%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO011-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:16:44 AM UTC 2026
% Result : Unsatisfiable 59.85s 23.29s
% Output : CNFRefutation 59.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 21 unt; 0 def)
% Number of atoms : 87 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 31 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 91 ( 13 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(colinearity1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( between(VAR_0,VAR_2,VAR_1)
| between(VAR_1,VAR_0,VAR_2)
| between(VAR_0,VAR_1,VAR_2)
| ~ colinear(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',colinearity1) ).
cnf(c_2,plain,
( between(A,C,B)
| between(B,A,C)
| between(A,B,C)
| ~ colinear(A,B,C) ),
inference(clausify,[status(thm)],[colinearity1]) ).
fof(prove_lower_dimension_points_not_colinear,axiom,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
cnf(c_5,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(clausify,[status(thm)],[prove_lower_dimension_points_not_colinear]) ).
cnf(c_6,plain,
( between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
fof(lower_dimension3,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('theBenchmark.p',lower_dimension3) ).
cnf(c_10,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(clausify,[status(thm)],[lower_dimension3]) ).
fof(lower_dimension2,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('theBenchmark.p',lower_dimension2) ).
cnf(c_11,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(clausify,[status(thm)],[lower_dimension2]) ).
fof(lower_dimension1,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('theBenchmark.p',lower_dimension1) ).
cnf(c_12,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(clausify,[status(thm)],[lower_dimension1]) ).
fof(segment_construction2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : equidistant(VAR_0,extension(VAR_1,VAR_0,VAR_2,VAR_3),VAR_2,VAR_3),
file('theBenchmark.p',segment_construction2) ).
cnf(c_13,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(clausify,[status(thm)],[segment_construction2]) ).
fof(segment_construction1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : between(VAR_0,VAR_1,extension(VAR_0,VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',segment_construction1) ).
cnf(c_14,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
fof(outer_pasch2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_4,VAR_1,outer_pasch(VAR_1,VAR_0,VAR_3,VAR_4,VAR_2))
| ~ between(VAR_3,VAR_2,VAR_4)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',outer_pasch2) ).
cnf(c_19,plain,
( between(E,B,outer_pasch(B,A,D,E,C))
| ~ between(D,C,E)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[outer_pasch2]) ).
fof(outer_pasch1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_0,outer_pasch(VAR_1,VAR_0,VAR_3,VAR_4,VAR_2),VAR_3)
| ~ between(VAR_3,VAR_2,VAR_4)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',outer_pasch1) ).
cnf(c_20,plain,
( between(A,outer_pasch(B,A,D,E,C),D)
| ~ between(D,C,E)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[outer_pasch1]) ).
fof(identity_for_equidistance,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_2) ),
file('theBenchmark.p',identity_for_equidistance) ).
cnf(c_22,plain,
( A = B
| ~ equidistant(A,B,C,C) ),
inference(clausify,[status(thm)],[identity_for_equidistance]) ).
fof(transitivity_for_betweeness,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_1,VAR_3,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',transitivity_for_betweeness) ).
cnf(c_25,plain,
( between(A,B,D)
| ~ between(B,D,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[transitivity_for_betweeness]) ).
fof(identity_for_betweeness,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',identity_for_betweeness) ).
cnf(c_26,plain,
( A = B
| ~ between(A,B,A) ),
inference(clausify,[status(thm)],[identity_for_betweeness]) ).
cnf(c_33,plain,
( between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3) ),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_9561,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_58,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_9561]) ).
cnf(c_87,plain,
( between(A,outer_pasch(B,A,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),lower_dimension_point_2)
| ~ between(A,B,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(resolve,[status(thm)],[c_33,c_20]) ).
cnf(c_89,plain,
( between(lower_dimension_point_3,B,outer_pasch(B,A,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1))
| ~ between(A,B,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(resolve,[status(thm)],[c_33,c_19]) ).
cnf(c_185,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_58,c_14]) ).
cnf(c_221,plain,
( between(C,A,B)
| ~ between(A,B,A) ),
inference(resolve,[status(thm)],[c_185,c_25]) ).
cnf(c_223,plain,
( between(D,outer_pasch(B,D,A,C,B),A)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_185,c_20]) ).
cnf(c_225,plain,
( between(C,B,outer_pasch(B,D,A,C,B))
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_185,c_19]) ).
cnf(c_705,plain,
( between(A,outer_pasch(lower_dimension_point_1,A,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(resolve,[status(thm)],[c_87,c_185]) ).
cnf(c_808,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,outer_pasch(lower_dimension_point_1,A,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1))
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(resolve,[status(thm)],[c_89,c_185]) ).
cnf(c_9562,plain,
( lower_dimension_point_2 = outer_pasch(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(resolve,[status(thm)],[c_705,c_26]) ).
cnf(c_4137,plain,
( outer_pasch(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) = lower_dimension_point_2
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(copy,[status(thm)],[c_9562]) ).
cnf(c_9563,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(paramod,[status(thm)],[c_4137,c_808]) ).
cnf(c_9564,plain,
( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2) ),
inference(copy,[status(thm)],[c_9563]) ).
cnf(c_5152,plain,
between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2),
inference(resolve,[status(thm)],[c_10,c_9564]) ).
cnf(c_5159,plain,
between(lower_dimension_point_2,lower_dimension_point_3,outer_pasch(lower_dimension_point_3,A,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),
inference(resolve,[status(thm)],[c_5152,c_225]) ).
cnf(c_5161,plain,
between(A,outer_pasch(lower_dimension_point_3,A,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),lower_dimension_point_1),
inference(resolve,[status(thm)],[c_5152,c_223]) ).
cnf(c_9565,plain,
( between(lower_dimension_point_2,lower_dimension_point_3,A)
| ~ between(lower_dimension_point_3,A,outer_pasch(lower_dimension_point_3,B,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)) ),
inference(resolve,[status(thm)],[c_25,c_5159]) ).
cnf(c_5887,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,outer_pasch(lower_dimension_point_3,A,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),
inference(resolve,[status(thm)],[c_9565,c_11]) ).
cnf(c_9559,plain,
between(A,lower_dimension_point_1,outer_pasch(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)),
inference(resolve,[status(thm)],[c_5161,c_221]) ).
cnf(c_9560,plain,
$false,
inference(resolve,[status(thm)],[c_9559,c_5887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO011-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/15.66 % Computer : n016.cluster.edu
% 0.15/15.66 % Model : x86_64 x86_64
% 0.15/15.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.66 % Memory : 8046.5625MB
% 0.15/15.66 % OS : Linux 6.8.0-71-generic
% 0.15/15.66 % CPULimit : 300
% 0.15/15.66 % WCLimit : 300
% 0.15/15.66 % DateTime : Fri Sep 25 12:35:59 UTC 2026
% 0.15/15.66 % CPUTime :
% 0.15/15.67 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/15.67 % Process 2384119 was started by sandbox2 on n016,
% 0.15/15.67 % Fri Sep 25 12:35:59 2026
% 0.15/15.67 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/15.67
% 0.15/15.67 % From the command line: assign(max_seconds, 300).
% 59.85/23.29
% 59.85/23.29 % SZS status Unsatisfiable for theBenchmark
% 59.85/23.29
% 59.85/23.29 % Proof 1 at 6.70 (+ 0.86) seconds.
% 59.85/23.29 % Length of proof is 30.
% 59.85/23.29 % Level of proof is 9.
% 59.85/23.29 % Maximum clause weight is 21.000.
% 59.85/23.29 % Given clauses 421.
% 59.85/23.29
% 59.85/23.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------