%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO002-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.08s 15.66s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 39 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 74 ( 12 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_3,plain,
( A = B
| ~ equidistant(A,B,C,C) ),
inference(clausify,[status(thm)],[identity_for_equidistance]) ).
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_4,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
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_5,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(clausify,[status(thm)],[segment_construction2]) ).
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_7,plain,
( A = B
| ~ between(A,B,A) ),
inference(clausify,[status(thm)],[identity_for_betweeness]) ).
fof(inner_pasch1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_1,inner_pasch(VAR_0,VAR_1,VAR_2,VAR_4,VAR_3),VAR_3)
| ~ between(VAR_3,VAR_4,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',inner_pasch1) ).
cnf(c_8,plain,
( between(B,inner_pasch(A,B,C,E,D),D)
| ~ between(D,E,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[inner_pasch1]) ).
fof(inner_pasch2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_4,inner_pasch(VAR_0,VAR_1,VAR_2,VAR_4,VAR_3),VAR_0)
| ~ between(VAR_3,VAR_4,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',inner_pasch2) ).
cnf(c_9,plain,
( between(E,inner_pasch(A,B,C,E,D),A)
| ~ between(D,E,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[inner_pasch2]) ).
fof(prove_a_between_a_and_b,axiom,
~ between(a,a,b),
file('theBenchmark.p',prove_a_between_a_and_b) ).
cnf(c_19,plain,
~ between(a,a,b),
inference(clausify,[status(thm)],[prove_a_between_a_and_b]) ).
cnf(c_462,plain,
A = extension(B,A,C,C),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_41,plain,
extension(A,B,C,C) = B,
inference(copy,[status(thm)],[c_462]) ).
cnf(c_126,plain,
between(A,B,B),
inference(paramod,[status(thm)],[c_41,c_4]) ).
cnf(c_463,plain,
( between(B,inner_pasch(D,C,C,B,A),D)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_126]) ).
cnf(c_179,plain,
between(A,inner_pasch(B,A,A,A,C),B),
inference(resolve,[status(thm)],[c_463,c_126]) ).
cnf(c_464,plain,
( between(C,inner_pasch(D,C,C,B,A),A)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_126]) ).
cnf(c_182,plain,
between(A,inner_pasch(B,A,A,A,C),C),
inference(resolve,[status(thm)],[c_464,c_126]) ).
cnf(c_465,plain,
A = inner_pasch(A,A,A,A,B),
inference(resolve,[status(thm)],[c_179,c_7]) ).
cnf(c_286,plain,
inner_pasch(A,A,A,A,B) = A,
inference(copy,[status(thm)],[c_465]) ).
cnf(c_460,plain,
between(A,A,B),
inference(paramod,[status(thm)],[c_286,c_182]) ).
cnf(c_461,plain,
$false,
inference(resolve,[status(thm)],[c_460,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/15.38 % Computer : n012.cluster.edu
% 0.04/15.38 % Model : x86_64 x86_64
% 0.04/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.38 % Memory : 8046.5625MB
% 0.04/15.38 % OS : Linux 6.8.0-71-generic
% 0.04/15.38 % CPULimit : 300
% 0.04/15.38 % WCLimit : 300
% 0.04/15.38 % DateTime : Fri Sep 25 12:29:21 UTC 2026
% 0.04/15.38 % CPUTime :
% 0.04/15.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/15.39 % Process 2084130 was started by sandbox on n012,
% 0.04/15.39 % Fri Sep 25 12:29:22 2026
% 0.04/15.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/15.39
% 0.04/15.39 % From the command line: assign(max_seconds, 300).
% 0.08/15.66
% 0.08/15.66 % SZS status Unsatisfiable for theBenchmark
% 0.08/15.66
% 0.08/15.66 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.08/15.66 % Length of proof is 14.
% 0.08/15.66 % Level of proof is 6.
% 0.08/15.66 % Maximum clause weight is 27.000.
% 0.08/15.66 % Given clauses 50.
% 0.08/15.66
% 0.08/15.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------