%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO040-2 : TPTP v9.3.1. Released v1.0.0.
% 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 07:16:52 AM UTC 2026
% Result : Unsatisfiable 1.91s 0.68s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 34 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 28 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_19,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(u_between_v_and_w,axiom,
between(v,u,w),
file('theBenchmark.p',u_between_v_and_w) ).
cnf(c_20,plain,
between(v,u,w),
inference(clausify,[status(thm)],[u_between_v_and_w]) ).
fof(prove_u_is_v,axiom,
u != v,
file('theBenchmark.p',prove_u_is_v) ).
cnf(c_21,plain,
u != v,
inference(clausify,[status(thm)],[prove_u_is_v]) ).
cnf(c_22,plain,
v != u,
inference(copy,[status(thm)],[c_21]) ).
cnf(c_547,plain,
( between(B,inner_pasch(u,v,w,B,A),u)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_9,c_19]) ).
cnf(c_138,plain,
between(u,inner_pasch(u,v,w,u,v),u),
inference(resolve,[status(thm)],[c_547,c_20]) ).
cnf(c_548,plain,
( between(v,inner_pasch(u,v,w,B,A),A)
| ~ between(A,B,w) ),
inference(resolve,[status(thm)],[c_8,c_19]) ).
cnf(c_140,plain,
between(v,inner_pasch(u,v,w,u,v),v),
inference(resolve,[status(thm)],[c_548,c_20]) ).
cnf(c_142,plain,
~ between(v,u,v),
inference(resolve,[status(thm)],[c_7,c_22]) ).
cnf(c_549,plain,
u = inner_pasch(u,v,w,u,v),
inference(resolve,[status(thm)],[c_138,c_7]) ).
cnf(c_536,plain,
inner_pasch(u,v,w,u,v) = u,
inference(copy,[status(thm)],[c_549]) ).
cnf(c_550,plain,
between(v,u,v),
inference(paramod,[status(thm)],[c_536,c_140]) ).
cnf(c_546,plain,
$false,
inference(resolve,[status(thm)],[c_142,c_550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO040-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n016.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 12:39:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2390729 was started by sandbox2 on n016,
% 0.11/0.37 % Fri Sep 25 12:39:59 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 1.91/0.68
% 1.91/0.68 % SZS status Unsatisfiable for theBenchmark
% 1.91/0.68
% 1.91/0.68 % Proof 1 at 0.22 (+ 0.04) seconds.
% 1.91/0.68 % Length of proof is 12.
% 1.91/0.68 % Level of proof is 3.
% 1.91/0.68 % Maximum clause weight is 27.000.
% 1.91/0.68 % Given clauses 68.
% 1.91/0.68
% 1.91/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------