%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO042-3 : 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 06:21:49 EDT 2022
% Result : Unsatisfiable 8.55s 8.73s
% Output : Refutation 8.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 8 unt; 2 nHn; 26 RR)
% Number of literals : 57 ( 0 equ; 31 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
equal(extension(u,v,w,w),v),
file('GEO042-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(u,extension(v,w,x,y))
| between(v,w,u) ),
file('GEO042-3.p',unknown),
[] ).
cnf(20,axiom,
( ~ between(u,v,w)
| equal(u,v)
| equal(extension(u,v,v,w),w) ),
file('GEO042-3.p',unknown),
[] ).
cnf(27,axiom,
( ~ between(u,v,w)
| between(w,v,u) ),
file('GEO042-3.p',unknown),
[] ).
cnf(33,axiom,
between(u__dfg,v__dfg,x__dfg),
file('GEO042-3.p',unknown),
[] ).
cnf(34,axiom,
between(v__dfg,w__dfg,x__dfg),
file('GEO042-3.p',unknown),
[] ).
cnf(35,axiom,
~ between(u__dfg,v__dfg,w__dfg),
file('GEO042-3.p',unknown),
[] ).
cnf(42,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO042-3.p',unknown),
[] ).
cnf(43,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO042-3.p',unknown),
[] ).
cnf(44,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO042-3.p',unknown),
[] ).
cnf(58,plain,
~ between(w__dfg,v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[27,35]),
[iquote('0:Res:27.1,35.0')] ).
cnf(106,plain,
between(x__dfg,w__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[34,27]),
[iquote('0:Res:34.0,27.0')] ).
cnf(359,plain,
( ~ equal(u,v)
| between(w,v,u) ),
inference(spl,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpL:10.0,11.0')] ).
cnf(363,plain,
( ~ equal(u,v)
| between(u,v,w) ),
inference(res,[status(thm),theory(equality)],[359,27]),
[iquote('0:Res:359.1,27.0')] ).
cnf(434,plain,
( ~ between(u,v,w)
| ~ equal(x,w)
| equal(u,v)
| between(u,v,x) ),
inference(spl,[status(thm),theory(equality)],[20,11]),
[iquote('0:SpL:20.2,11.0')] ).
cnf(437,plain,
( ~ between(u,v,w)
| ~ equal(x,w)
| between(u,v,x) ),
inference(mrr,[status(thm)],[434,363]),
[iquote('0:MRR:434.2,363.0')] ).
cnf(543,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[44,42]),
[iquote('0:Res:44.2,42.0')] ).
cnf(1098,plain,
( ~ equal(u,v__dfg)
| between(x__dfg,w__dfg,u) ),
inference(res,[status(thm),theory(equality)],[106,437]),
[iquote('0:Res:106.0,437.0')] ).
cnf(1177,plain,
( ~ equal(u,v__dfg)
| between(u,w__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[1098,27]),
[iquote('0:Res:1098.1,27.0')] ).
cnf(1316,plain,
( ~ equal(u,v__dfg)
| ~ equal(v,x__dfg)
| between(u,w__dfg,v) ),
inference(res,[status(thm),theory(equality)],[1177,437]),
[iquote('0:Res:1177.1,437.0')] ).
cnf(1519,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)],[543,43]),
[iquote('0:SpR:543.2,43.2')] ).
cnf(1521,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[1519]),
[iquote('0:Obv:1519.1')] ).
cnf(9115,plain,
( ~ between(v__dfg,u,x__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[33,1521]),
[iquote('0:Res:33.0,1521.0')] ).
cnf(9184,plain,
( ~ equal(v__dfg,v__dfg)
| ~ equal(x__dfg,x__dfg)
| between(w__dfg,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[1316,9115]),
[iquote('0:Res:1316.2,9115.0')] ).
cnf(9206,plain,
between(w__dfg,v__dfg,u__dfg),
inference(obv,[status(thm),theory(equality)],[9184]),
[iquote('0:Obv:9184.1')] ).
cnf(9207,plain,
$false,
inference(mrr,[status(thm)],[9206,58]),
[iquote('0:MRR:9206.0,58.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO042-3 : TPTP v8.1.0. Released v1.0.0.
% 0.14/0.15 % Command : run_spass %d %s
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sat Jun 18 11:35:29 EDT 2022
% 0.15/0.37 % CPUTime :
% 8.55/8.73
% 8.55/8.73 SPASS V 3.9
% 8.55/8.73 SPASS beiseite: Proof found.
% 8.55/8.73 % SZS status Theorem
% 8.55/8.73 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.55/8.73 SPASS derived 7494 clauses, backtracked 0 clauses, performed 1 splits and kept 2783 clauses.
% 8.55/8.73 SPASS allocated 71919 KBytes.
% 8.55/8.73 SPASS spent 0:00:08.23 on the problem.
% 8.55/8.73 0:00:00.04 for the input.
% 8.55/8.73 0:00:00.00 for the FLOTTER CNF translation.
% 8.55/8.73 0:00:00.14 for inferences.
% 8.55/8.73 0:00:00.01 for the backtracking.
% 8.55/8.73 0:00:07.99 for the reduction.
% 8.55/8.73
% 8.55/8.73
% 8.55/8.73 Here is a proof with depth 5, length 26 :
% 8.55/8.73 % SZS output start Refutation
% See solution above
% 8.55/8.73 Formulae used in the proof : e1 b0 d10_1 t1 v_between_u_and_x w_between_v_and_x prove_v_between_u_and_w identity_for_betweeness inner_pasch1 inner_pasch2
% 8.55/8.73
%------------------------------------------------------------------------------