%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO126-1 : 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 : n026.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 4.87s 1.14s
% Output : CNFRefutation 4.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 16 unt; 0 def)
% Number of atoms : 67 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 20 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 44 ( 1 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inner_point_defn_22,axiom,
! [VAR_0,VAR_1] :
( ~ end_point(VAR_0,VAR_1)
| ~ inner_point(VAR_0,VAR_1) ),
file('theBenchmark.p',inner_point_defn_22) ).
cnf(c_2,plain,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[inner_point_defn_22]) ).
fof(inner_point_defn_21,axiom,
! [VAR_0,VAR_1] :
( incident_c(VAR_0,VAR_1)
| ~ inner_point(VAR_0,VAR_1) ),
file('theBenchmark.p',inner_point_defn_21) ).
cnf(c_3,plain,
( incident_c(A,B)
| ~ inner_point(A,B) ),
inference(clausify,[status(thm)],[inner_point_defn_21]) ).
fof(c3_37,axiom,
! [VAR_0] : inner_point(ax0_sk8(VAR_0),VAR_0),
file('theBenchmark.p',c3_37) ).
cnf(c_4,plain,
inner_point(ax0_sk8(A),A),
inference(clausify,[status(thm)],[c3_37]) ).
fof(open_defn_33,axiom,
! [VAR_0] :
( end_point(ax0_sk7(VAR_0),VAR_0)
| ~ open(VAR_0) ),
file('theBenchmark.p',open_defn_33) ).
cnf(c_13,plain,
( end_point(ax0_sk7(A),A)
| ~ open(A) ),
inference(clausify,[status(thm)],[open_defn_33]) ).
fof(o2_19,axiom,
! [VAR_0] : open(ax2_sk3(VAR_0)),
file('theBenchmark.p',o2_19) ).
cnf(c_15,plain,
open(ax2_sk3(A)),
inference(clausify,[status(thm)],[o2_19]) ).
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(o4_29,axiom,
! [VAR_0] : start_point(ax2_sk6(VAR_0),VAR_0),
file('theBenchmark.p',o4_29) ).
cnf(c_37,plain,
start_point(ax2_sk6(A),A),
inference(clausify,[status(thm)],[o4_29]) ).
fof(end_point_defn_13,axiom,
! [VAR_0,VAR_1] :
( incident_c(VAR_0,VAR_1)
| ~ end_point(VAR_0,VAR_1) ),
file('theBenchmark.p',end_point_defn_13) ).
cnf(c_88,plain,
( incident_c(A,B)
| ~ end_point(A,B) ),
inference(clausify,[status(thm)],[end_point_defn_13]) ).
fof(o2_21,axiom,
! [VAR_0,VAR_1] :
( incident_o(VAR_0,VAR_1)
| ~ incident_c(VAR_0,ax2_sk3(VAR_1)) ),
file('theBenchmark.p',o2_21) ).
cnf(c_118,plain,
( incident_o(A,B)
| ~ incident_c(A,ax2_sk3(B)) ),
inference(clausify,[status(thm)],[o2_21]) ).
fof(theorem_4_11_133,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ ordered_by(sk25,VAR_0,VAR_1) ),
file('theBenchmark.p',theorem_4_11_133) ).
cnf(c_131,plain,
( A = B
| ~ ordered_by(sk25,A,B) ),
inference(clausify,[status(thm)],[theorem_4_11_133]) ).
cnf(c_132,plain,
~ end_point(ax0_sk8(A),A),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_133,plain,
incident_c(ax0_sk8(A),A),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_150,plain,
end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_164,plain,
( ordered_by(A,ax2_sk6(A),B)
| ~ incident_o(B,A)
| ax2_sk6(A) = B ),
inference(resolve,[status(thm)],[c_37,c_33]) ).
cnf(c_417,plain,
incident_o(ax0_sk8(ax2_sk3(A)),A),
inference(resolve,[status(thm)],[c_133,c_118]) ).
cnf(c_458,plain,
incident_c(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),
inference(resolve,[status(thm)],[c_150,c_88]) ).
cnf(c_700,plain,
( ordered_by(A,ax2_sk6(A),ax0_sk8(ax2_sk3(A)))
| ax2_sk6(A) = ax0_sk8(ax2_sk3(A)) ),
inference(resolve,[status(thm)],[c_417,c_164]) ).
cnf(c_801,plain,
incident_o(ax0_sk7(ax2_sk3(A)),A),
inference(resolve,[status(thm)],[c_458,c_118]) ).
cnf(c_809,plain,
( ordered_by(A,ax2_sk6(A),ax0_sk7(ax2_sk3(A)))
| ax2_sk6(A) = ax0_sk7(ax2_sk3(A)) ),
inference(resolve,[status(thm)],[c_801,c_164]) ).
cnf(c_5686,plain,
( ax2_sk6(sk25) = ax0_sk8(ax2_sk3(sk25))
| ax2_sk6(sk25) = ax0_sk8(ax2_sk3(sk25)) ),
inference(resolve,[status(thm)],[c_700,c_131]) ).
cnf(c_5596,plain,
ax2_sk6(sk25) = ax0_sk8(ax2_sk3(sk25)),
inference(copy,[status(thm)],[c_5686]) ).
cnf(c_5687,plain,
( ax2_sk6(sk25) = ax0_sk7(ax2_sk3(sk25))
| ax2_sk6(sk25) = ax0_sk7(ax2_sk3(sk25)) ),
inference(resolve,[status(thm)],[c_809,c_131]) ).
cnf(c_5688,plain,
( ax2_sk6(sk25) = ax0_sk7(ax2_sk3(sk25))
| ax0_sk8(ax2_sk3(sk25)) = ax0_sk7(ax2_sk3(sk25)) ),
inference(paramod,[status(thm)],[c_5596,c_5687]) ).
cnf(c_5689,plain,
( ax0_sk8(ax2_sk3(sk25)) = ax0_sk7(ax2_sk3(sk25))
| ax0_sk8(ax2_sk3(sk25)) = ax0_sk7(ax2_sk3(sk25)) ),
inference(paramod,[status(thm)],[c_5596,c_5688]) ).
cnf(c_5690,plain,
( ax0_sk8(ax2_sk3(sk25)) = ax0_sk7(ax2_sk3(sk25))
| ax0_sk7(ax2_sk3(sk25)) = ax0_sk8(ax2_sk3(sk25)) ),
inference(copy,[status(thm)],[c_5689]) ).
cnf(c_5691,plain,
( ax0_sk7(ax2_sk3(sk25)) = ax0_sk8(ax2_sk3(sk25))
| ax0_sk7(ax2_sk3(sk25)) = ax0_sk8(ax2_sk3(sk25)) ),
inference(copy,[status(thm)],[c_5690]) ).
cnf(c_5672,plain,
ax0_sk7(ax2_sk3(sk25)) = ax0_sk8(ax2_sk3(sk25)),
inference(copy,[status(thm)],[c_5691]) ).
cnf(c_5692,plain,
end_point(ax0_sk8(ax2_sk3(sk25)),ax2_sk3(sk25)),
inference(paramod,[status(thm)],[c_5672,c_150]) ).
cnf(c_5685,plain,
$false,
inference(resolve,[status(thm)],[c_132,c_5692]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO126-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 12:53:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2557801 was started by sandbox2 on n026,
% 0.09/0.37 % Fri Sep 25 12:53:25 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 4.87/1.14
% 4.87/1.14 % given #500 (T,wt=12): 4499 ax2_sk3(A) != sum(B,sum(C,D)) | incident_o(ax0_sk8(C),A). [back_rewrite(2326),rewrite([4444(1)])].
% 4.87/1.14
% 4.87/1.14 % SZS status Unsatisfiable for theBenchmark
% 4.87/1.14
% 4.87/1.14 % Proof 1 at 0.56 (+ 0.13) seconds.
% 4.87/1.14 % Length of proof is 22.
% 4.87/1.14 % Level of proof is 6.
% 4.87/1.14 % Maximum clause weight is 13.000.
% 4.87/1.14 % Given clauses 580.
% 4.87/1.14
% 4.87/1.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------