%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO043-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 06:21:50 EDT 2022
% Result : Unsatisfiable 7.69s 7.87s
% Output : Refutation 7.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 11 unt; 5 nHn; 32 RR)
% Number of literals : 69 ( 0 equ; 37 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('GEO043-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(u,extension(v,w,x,y))
| between(v,w,u) ),
file('GEO043-3.p',unknown),
[] ).
cnf(20,axiom,
( ~ between(u,v,w)
| equal(u,v)
| equal(extension(u,v,v,w),w) ),
file('GEO043-3.p',unknown),
[] ).
cnf(27,axiom,
( ~ between(u,v,w)
| between(w,v,u) ),
file('GEO043-3.p',unknown),
[] ).
cnf(34,axiom,
between(u__dfg,v__dfg,w__dfg),
file('GEO043-3.p',unknown),
[] ).
cnf(35,axiom,
between(u__dfg,w__dfg,x__dfg),
file('GEO043-3.p',unknown),
[] ).
cnf(36,axiom,
~ between(v__dfg,w__dfg,x__dfg),
file('GEO043-3.p',unknown),
[] ).
cnf(43,axiom,
( ~ between(u,v,u)
| equal(u,v) ),
file('GEO043-3.p',unknown),
[] ).
cnf(44,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(y,inner_pasch(x,y,w,v,u),u) ),
file('GEO043-3.p',unknown),
[] ).
cnf(45,axiom,
( ~ between(u,v,w)
| ~ between(x,y,w)
| between(v,inner_pasch(x,y,w,v,u),x) ),
file('GEO043-3.p',unknown),
[] ).
cnf(59,plain,
~ between(x__dfg,w__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[27,36]),
[iquote('0:Res:27.1,36.0')] ).
cnf(60,plain,
~ equal(extension(v__dfg,w__dfg,u,v),x__dfg),
inference(res,[status(thm),theory(equality)],[11,36]),
[iquote('0:Res:11.1,36.0')] ).
cnf(84,plain,
~ equal(x__dfg,w__dfg),
inference(spl,[status(thm),theory(equality)],[10,60]),
[iquote('0:SpL:10.0,60.0')] ).
cnf(109,plain,
between(x__dfg,w__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[35,27]),
[iquote('0:Res:35.0,27.0')] ).
cnf(361,plain,
( ~ equal(u,v)
| between(w,v,u) ),
inference(spl,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpL:10.0,11.0')] ).
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(442,plain,
( ~ equal(u,v)
| between(u,v,w) ),
inference(res,[status(thm),theory(equality)],[361,27]),
[iquote('0:Res:361.1,27.0')] ).
cnf(535,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| equal(inner_pasch(v,x,w,v,u),v) ),
inference(res,[status(thm),theory(equality)],[45,43]),
[iquote('0:Res:45.2,43.0')] ).
cnf(1796,plain,
( ~ equal(u,w__dfg)
| equal(v__dfg,u__dfg)
| between(u__dfg,v__dfg,u) ),
inference(res,[status(thm),theory(equality)],[34,434]),
[iquote('0:Res:34.0,434.0')] ).
cnf(1804,plain,
( ~ equal(u,u__dfg)
| equal(x__dfg,w__dfg)
| between(x__dfg,w__dfg,u) ),
inference(res,[status(thm),theory(equality)],[109,434]),
[iquote('0:Res:109.0,434.0')] ).
cnf(1817,plain,
( ~ equal(u,u__dfg)
| between(x__dfg,w__dfg,u) ),
inference(mrr,[status(thm)],[1804,84]),
[iquote('0:MRR:1804.1,84.0')] ).
cnf(1855,plain,
~ equal(v__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[1817,59]),
[iquote('0:Res:1817.1,59.0')] ).
cnf(1862,plain,
( ~ equal(u,w__dfg)
| between(u__dfg,v__dfg,u) ),
inference(mrr,[status(thm)],[1796,1855]),
[iquote('0:MRR:1796.1,1855.0')] ).
cnf(1936,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)],[535,44]),
[iquote('0:SpR:535.2,44.2')] ).
cnf(1938,plain,
( ~ between(u,v,w)
| ~ between(v,x,w)
| between(x,v,u) ),
inference(obv,[status(thm),theory(equality)],[1936]),
[iquote('0:Obv:1936.1')] ).
cnf(1966,plain,
( ~ equal(u,w__dfg)
| between(u,v__dfg,u__dfg) ),
inference(res,[status(thm),theory(equality)],[1862,27]),
[iquote('0:Res:1862.1,27.0')] ).
cnf(2006,plain,
( ~ equal(u,w__dfg)
| ~ equal(v,u__dfg)
| equal(u,v__dfg)
| between(u,v__dfg,v) ),
inference(res,[status(thm),theory(equality)],[1966,434]),
[iquote('0:Res:1966.1,434.0')] ).
cnf(2014,plain,
( ~ equal(u,w__dfg)
| ~ equal(v,u__dfg)
| between(u,v__dfg,v) ),
inference(mrr,[status(thm)],[2006,442]),
[iquote('0:MRR:2006.2,442.0')] ).
cnf(9167,plain,
( ~ between(w__dfg,u,u__dfg)
| between(u,w__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[109,1938]),
[iquote('0:Res:109.0,1938.0')] ).
cnf(9241,plain,
( ~ equal(w__dfg,w__dfg)
| ~ equal(u__dfg,u__dfg)
| between(v__dfg,w__dfg,x__dfg) ),
inference(res,[status(thm),theory(equality)],[2014,9167]),
[iquote('0:Res:2014.2,9167.0')] ).
cnf(9261,plain,
between(v__dfg,w__dfg,x__dfg),
inference(obv,[status(thm),theory(equality)],[9241]),
[iquote('0:Obv:9241.1')] ).
cnf(9262,plain,
$false,
inference(mrr,[status(thm)],[9261,36]),
[iquote('0:MRR:9261.0,36.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO043-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 11:05:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 7.69/7.87
% 7.69/7.87 SPASS V 3.9
% 7.69/7.87 SPASS beiseite: Proof found.
% 7.69/7.87 % SZS status Theorem
% 7.69/7.87 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.69/7.87 SPASS derived 7531 clauses, backtracked 0 clauses, performed 1 splits and kept 2816 clauses.
% 7.69/7.87 SPASS allocated 71905 KBytes.
% 7.69/7.87 SPASS spent 0:00:07.41 on the problem.
% 7.69/7.87 0:00:00.04 for the input.
% 7.69/7.87 0:00:00.00 for the FLOTTER CNF translation.
% 7.69/7.87 0:00:00.12 for inferences.
% 7.69/7.87 0:00:00.01 for the backtracking.
% 7.69/7.87 0:00:07.19 for the reduction.
% 7.69/7.87
% 7.69/7.87
% 7.69/7.87 Here is a proof with depth 5, length 32 :
% 7.69/7.87 % SZS output start Refutation
% See solution above
% 7.69/7.87 Formulae used in the proof : e1 b0 d10_1 t1 v_between_u_and_w w_between_u_and_x prove_w_between_v_and_x identity_for_betweeness inner_pasch1 inner_pasch2
% 7.69/7.87
%------------------------------------------------------------------------------