%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO258+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 07:17:44 AM UTC 2026
% Result : Theorem 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 21 ~; 23 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 40 ( 2 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a9_defns,axiom,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
<=> ( ( before_on_line(L,B,A)
& before_on_line(L,C,B) )
| ( before_on_line(L,B,C)
& before_on_line(L,A,B) ) ) ),
file('theBenchmark.p',a9_defns) ).
fof(con,conjecture,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_83,plain,
( ~ before_on_line(A,C,D)
| ~ before_on_line(A,B,C)
| between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[a9_defns]) ).
cnf(c_84,plain,
( before_on_line(A,C,B)
| before_on_line(A,C,D)
| ~ between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[a9_defns]) ).
cnf(c_85,plain,
( before_on_line(A,D,C)
| before_on_line(A,C,D)
| ~ between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[a9_defns]) ).
cnf(c_86,plain,
( before_on_line(A,C,B)
| before_on_line(A,B,C)
| ~ between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[a9_defns]) ).
cnf(c_87,plain,
( before_on_line(A,D,C)
| before_on_line(A,B,C)
| ~ between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[a9_defns]) ).
cnf(c_88,plain,
( ~ before_on_line(A,C,B)
| ~ before_on_line(A,D,C)
| between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[a9_defns]) ).
fof(nnf_37,plain,
? [L,A,B,C] :
( ~ between_on_line(L,C,B,A)
& between_on_line(L,A,B,C) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ between_on_line(sK0,sK3,sK2,sK1)
& between_on_line(sK0,sK1,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(L,sK0),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_37]) ).
cnf(c_89,negated_conjecture,
between_on_line(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_90,negated_conjecture,
~ between_on_line(sK0,sK3,sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_91,negated_conjecture,
( ~ before_on_line(sK0,sK2,sK1)
| ~ before_on_line(sK0,sK3,sK2) ),
inference(resolve,[status(thm)],[c_90,c_83]) ).
cnf(c_92,negated_conjecture,
( ~ before_on_line(sK0,sK2,sK3)
| ~ before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_90,c_88]) ).
cnf(c_93,negated_conjecture,
( before_on_line(sK0,sK3,sK2)
| before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_89,c_87]) ).
cnf(c_94,negated_conjecture,
( before_on_line(sK0,sK2,sK1)
| before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_89,c_86]) ).
cnf(c_95,negated_conjecture,
( before_on_line(sK0,sK3,sK2)
| before_on_line(sK0,sK2,sK3) ),
inference(resolve,[status(thm)],[c_89,c_85]) ).
cnf(c_96,negated_conjecture,
( before_on_line(sK0,sK2,sK1)
| before_on_line(sK0,sK2,sK3) ),
inference(resolve,[status(thm)],[c_89,c_84]) ).
cnf(c_136,plain,
( ~ before_on_line(sK0,sK2,sK1)
| before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_93,c_91]) ).
cnf(c_138,plain,
( ~ before_on_line(sK0,sK2,sK1)
| before_on_line(sK0,sK2,sK3) ),
inference(resolve,[status(thm)],[c_95,c_91]) ).
cnf(c_139,plain,
( ~ before_on_line(sK0,sK1,sK2)
| before_on_line(sK0,sK2,sK1) ),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_168,negated_conjecture,
( before_on_line(sK0,sK1,sK2)
| before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_136,c_94]) ).
cnf(c_164,negated_conjecture,
before_on_line(sK0,sK1,sK2),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_165,plain,
before_on_line(sK0,sK2,sK1),
inference(resolve,[status(thm)],[c_164,c_139]) ).
cnf(c_166,negated_conjecture,
~ before_on_line(sK0,sK2,sK3),
inference(resolve,[status(thm)],[c_164,c_92]) ).
cnf(c_169,negated_conjecture,
~ before_on_line(sK0,sK2,sK1),
inference(resolve,[status(thm)],[c_166,c_138]) ).
cnf(c_167,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_165,c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO258+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:11:22 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 2834086 was started by sandbox2 on n019,
% 0.09/0.37 % Fri Sep 25 13:11:22 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 0.15/0.42
% 0.15/0.42 % SZS status Theorem for theBenchmark
% 0.15/0.42
% 0.15/0.42 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.42 % Length of proof is 23.
% 0.15/0.42 % Level of proof is 6.
% 0.15/0.42 % Maximum clause weight is 13.000.
% 0.15/0.42 % Given clauses 31.
% 0.15/0.42
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------