%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO180+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:17:18 AM UTC 2026
% Result : Theorem 0.21s 0.65s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 24 ~; 53 |; 5 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('theBenchmark.p',apart4) ).
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('theBenchmark.p',ci1) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('theBenchmark.p',ci2) ).
fof(cu1,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('theBenchmark.p',cu1) ).
fof(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('theBenchmark.p',ceq1) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq2) ).
fof(con,conjecture,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(X,line_connecting(Z,Y)) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(X,line_connecting(Z,Y)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_16,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_19,plain,
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[apart4]) ).
cnf(c_22,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_23,plain,
( ~ apart_point_and_line(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci2]) ).
cnf(c_26,plain,
( apart_point_and_line(B,D)
| apart_point_and_line(B,C)
| apart_point_and_line(A,D)
| apart_point_and_line(A,C)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[cu1]) ).
cnf(c_27,plain,
( apart_point_and_line(C,B)
| distinct_points(A,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq1]) ).
cnf(c_28,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
fof(nnf_15,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(X,line_connecting(Z,Y))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK2,sK1))
& apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_15]) ).
cnf(c_30,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,negated_conjecture,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
~ apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_33,plain,
( apart_point_and_line(sK1,B)
| apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,B)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_30,c_26]) ).
cnf(c_34,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_30,c_23]) ).
cnf(c_35,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_36,plain,
( distinct_points(sK1,A)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_30,c_19]) ).
cnf(c_37,plain,
( apart_point_and_line(sK2,A)
| distinct_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_31,c_28]) ).
cnf(c_42,plain,
( distinct_points(A,B)
| distinct_points(sK1,B)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_36,c_19]) ).
cnf(c_170,plain,
( distinct_points(sK1,sK0)
| distinct_points(sK0,sK0) ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_43,plain,
distinct_points(sK1,sK0),
inference(resolve,[status(thm)],[c_16,c_170]) ).
cnf(c_44,plain,
~ apart_point_and_line(sK0,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_43,c_23]) ).
cnf(c_45,plain,
~ apart_point_and_line(sK1,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_43,c_22]) ).
cnf(c_171,plain,
( apart_point_and_line(sK1,A)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,A)
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,A) ),
inference(resolve,[status(thm)],[c_37,c_33]) ).
cnf(c_172,plain,
( apart_point_and_line(sK1,A)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,A)
| apart_point_and_line(sK2,A) ),
inference(resolve,[status(thm)],[c_35,c_171]) ).
cnf(c_86,plain,
( apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A)
| apart_point_and_line(sK2,A) ),
inference(resolve,[status(thm)],[c_34,c_172]) ).
cnf(c_127,plain,
( apart_point_and_line(B,A)
| distinct_points(sK2,B)
| apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A) ),
inference(resolve,[status(thm)],[c_86,c_27]) ).
cnf(c_151,plain,
( distinct_points(sK2,sK1)
| apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A) ),
inference(factor,[status(thm)],[c_127]) ).
cnf(c_159,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK2,sK1))
| apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A) ),
inference(resolve,[status(thm)],[c_151,c_23]) ).
cnf(c_173,plain,
( apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A)
| ~ apart_point_and_line(sK2,line_connecting(sK2,sK1)) ),
inference(resolve,[status(thm)],[c_22,c_151]) ).
cnf(c_174,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK1))
| apart_point_and_line(sK0,line_connecting(sK2,sK1))
| apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A) ),
inference(resolve,[status(thm)],[c_173,c_86]) ).
cnf(c_162,negated_conjecture,
( apart_point_and_line(sK1,line_connecting(sK2,sK1))
| apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A) ),
inference(resolve,[status(thm)],[c_32,c_174]) ).
cnf(c_175,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK1))
| apart_point_and_line(sK0,line_connecting(sK2,sK1)) ),
inference(factor,[status(thm)],[c_162]) ).
cnf(c_163,negated_conjecture,
apart_point_and_line(sK1,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_32,c_175]) ).
cnf(c_164,plain,
( apart_point_and_line(sK1,A)
| apart_point_and_line(sK0,A) ),
inference(resolve,[status(thm)],[c_163,c_159]) ).
cnf(c_176,plain,
apart_point_and_line(sK0,line_connecting(sK1,sK0)),
inference(resolve,[status(thm)],[c_164,c_45]) ).
cnf(c_169,plain,
$false,
inference(resolve,[status(thm)],[c_44,c_176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO180+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.60 % Computer : n017.cluster.edu
% 0.17/0.60 % Model : x86_64 x86_64
% 0.17/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.60 % Memory : 8046.5625MB
% 0.17/0.60 % OS : Linux 6.8.0-71-generic
% 0.17/0.60 % CPULimit : 300
% 0.17/0.60 % WCLimit : 300
% 0.17/0.60 % DateTime : Fri Sep 25 12:57:32 UTC 2026
% 0.17/0.61 % CPUTime :
% 0.17/0.61 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.61 % Process 2319881 was started by sandbox on n017,
% 0.17/0.61 % Fri Sep 25 12:57:32 2026
% 0.17/0.61 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.62
% 0.17/0.62 % From the command line: assign(max_seconds, 300).
% 0.21/0.65
% 0.21/0.65 % SZS status Theorem for theBenchmark
% 0.21/0.65
% 0.21/0.65 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.21/0.65 % Length of proof is 35.
% 0.21/0.65 % Level of proof is 9.
% 0.21/0.65 % Maximum clause weight is 23.000.
% 0.21/0.65 % Given clauses 41.
% 0.21/0.65
% 0.21/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------