%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO067-2 : TPTP v8.1.0. Released v1.0.0.
% 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 06:22:02 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 10 unt; 0 nHn; 18 RR)
% Number of literals : 32 ( 0 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ colinear(y__dfg,x__dfg,x__dfg)
| ~ colinear(x__dfg,y__dfg,x__dfg)
| ~ colinear(x__dfg,x__dfg,y__dfg)
| equal(y__dfg,x__dfg) ),
file('GEO067-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ colinear(x__dfg,x__dfg,y__dfg)
| ~ colinear(x__dfg,y__dfg,x__dfg)
| ~ colinear(y__dfg,x__dfg,x__dfg)
| ~ colinear(x__dfg,z__dfg,y__dfg) ),
file('GEO067-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO067-2.p',unknown),
[] ).
cnf(6,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO067-2.p',unknown),
[] ).
cnf(7,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO067-2.p',unknown),
[] ).
cnf(21,axiom,
( ~ between(u,v,w)
| colinear(u,v,w) ),
file('GEO067-2.p',unknown),
[] ).
cnf(22,axiom,
( ~ between(u,v,w)
| colinear(w,u,v) ),
file('GEO067-2.p',unknown),
[] ).
cnf(23,axiom,
( ~ between(u,v,w)
| colinear(v,w,u) ),
file('GEO067-2.p',unknown),
[] ).
cnf(25,plain,
( ~ colinear(x__dfg,z__dfg,x__dfg)
| ~ colinear(y__dfg,x__dfg,x__dfg)
| ~ colinear(x__dfg,y__dfg,x__dfg)
| ~ colinear(x__dfg,x__dfg,y__dfg) ),
inference(rew,[status(thm),theory(equality)],[1,2]),
[iquote('0:Rew:1.3,2.3')] ).
cnf(26,plain,
colinear(u,extension(v,u,w,x),v),
inference(res,[status(thm),theory(equality)],[6,23]),
[iquote('0:Res:6.0,23.0')] ).
cnf(27,plain,
colinear(extension(u,v,w,x),u,v),
inference(res,[status(thm),theory(equality)],[6,22]),
[iquote('0:Res:6.0,22.0')] ).
cnf(28,plain,
colinear(u,v,extension(u,v,w,x)),
inference(res,[status(thm),theory(equality)],[6,21]),
[iquote('0:Res:6.0,21.0')] ).
cnf(30,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.0,5.0')] ).
cnf(35,plain,
colinear(u,v,u),
inference(spr,[status(thm),theory(equality)],[30,27]),
[iquote('0:SpR:30.0,27.0')] ).
cnf(36,plain,
colinear(u,v,v),
inference(spr,[status(thm),theory(equality)],[30,28]),
[iquote('0:SpR:30.0,28.0')] ).
cnf(37,plain,
colinear(u,u,v),
inference(spr,[status(thm),theory(equality)],[30,26]),
[iquote('0:SpR:30.0,26.0')] ).
cnf(41,plain,
( ~ colinear(y__dfg,x__dfg,x__dfg)
| ~ colinear(x__dfg,x__dfg,y__dfg) ),
inference(mrr,[status(thm)],[25,35]),
[iquote('0:MRR:25.0,25.2,35.0')] ).
cnf(42,plain,
$false,
inference(mrr,[status(thm)],[41,36,37]),
[iquote('0:MRR:41.0,41.1,36.0,37.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO067-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 15:20:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 16 clauses, backtracked 0 clauses, performed 0 splits and kept 35 clauses.
% 0.19/0.42 SPASS allocated 63134 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.00 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 2, length 18 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : part_1 part_2 identity_for_equidistance segment_construction1 segment_construction2 colinearity1 colinearity2 colinearity3
% 0.19/0.42
%------------------------------------------------------------------------------