res:115.2,60.1')] ).
cnf(842,plain,
( ~ sum__dfg(u,d,c)
| ~ sum__dfg(a,u,b) ),
inference(ssi,[status(thm)],[838,4,2]),
[iquote('0:SSi:838.1,838.0,4.0,2.0')] ).
cnf(887,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(d,u,c) ),
inference(res,[status(thm),theory(equality)],[669,12]),
[iquote('0:Res:669.1,12.0')] ).
cnf(1369,plain,
( ~ defined(a)
| ~ sum__dfg(b,u,a)
| sum__dfg(additive_identity,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[227,170]),
[iquote('0:Res:227.0,170.2')] ).
cnf(1375,plain,
( ~ sum__dfg(b,u,a)
| sum__dfg(additive_identity,u,additive_identity) ),
inference(ssi,[status(thm)],[1369,1]),
[iquote('0:SSi:1369.0,1.0')] ).
cnf(2656,plain,
sum__dfg(additive_identity,add(additive_identity,additive_identity),additive_identity),
inference(res,[status(thm),theory(equality)],[712,1375]),
[iquote('0:Res:712.0,1375.0')] ).
cnf(2755,plain,
sum__dfg(add(additive_identity,additive_identity),additive_identity,additive_identity),
inference(res,[status(thm),theory(equality)],[2656,12]),
[iquote('0:Res:2656.0,12.0')] ).
cnf(2762,plain,
sum__dfg(d,add(additive_identity,additive_identity),c),
inference(res,[status(thm),theory(equality)],[2755,887]),
[iquote('0:Res:2755.0,887.0')] ).
cnf(2792,plain,
sum__dfg(add(additive_identity,additive_identity),d,c),
inference(res,[status(thm),theory(equality)],[2762,12]),
[iquote('0:Res:2762.0,12.0')] ).
cnf(6585,plain,
~ sum__dfg(a,add(additive_identity,additive_identity),b),
inference(res,[status(thm),theory(equality)],[2792,842]),
[iquote('0:Res:2792.0,842.0')] ).
cnf(6592,plain,
$false,
inference(mrr,[status(thm)],[6585,696]),
[iquote('0:MRR:6585.0,696.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD013-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 03:53:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.41/2.66
% 2.41/2.66 SPASS V 3.9
% 2.41/2.66 SPASS beiseite: Proof found.
% 2.41/2.66 % SZS status Theorem
% 2.41/2.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.41/2.66 SPASS derived 5119 clauses, backtracked 0 clauses, performed 5 splits and kept 3780 clauses.
% 2.41/2.66 SPASS allocated 80572 KBytes.
% 2.41/2.66 SPASS spent 0:00:02.28 on the problem.
% 2.41/2.66 0:00:00.04 for the input.
% 2.41/2.66 0:00:00.00 for the FLOTTER CNF translation.
% 2.41/2.66 0:00:00.05 for inferences.
% 2.41/2.66 0:00:00.02 for the backtracking.
% 2.41/2.66 0:00:02.12 for the reduction.
% 2.41/2.66
% 2.41/2.66
% 2.41/2.66 Here is a proof with depth 13, length 55 :
% 2.41/2.66 % SZS output start Refutation
% See solution above
% 2.41/2.66 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 well_definedness_of_additive_identity totality_of_addition
% 2.41/2.66
%------------------------------------------------------------------------------