%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 07:16:42 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 31 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 132 ( 31 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(clausify,[status(thm)],[segment_construction2]) ).
fof(identity_for_equidistance,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(VAR_0,VAR_1)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_2) ),
file('theBenchmark.p',identity_for_equidistance) ).
cnf(c_2,plain,
( equalish(A,B)
| ~ equidistant(A,B,C,C) ),
inference(clausify,[status(thm)],[identity_for_equidistance]) ).
fof(between_substitution3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_2,VAR_3,VAR_1)
| ~ between(VAR_2,VAR_3,VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',between_substitution3) ).
cnf(c_3,plain,
( between(C,D,B)
| ~ between(C,D,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[between_substitution3]) ).
cnf(c_4,plain,
equalish(A,extension(B,A,C,C)),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
( between(A,B,extension(D,C,E,E))
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
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_6,plain,
( between(A,B,D)
| ~ between(B,D,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[transitivity_for_betweeness]) ).
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_7,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(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_8,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(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_9,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
fof(prove_a_between_a_and_b,axiom,
~ between(a,a,b),
file('theBenchmark.p',prove_a_between_a_and_b) ).
cnf(c_10,plain,
~ between(a,a,b),
inference(clausify,[status(thm)],[prove_a_between_a_and_b]) ).
cnf(c_214,plain,
( between(C,A,B)
| ~ between(A,B,extension(C,A,D,E)) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_13,plain,
between(A,A,A),
inference(resolve,[status(thm)],[c_214,c_9]) ).
cnf(c_215,plain,
( between(A,B,C)
| ~ between(A,B,extension(B,C,D,E)) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_16,plain,
~ between(a,a,extension(a,b,A,B)),
inference(resolve,[status(thm)],[c_215,c_10]) ).
cnf(c_49,plain,
between(A,A,extension(B,A,C,C)),
inference(resolve,[status(thm)],[c_5,c_13]) ).
cnf(c_216,plain,
( between(C,A,B)
| ~ between(A,B,extension(C,A,D,E)) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_66,plain,
between(A,B,B),
inference(resolve,[status(thm)],[c_216,c_49]) ).
cnf(c_217,plain,
( between(C,B,outer_pasch(B,D,A,C,B))
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_66]) ).
cnf(c_69,plain,
between(A,A,outer_pasch(A,B,C,A,A)),
inference(resolve,[status(thm)],[c_217,c_66]) ).
cnf(c_218,plain,
( between(D,outer_pasch(B,D,A,C,B),A)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_66]) ).
cnf(c_76,plain,
between(A,outer_pasch(B,A,C,B,B),C),
inference(resolve,[status(thm)],[c_218,c_66]) ).
cnf(c_83,plain,
between(A,B,extension(C,B,D,D)),
inference(resolve,[status(thm)],[c_5,c_66]) ).
cnf(c_219,plain,
( between(C,A,B)
| ~ between(A,B,A) ),
inference(resolve,[status(thm)],[c_6,c_66]) ).
cnf(c_101,plain,
between(A,extension(B,C,D,D),C),
inference(resolve,[status(thm)],[c_219,c_83]) ).
cnf(c_220,plain,
( between(A,A,B)
| ~ between(A,B,outer_pasch(A,C,D,A,A)) ),
inference(resolve,[status(thm)],[c_6,c_69]) ).
cnf(c_187,plain,
~ between(a,extension(a,b,A,B),outer_pasch(a,C,D,a,a)),
inference(resolve,[status(thm)],[c_220,c_16]) ).
cnf(c_221,plain,
( between(E,extension(A,B,C,C),D)
| ~ between(extension(A,B,C,C),D,B) ),
inference(resolve,[status(thm)],[c_6,c_101]) ).
cnf(c_212,plain,
between(A,extension(B,C,D,D),outer_pasch(E,extension(B,C,D,D),C,E,E)),
inference(resolve,[status(thm)],[c_221,c_76]) ).
cnf(c_213,plain,
$false,
inference(resolve,[status(thm)],[c_212,c_187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 12:34:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3281205 was started by sandbox on n001,
% 0.09/0.37 % Fri Sep 25 12:34:54 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.39 % Length of proof is 21.
% 0.09/0.39 % Level of proof is 8.
% 0.09/0.39 % Maximum clause weight is 17.000.
% 0.09/0.39 % Given clauses 23.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------