TSTP Solution File: GEO066-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO066-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 9 unt; 0 nHn; 18 RR)
% Number of literals : 34 ( 0 equ; 18 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
between(v__dfg,u__dfg,w__dfg),
file('GEO066-2.p',unknown),
[] ).
cnf(2,axiom,
~ colinear(u__dfg,v__dfg,w__dfg),
file('GEO066-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO066-2.p',unknown),
[] ).
cnf(6,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO066-2.p',unknown),
[] ).
cnf(7,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO066-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO066-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO066-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO066-2.p',unknown),
[] ).
cnf(23,axiom,
( ~ between(u,v,w)
| colinear(v,w,u) ),
file('GEO066-2.p',unknown),
[] ).
cnf(25,plain,
~ between(w__dfg,u__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[23,2]),
[iquote('0:Res:23.1,2.0')] ).
cnf(32,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.0,5.0')] ).
cnf(33,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[32,6]),
[iquote('0:SpR:32.0,6.0')] ).
cnf(53,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[11,9]),
[iquote('0:Res:11.2,9.0')] ).
cnf(499,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(spr,[status(thm),theory(equality)],[53,10]),
[iquote('0:SpR:53.2,10.2')] ).
cnf(501,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[499]),
[iquote('0:Obv:499.1')] ).
cnf(605,plain,
( ~ between(u__dfg,u,w__dfg)
| between(u,u__dfg,v__dfg) ),
inference(res,[status(thm),theory(equality)],[1,501]),
[iquote('0:Res:1.0,501.0')] ).
cnf(620,plain,
between(w__dfg,u__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[33,605]),
[iquote('0:Res:33.0,605.0')] ).
cnf(623,plain,
$false,
inference(mrr,[status(thm)],[620,25]),
[iquote('0:MRR:620.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO066-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n011.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 09:42:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 514 clauses, backtracked 0 clauses, performed 0 splits and kept 241 clauses.
% 0.19/0.53 SPASS allocated 63758 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.53 0:00:00.03 for the input.
% 0.19/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.01 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.10 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 4, length 18 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : u_between_v_and_w prove_uvw_colinear identity_for_equidistance segment_construction1 segment_construction2 identity_for_betweeness inner_pasch1 inner_pasch2 colinearity3
% 0.19/0.53
%------------------------------------------------------------------------------