%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO117-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 07:17:06 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.52s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 24 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 35 ( 5 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(o3_24,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between_c(ax2_sk4(VAR_0,VAR_3,VAR_2,VAR_1),VAR_1,VAR_2,VAR_3)
| ~ between_o(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',o3_24) ).
cnf(c_19,plain,
( between_c(ax2_sk4(A,D,C,B),B,C,D)
| ~ between_o(A,B,C,D) ),
inference(clausify,[status(thm)],[o3_24]) ).
fof(between_o_defn_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between_o(VAR_0,VAR_1,VAR_2,VAR_3)
| ~ ordered_by(VAR_0,VAR_2,VAR_3)
| ~ ordered_by(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',between_o_defn_5) ).
cnf(c_27,plain,
( between_o(A,B,C,D)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(clausify,[status(thm)],[between_o_defn_5]) ).
cnf(c_55,plain,
( between_c(ax2_sk4(A,D,C,B),B,C,D)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(resolve,[status(thm)],[c_27,c_19]) ).
fof(between_c_defn_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 != VAR_3
| ~ between_c(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',between_c_defn_1) ).
cnf(c_111,plain,
( B != D
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_1]) ).
fof(theorem_4_4_133,axiom,
ordered_by(sk25,sk26,sk26),
file('theBenchmark.p',theorem_4_4_133) ).
cnf(c_131,plain,
ordered_by(sk25,sk26,sk26),
inference(clausify,[status(thm)],[theorem_4_4_133]) ).
cnf(c_174,plain,
( between_c(ax2_sk4(A,B,B,B),B,B,B)
| ~ ordered_by(A,B,B) ),
inference(factor,[status(thm)],[c_55]) ).
cnf(c_499,plain,
~ between_c(A,B,C,B),
inference(xxres,[status(thm)],[c_111]) ).
cnf(c_500,plain,
~ ordered_by(A,B,B),
inference(resolve,[status(thm)],[c_499,c_174]) ).
cnf(c_501,plain,
$false,
inference(resolve,[status(thm)],[c_500,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO117-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n006.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 12:48:41 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2944966 was started by sandbox2 on n006,
% 0.19/0.45 % Fri Sep 25 12:48:41 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.52
% 0.23/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.52
% 0.23/0.52 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.23/0.52 % Length of proof is 9.
% 0.23/0.52 % Level of proof is 4.
% 0.23/0.52 % Maximum clause weight is 27.000.
% 0.23/0.52 % Given clauses 57.
% 0.23/0.52
% 0.23/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------