TSTP Solution File: GEO030-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO030-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 06:21:42 EDT 2022
% Result : Unsatisfiable 1.31s 1.48s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 12 unt; 3 nHn; 23 RR)
% Number of literals : 53 ( 0 equ; 30 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
between(u__dfg,v__dfg,w__dfg),
file('GEO030-2.p',unknown),
[] ).
cnf(2,axiom,
equidistant(u__dfg,w__dfg,u__dfg,w1),
file('GEO030-2.p',unknown),
[] ).
cnf(3,axiom,
equidistant(v__dfg,w__dfg,v__dfg,w1),
file('GEO030-2.p',unknown),
[] ).
cnf(4,axiom,
~ equal(v__dfg,u__dfg),
file('GEO030-2.p',unknown),
[] ).
cnf(5,axiom,
~ equal(w1,w__dfg),
file('GEO030-2.p',unknown),
[] ).
cnf(6,axiom,
equidistant(u,v,v,u),
file('GEO030-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO030-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO030-2.p',unknown),
[] ).
cnf(10,axiom,
equidistant(u,extension(v,u,w,x),w,x),
file('GEO030-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ between(u,v,w)
| ~ between(x,y,z)
| ~ equidistant(y,x1,v,x2)
| ~ equidistant(x,x1,u,x2)
| ~ equidistant(y,z,v,w)
| ~ equidistant(x,y,u,v)
| equal(x,y)
| equidistant(z,x1,w,x2) ),
file('GEO030-2.p',unknown),
[] ).
cnf(35,plain,
~ equidistant(w__dfg,w1,u,u),
inference(res,[status(thm),theory(equality)],[8,5]),
[iquote('0:Res:8.1,5.0')] ).
cnf(39,plain,
equal(extension(u,v,w,w),v),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.0,8.0')] ).
cnf(41,plain,
equidistant(u,u,v,v),
inference(spr,[status(thm),theory(equality)],[39,10]),
[iquote('0:SpR:39.0,10.0')] ).
cnf(46,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,v,u) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(49,plain,
( ~ equidistant(u,u,v,w)
| equidistant(v,w,x,x) ),
inference(res,[status(thm),theory(equality)],[41,7]),
[iquote('0:Res:41.0,7.0')] ).
cnf(70,plain,
equidistant(u,v,u,v),
inference(res,[status(thm),theory(equality)],[6,46]),
[iquote('0:Res:6.0,46.0')] ).
cnf(185,plain,
( ~ between(u,v__dfg,v)
| ~ between(w,v__dfg,x)
| ~ equidistant(w,w__dfg,u,w1)
| ~ equidistant(v__dfg,x,v__dfg,v)
| ~ equidistant(w,v__dfg,u,v__dfg)
| equal(w,v__dfg)
| equidistant(x,w__dfg,v,w1) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.0,11.2')] ).
cnf(667,plain,
( ~ between(u__dfg,v__dfg,u)
| ~ between(u__dfg,v__dfg,v)
| ~ equidistant(v__dfg,v,v__dfg,u)
| ~ equidistant(u__dfg,v__dfg,u__dfg,v__dfg)
| equal(v__dfg,u__dfg)
| equidistant(v,w__dfg,u,w1) ),
inference(res,[status(thm),theory(equality)],[2,185]),
[iquote('0:Res:2.0,185.2')] ).
cnf(684,plain,
( ~ between(u__dfg,v__dfg,u)
| ~ between(u__dfg,v__dfg,v)
| ~ equidistant(v__dfg,v,v__dfg,u)
| equidistant(v,w__dfg,u,w1) ),
inference(mrr,[status(thm)],[667,70,4]),
[iquote('0:MRR:667.3,667.4,70.0,4.0')] ).
cnf(1670,plain,
( ~ between(u__dfg,v__dfg,u)
| ~ between(u__dfg,v__dfg,u)
| equidistant(u,w__dfg,u,w1) ),
inference(res,[status(thm),theory(equality)],[70,684]),
[iquote('0:Res:70.0,684.2')] ).
cnf(1681,plain,
( ~ between(u__dfg,v__dfg,u)
| equidistant(u,w__dfg,u,w1) ),
inference(obv,[status(thm),theory(equality)],[1670]),
[iquote('0:Obv:1670.0')] ).
cnf(1773,plain,
( ~ between(u__dfg,v__dfg,w__dfg)
| equidistant(w__dfg,w1,u,u) ),
inference(res,[status(thm),theory(equality)],[1681,49]),
[iquote('0:Res:1681.1,49.0')] ).
cnf(1774,plain,
$false,
inference(mrr,[status(thm)],[1773,1,35]),
[iquote('0:MRR:1773.0,1773.1,1.0,35.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GEO030-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Fri Jun 17 16:36:31 EDT 2022
% 0.09/0.28 % CPUTime :
% 1.31/1.48
% 1.31/1.48 SPASS V 3.9
% 1.31/1.48 SPASS beiseite: Proof found.
% 1.31/1.48 % SZS status Theorem
% 1.31/1.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.31/1.48 SPASS derived 1679 clauses, backtracked 0 clauses, performed 0 splits and kept 1090 clauses.
% 1.31/1.48 SPASS allocated 65812 KBytes.
% 1.31/1.48 SPASS spent 0:00:01.17 on the problem.
% 1.31/1.48 0:00:00.03 for the input.
% 1.31/1.48 0:00:00.00 for the FLOTTER CNF translation.
% 1.31/1.48 0:00:00.04 for inferences.
% 1.31/1.48 0:00:00.00 for the backtracking.
% 1.31/1.48 0:00:01.07 for the reduction.
% 1.31/1.48
% 1.31/1.48
% 1.31/1.48 Here is a proof with depth 4, length 23 :
% 1.31/1.48 % SZS output start Refutation
% See solution above
% 1.31/1.48 Formulae used in the proof : v_between_u_and_w u_to_w_equals_u_to_w1 v_to_w_equals_v_to_w1 u_not_v prove_w_is_w1 reflexivity_for_equidistance transitivity_for_equidistance identity_for_equidistance segment_construction2 outer_five_segment
% 1.31/1.48
%------------------------------------------------------------------------------