%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO258+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.11s 0.39s
% Output : CNFRefutation 0.11s
% 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 : 50 ( 20 ~; 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(bet_def,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',bet_def) ).
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]) ).
fof(nnf_32,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_32]) ).
cnf(c_50,negated_conjecture,
between_on_line(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_51,negated_conjecture,
~ between_on_line(sK0,sK3,sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_52,plain,
( ~ before_on_line(A,C,B)
| ~ before_on_line(A,D,C)
| between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[bet_def]) ).
cnf(c_53,plain,
( ~ before_on_line(A,C,D)
| ~ before_on_line(A,B,C)
| between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[bet_def]) ).
cnf(c_54,plain,
( before_on_line(A,C,B)
| before_on_line(A,C,D)
| ~ between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[bet_def]) ).
cnf(c_55,plain,
( before_on_line(A,D,C)
| before_on_line(A,C,D)
| ~ between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[bet_def]) ).
cnf(c_56,plain,
( before_on_line(A,C,B)
| before_on_line(A,B,C)
| ~ between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[bet_def]) ).
cnf(c_57,plain,
( before_on_line(A,D,C)
| before_on_line(A,B,C)
| ~ between_on_line(A,B,C,D) ),
inference(clausify,[status(thm)],[bet_def]) ).
cnf(c_58,negated_conjecture,
( before_on_line(sK0,sK3,sK2)
| before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_57,c_50]) ).
cnf(c_59,negated_conjecture,
( before_on_line(sK0,sK2,sK1)
| before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_56,c_50]) ).
cnf(c_60,negated_conjecture,
( before_on_line(sK0,sK3,sK2)
| before_on_line(sK0,sK2,sK3) ),
inference(resolve,[status(thm)],[c_55,c_50]) ).
cnf(c_61,negated_conjecture,
( before_on_line(sK0,sK2,sK1)
| before_on_line(sK0,sK2,sK3) ),
inference(resolve,[status(thm)],[c_54,c_50]) ).
cnf(c_62,negated_conjecture,
( ~ before_on_line(sK0,sK2,sK1)
| ~ before_on_line(sK0,sK3,sK2) ),
inference(resolve,[status(thm)],[c_53,c_51]) ).
cnf(c_63,negated_conjecture,
( ~ before_on_line(sK0,sK2,sK3)
| ~ before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_52,c_51]) ).
cnf(c_99,plain,
( before_on_line(sK0,sK2,sK3)
| ~ before_on_line(sK0,sK2,sK1) ),
inference(resolve,[status(thm)],[c_62,c_60]) ).
cnf(c_100,plain,
( before_on_line(sK0,sK1,sK2)
| ~ before_on_line(sK0,sK2,sK1) ),
inference(resolve,[status(thm)],[c_62,c_58]) ).
cnf(c_101,plain,
( before_on_line(sK0,sK2,sK1)
| ~ before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_63,c_61]) ).
cnf(c_142,negated_conjecture,
( before_on_line(sK0,sK1,sK2)
| before_on_line(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_100,c_59]) ).
cnf(c_137,negated_conjecture,
before_on_line(sK0,sK1,sK2),
inference(copy,[status(thm)],[c_142]) ).
cnf(c_139,plain,
before_on_line(sK0,sK2,sK1),
inference(resolve,[status(thm)],[c_137,c_101]) ).
cnf(c_140,negated_conjecture,
~ before_on_line(sK0,sK2,sK3),
inference(resolve,[status(thm)],[c_137,c_63]) ).
cnf(c_143,plain,
before_on_line(sK0,sK2,sK3),
inference(resolve,[status(thm)],[c_139,c_99]) ).
cnf(c_141,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_140,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO258+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.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 13:11:22 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 3242137 was started by sandbox on n004,
% 0.11/0.36 % Fri Sep 25 13:11:22 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).
% 0.11/0.39
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 23.
% 0.11/0.39 % Level of proof is 6.
% 0.11/0.39 % Maximum clause weight is 8.000.
% 0.11/0.39 % Given clauses 37.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------