%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO124-1 : 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 : 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 07:17:07 AM UTC 2026
% Result : Unsatisfiable 2.72s 0.80s
% Output : CNFRefutation 2.72s
% 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(start_point_defn_8,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ordered_by(VAR_1,VAR_0,VAR_2)
| ~ incident_o(VAR_2,VAR_1)
| VAR_0 = VAR_2
| ~ start_point(VAR_0,VAR_1) ),
file('theBenchmark.p',start_point_defn_8) ).
cnf(c_33,plain,
( ordered_by(B,A,C)
| ~ incident_o(C,B)
| A = C
| ~ start_point(A,B) ),
inference(clausify,[status(thm)],[start_point_defn_8]) ).
fof(start_point_defn_7,axiom,
! [VAR_0,VAR_1] :
( incident_o(VAR_0,VAR_1)
| ~ start_point(VAR_0,VAR_1) ),
file('theBenchmark.p',start_point_defn_7) ).
cnf(c_34,plain,
( incident_o(A,B)
| ~ start_point(A,B) ),
inference(clausify,[status(thm)],[start_point_defn_7]) ).
fof(corollary_4_10_1_133,axiom,
start_point(sk26,sk25),
file('theBenchmark.p',corollary_4_10_1_133) ).
cnf(c_38,plain,
start_point(sk26,sk25),
inference(clausify,[status(thm)],[corollary_4_10_1_133]) ).
fof(corollary_4_10_1_134,axiom,
start_point(sk27,sk25),
file('theBenchmark.p',corollary_4_10_1_134) ).
cnf(c_39,plain,
start_point(sk27,sk25),
inference(clausify,[status(thm)],[corollary_4_10_1_134]) ).
cnf(c_60,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_113,plain,
( B != D
| ~ between_c(A,B,C,D) ),
inference(clausify,[status(thm)],[between_c_defn_1]) ).
fof(corollary_4_10_1_135,axiom,
sk26 != sk27,
file('theBenchmark.p',corollary_4_10_1_135) ).
cnf(c_133,plain,
sk26 != sk27,
inference(clausify,[status(thm)],[corollary_4_10_1_135]) ).
cnf(c_134,plain,
sk27 != sk26,
inference(copy,[status(thm)],[c_133]) ).
cnf(c_169,plain,
( ordered_by(sk25,sk26,A)
| ~ incident_o(A,sk25)
| sk26 = A ),
inference(resolve,[status(thm)],[c_38,c_33]) ).
cnf(c_170,plain,
incident_o(sk26,sk25),
inference(resolve,[status(thm)],[c_38,c_34]) ).
cnf(c_171,plain,
( ordered_by(sk25,sk27,A)
| ~ incident_o(A,sk25)
| sk27 = A ),
inference(resolve,[status(thm)],[c_39,c_33]) ).
cnf(c_172,plain,
incident_o(sk27,sk25),
inference(resolve,[status(thm)],[c_39,c_34]) ).
cnf(c_2045,plain,
( ordered_by(sk25,sk27,sk26)
| sk27 = sk26 ),
inference(resolve,[status(thm)],[c_171,c_170]) ).
cnf(c_571,plain,
ordered_by(sk25,sk27,sk26),
inference(resolve,[status(thm)],[c_134,c_2045]) ).
cnf(c_2046,plain,
( ordered_by(sk25,sk26,sk27)
| sk26 = sk27 ),
inference(resolve,[status(thm)],[c_172,c_169]) ).
cnf(c_2047,plain,
( ordered_by(sk25,sk26,sk27)
| sk27 = sk26 ),
inference(copy,[status(thm)],[c_2046]) ).
cnf(c_574,plain,
ordered_by(sk25,sk26,sk27),
inference(resolve,[status(thm)],[c_134,c_2047]) ).
cnf(c_763,plain,
( between_c(ax2_sk4(sk25,A,sk27,sk26),sk26,sk27,A)
| ~ ordered_by(sk25,A,sk27) ),
inference(resolve,[status(thm)],[c_571,c_60]) ).
cnf(c_2030,plain,
between_c(ax2_sk4(sk25,sk26,sk27,sk26),sk26,sk27,sk26),
inference(resolve,[status(thm)],[c_763,c_574]) ).
cnf(c_2048,plain,
sk26 != sk26,
inference(resolve,[status(thm)],[c_2030,c_113]) ).
cnf(c_2044,plain,
$false,
inference(copy,[status(thm)],[c_2048]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO124-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n016.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 12:55:15 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2413318 was started by sandbox2 on n016,
% 0.12/0.37 % Fri Sep 25 12:55:15 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 2.72/0.80
% 2.72/0.80 % SZS status Unsatisfiable for theBenchmark
% 2.72/0.80
% 2.72/0.80 % Proof 1 at 0.28 (+ 0.08) seconds.
% 2.72/0.80 % Length of proof is 19.
% 2.72/0.80 % Level of proof is 5.
% 2.72/0.80 % Maximum clause weight is 27.000.
% 2.72/0.80 % Given clauses 277.
% 2.72/0.80
% 2.72/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------