%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO125-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:17:08 AM UTC 2026
% Result : Unsatisfiable 1.74s 0.63s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 57 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 41 ( 2 sgn 17 !; 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_6,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between_o(VAR_0,VAR_3,VAR_2,VAR_1)
| ~ ordered_by(VAR_0,VAR_2,VAR_3)
| ~ ordered_by(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',between_o_defn_6) ).
cnf(c_26,plain,
( between_o(A,D,C,B)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(clausify,[status(thm)],[between_o_defn_6]) ).
fof(finish_point_defn_13,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ordered_by(VAR_1,VAR_2,VAR_0)
| ~ incident_o(VAR_2,VAR_1)
| VAR_0 = VAR_2
| ~ finish_point(VAR_0,VAR_1) ),
file('theBenchmark.p',finish_point_defn_13) ).
cnf(c_38,plain,
( ordered_by(B,C,A)
| ~ incident_o(C,B)
| A = C
| ~ finish_point(A,B) ),
inference(clausify,[status(thm)],[finish_point_defn_13]) ).
fof(corollary_4_10_2_133,axiom,
finish_point(sk26,sk25),
file('theBenchmark.p',corollary_4_10_2_133) ).
cnf(c_42,plain,
finish_point(sk26,sk25),
inference(clausify,[status(thm)],[corollary_4_10_2_133]) ).
fof(corollary_4_10_2_134,axiom,
finish_point(sk27,sk25),
file('theBenchmark.p',corollary_4_10_2_134) ).
cnf(c_43,plain,
finish_point(sk27,sk25),
inference(clausify,[status(thm)],[corollary_4_10_2_134]) ).
fof(finish_point_defn_12,axiom,
! [VAR_0,VAR_1] :
( incident_o(VAR_0,VAR_1)
| ~ finish_point(VAR_0,VAR_1) ),
file('theBenchmark.p',finish_point_defn_12) ).
cnf(c_44,plain,
( incident_o(A,B)
| ~ finish_point(A,B) ),
inference(clausify,[status(thm)],[finish_point_defn_12]) ).
cnf(c_45,plain,
incident_o(sk27,sk25),
inference(resolve,[status(thm)],[c_44,c_43]) ).
cnf(c_46,plain,
incident_o(sk26,sk25),
inference(resolve,[status(thm)],[c_44,c_42]) ).
cnf(c_47,plain,
( ordered_by(sk25,A,sk27)
| ~ incident_o(A,sk25)
| sk27 = A ),
inference(resolve,[status(thm)],[c_38,c_43]) ).
cnf(c_48,plain,
( ordered_by(sk25,A,sk26)
| ~ incident_o(A,sk25)
| sk26 = A ),
inference(resolve,[status(thm)],[c_38,c_42]) ).
cnf(c_64,plain,
( between_c(ax2_sk4(A,B,C,D),D,C,B)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(resolve,[status(thm)],[c_26,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_117,plain,
( B != D
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_1]) ).
fof(corollary_4_10_2_135,axiom,
sk26 != sk27,
file('theBenchmark.p',corollary_4_10_2_135) ).
cnf(c_137,plain,
sk26 != sk27,
inference(clausify,[status(thm)],[corollary_4_10_2_135]) ).
cnf(c_138,plain,
sk27 != sk26,
inference(copy,[status(thm)],[c_137]) ).
cnf(c_1978,plain,
( ordered_by(sk25,sk26,sk27)
| sk27 = sk26 ),
inference(resolve,[status(thm)],[c_47,c_46]) ).
cnf(c_210,plain,
ordered_by(sk25,sk26,sk27),
inference(resolve,[status(thm)],[c_138,c_1978]) ).
cnf(c_1979,plain,
( ordered_by(sk25,sk27,sk26)
| sk26 = sk27 ),
inference(resolve,[status(thm)],[c_48,c_45]) ).
cnf(c_1980,plain,
( ordered_by(sk25,sk27,sk26)
| sk27 = sk26 ),
inference(copy,[status(thm)],[c_1979]) ).
cnf(c_211,plain,
ordered_by(sk25,sk27,sk26),
inference(resolve,[status(thm)],[c_138,c_1980]) ).
cnf(c_705,plain,
( between_c(ax2_sk4(sk25,A,sk26,sk27),sk27,sk26,A)
| ~ ordered_by(sk25,A,sk26) ),
inference(resolve,[status(thm)],[c_210,c_64]) ).
cnf(c_1963,plain,
between_c(ax2_sk4(sk25,sk27,sk26,sk27),sk27,sk26,sk27),
inference(resolve,[status(thm)],[c_705,c_211]) ).
cnf(c_1981,plain,
sk27 != sk27,
inference(resolve,[status(thm)],[c_1963,c_117]) ).
cnf(c_1977,plain,
$false,
inference(copy,[status(thm)],[c_1981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO125-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 12:46:03 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2301480 was started by sandbox on n017,
% 0.11/0.36 % Fri Sep 25 12:46:03 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 1.74/0.63
% 1.74/0.63 % SZS status Unsatisfiable for theBenchmark
% 1.74/0.63
% 1.74/0.63 % Proof 1 at 0.21 (+ 0.04) seconds.
% 1.74/0.63 % Length of proof is 19.
% 1.74/0.63 % Level of proof is 5.
% 1.74/0.63 % Maximum clause weight is 27.000.
% 1.74/0.63 % Given clauses 268.
% 1.74/0.63
% 1.74/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------