%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO025-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 06:21:40 EDT 2022
% Result : Unsatisfiable 11.83s 12.02s
% Output : Refutation 11.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of clauses : 46 ( 24 unt; 1 nHn; 46 RR)
% Number of literals : 92 ( 0 equ; 48 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 : 17 ( 17 usr; 14 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,u,v) ),
file('GEO025-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ equidistant(u,v,w,x)
| equidistant(x,w,u,v) ),
file('GEO025-3.p',unknown),
[] ).
cnf(10,axiom,
equal(extension(u,v,w,w),v),
file('GEO025-3.p',unknown),
[] ).
cnf(13,axiom,
equidistant(u,reflection(v,u),v,u),
file('GEO025-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(u,v)
| equal(reflection(u,v),v) ),
file('GEO025-3.p',unknown),
[] ).
cnf(17,axiom,
equidistant(u,u,v,v),
file('GEO025-3.p',unknown),
[] ).
cnf(18,axiom,
equidistant(u__dfg,v__dfg,u1,v1),
file('GEO025-3.p',unknown),
[] ).
cnf(19,axiom,
equidistant(v__dfg,w__dfg,v1,w1),
file('GEO025-3.p',unknown),
[] ).
cnf(20,axiom,
between(u__dfg,v__dfg,w__dfg),
file('GEO025-3.p',unknown),
[] ).
cnf(21,axiom,
between(u1,v1,w1),
file('GEO025-3.p',unknown),
[] ).
cnf(22,axiom,
~ equidistant(u__dfg,w__dfg,u1,w1),
file('GEO025-3.p',unknown),
[] ).
cnf(24,axiom,
( ~ equidistant(u,v,w,x)
| ~ equidistant(u,v,y,z)
| equidistant(y,z,w,x) ),
file('GEO025-3.p',unknown),
[] ).
cnf(25,axiom,
( ~ equidistant(u,v,w,w)
| equal(u,v) ),
file('GEO025-3.p',unknown),
[] ).
cnf(26,axiom,
between(u,v,extension(u,v,w,x)),
file('GEO025-3.p',unknown),
[] ).
cnf(28,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('GEO025-3.p',unknown),
[] ).
cnf(29,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO025-3.p',unknown),
[] ).
cnf(30,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO025-3.p',unknown),
[] ).
cnf(31,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO025-3.p',unknown),
[] ).
cnf(51,plain,
( ~ between(u,v,u1)
| ~ between(w,x,u__dfg)
| ~ equidistant(w,x,u,v)
| ~ equidistant(x,w__dfg,v,w1)
| ~ equidistant(w,w__dfg,u,w1)
| ~ equidistant(x,u__dfg,v,u1)
| equal(w,x) ),
inference(res,[status(thm),theory(equality)],[28,22]),
[iquote('0:Res:28.7,22.0')] ).
cnf(57,plain,
between(u,v,v),
inference(spr,[status(thm),theory(equality)],[10,26]),
[iquote('0:SpR:10.0,26.0')] ).
cnf(85,plain,
equidistant(w1,v1,v__dfg,w__dfg),
inference(res,[status(thm),theory(equality)],[19,7]),
[iquote('0:Res:19.0,7.0')] ).
cnf(86,plain,
equidistant(v1,u1,u__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[18,7]),
[iquote('0:Res:18.0,7.0')] ).
cnf(88,plain,
equidistant(u,v,u,reflection(v,u)),
inference(res,[status(thm),theory(equality)],[13,7]),
[iquote('0:Res:13.0,7.0')] ).
cnf(96,plain,
equidistant(w__dfg,v__dfg,w1,v1),
inference(res,[status(thm),theory(equality)],[85,7]),
[iquote('0:Res:85.0,7.0')] ).
cnf(98,plain,
equidistant(v__dfg,u__dfg,v1,u1),
inference(res,[status(thm),theory(equality)],[86,7]),
[iquote('0:Res:86.0,7.0')] ).
cnf(328,plain,
( ~ equidistant(v__dfg,w__dfg,u,v)
| equidistant(u,v,v1,w1) ),
inference(res,[status(thm),theory(equality)],[19,24]),
[iquote('0:Res:19.0,24.0')] ).
cnf(476,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[31,29]),
[iquote('0:Res:31.2,29.0')] ).
cnf(486,plain,
equidistant(v__dfg,reflection(w__dfg,v__dfg),v1,w1),
inference(res,[status(thm),theory(equality)],[88,328]),
[iquote('0:Res:88.0,328.0')] ).
cnf(500,plain,
equidistant(v1,w1,v__dfg,reflection(w__dfg,v__dfg)),
inference(res,[status(thm),theory(equality)],[486,2]),
[iquote('0:Res:486.0,2.0')] ).
cnf(537,plain,
( ~ equal(w__dfg,v__dfg)
| equidistant(v1,w1,v__dfg,v__dfg) ),
inference(spr,[status(thm),theory(equality)],[14,500]),
[iquote('0:SpR:14.1,500.0')] ).
cnf(693,plain,
( ~ equal(w__dfg,v__dfg)
| equal(w1,v1) ),
inference(res,[status(thm),theory(equality)],[537,25]),
[iquote('0:Res:537.1,25.0')] ).
cnf(1743,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)],[476,30]),
[iquote('0:SpR:476.2,30.2')] ).
cnf(1745,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[1743]),
[iquote('0:Obv:1743.1')] ).
cnf(3127,plain,
( ~ between(w1,v1,u1)
| ~ between(w__dfg,v__dfg,u__dfg)
| ~ equidistant(v__dfg,w__dfg,v1,w1)
| ~ equidistant(w__dfg,w__dfg,w1,w1)
| ~ equidistant(v__dfg,u__dfg,v1,u1)
| equal(w__dfg,v__dfg) ),
inference(res,[status(thm),theory(equality)],[96,51]),
[iquote('0:Res:96.0,51.2')] ).
cnf(3221,plain,
( ~ between(w1,v1,u1)
| ~ between(w__dfg,v__dfg,u__dfg)
| equal(w__dfg,v__dfg) ),
inference(mrr,[status(thm)],[3127,19,17,98]),
[iquote('0:MRR:3127.2,3127.3,3127.4,19.0,17.0,98.0')] ).
cnf(8797,plain,
( ~ between(v1,u,w1)
| between(u,v1,u1) ),
inference(res,[status(thm),theory(equality)],[21,1745]),
[iquote('0:Res:21.0,1745.0')] ).
cnf(8798,plain,
( ~ between(v__dfg,u,w__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[20,1745]),
[iquote('0:Res:20.0,1745.0')] ).
cnf(8812,plain,
between(w1,v1,u1),
inference(res,[status(thm),theory(equality)],[57,8797]),
[iquote('0:Res:57.0,8797.0')] ).
cnf(8818,plain,
( ~ between(w__dfg,v__dfg,u__dfg)
| equal(w__dfg,v__dfg) ),
inference(mrr,[status(thm)],[3221,8812]),
[iquote('0:MRR:3221.0,8812.0')] ).
cnf(8903,plain,
between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[57,8798]),
[iquote('0:Res:57.0,8798.0')] ).
cnf(8909,plain,
equal(w__dfg,v__dfg),
inference(mrr,[status(thm)],[8818,8903]),
[iquote('0:MRR:8818.0,8903.0')] ).
cnf(8912,plain,
~ equidistant(u__dfg,v__dfg,u1,w1),
inference(rew,[status(thm),theory(equality)],[8909,22]),
[iquote('0:Rew:8909.0,22.0')] ).
cnf(8969,plain,
( ~ equal(v__dfg,v__dfg)
| equal(w1,v1) ),
inference(rew,[status(thm),theory(equality)],[8909,693]),
[iquote('0:Rew:8909.0,693.0')] ).
cnf(10402,plain,
equal(w1,v1),
inference(obv,[status(thm),theory(equality)],[8969]),
[iquote('0:Obv:8969.0')] ).
cnf(10423,plain,
~ equidistant(u__dfg,v__dfg,u1,v1),
inference(rew,[status(thm),theory(equality)],[10402,8912]),
[iquote('0:Rew:10402.0,8912.0')] ).
cnf(10431,plain,
$false,
inference(mrr,[status(thm)],[10423,18]),
[iquote('0:MRR:10423.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO025-3 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n013.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Fri Jun 17 17:16:14 EDT 2022
% 0.09/0.29 % CPUTime :
% 11.83/12.02
% 11.83/12.02 SPASS V 3.9
% 11.83/12.02 SPASS beiseite: Proof found.
% 11.83/12.02 % SZS status Theorem
% 11.83/12.02 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.83/12.02 SPASS derived 9832 clauses, backtracked 0 clauses, performed 0 splits and kept 3861 clauses.
% 11.83/12.02 SPASS allocated 74390 KBytes.
% 11.83/12.02 SPASS spent 0:0:11.64 on the problem.
% 11.83/12.02 0:00:00.03 for the input.
% 11.83/12.02 0:00:00.00 for the FLOTTER CNF translation.
% 11.83/12.02 0:00:00.19 for inferences.
% 11.83/12.02 0:00:00.00 for the backtracking.
% 11.83/12.02 0:0:11.35 for the reduction.
% 11.83/12.02
% 11.83/12.02
% 11.83/12.02 Here is a proof with depth 5, length 46 :
% 11.83/12.02 % SZS output start Refutation
% See solution above
% 11.83/12.02 Formulae used in the proof : d2 d4_4 e1 r2_2 r3_1 d7 u_to_v_equals_u1_to_v1 v_to_w_equals_v1_to_w1 v_between_u_and_w v1_between_u1_and_w1 prove_equal_sums transitivity_for_equidistance identity_for_equidistance segment_construction1 outer_five_segment identity_for_betweeness inner_pasch1 inner_pasch2
% 11.83/12.02
%------------------------------------------------------------------------------