%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO187+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 : n009.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 07:17:20 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 37 ~; 28 |; 17 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(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,U,V] :
( ( ~ apart_point_and_line(Y,line_connecting(U,V))
& ~ apart_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( ~ apart_point_and_line(V,line_connecting(X,Y))
& ~ apart_point_and_line(U,line_connecting(X,Y)) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ~ apart_point_and_line(Y,line_connecting(U,V))
& ~ apart_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) )
=> ( ~ apart_point_and_line(V,line_connecting(X,Y))
& ~ apart_point_and_line(U,line_connecting(X,Y)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
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_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,U,V] :
( ( apart_point_and_line(V,line_connecting(X,Y))
| apart_point_and_line(U,line_connecting(X,Y)) )
& ~ apart_point_and_line(Y,line_connecting(U,V))
& ~ apart_point_and_line(X,line_connecting(U,V))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) )
& ~ apart_point_and_line(sK1,line_connecting(sK2,sK3))
& ~ apart_point_and_line(sK0,line_connecting(sK2,sK3))
& distinct_points(sK2,sK3)
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(U,sK2),skolemize(V,sK3)],[nnf_15]) ).
cnf(c_30,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,negated_conjecture,
distinct_points(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
~ apart_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_33,negated_conjecture,
~ apart_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_34,negated_conjecture,
( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_35,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_30,c_23]) ).
cnf(c_36,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_38,plain,
~ apart_point_and_line(sK3,line_connecting(sK2,sK3)),
inference(resolve,[status(thm)],[c_31,c_23]) ).
cnf(c_39,plain,
~ apart_point_and_line(sK2,line_connecting(sK2,sK3)),
inference(resolve,[status(thm)],[c_31,c_22]) ).
cnf(c_63,negated_conjecture,
( 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_26,c_30]) ).
cnf(c_64,negated_conjecture,
( apart_point_and_line(sK1,A)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,A)
| ~ distinct_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_63,c_36]) ).
cnf(c_65,negated_conjecture,
( apart_point_and_line(sK1,line_connecting(sK2,sK3))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_64,c_32]) ).
cnf(c_66,negated_conjecture,
( apart_point_and_line(sK1,line_connecting(sK2,sK3))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_65,c_35]) ).
cnf(c_47,negated_conjecture,
~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK3)),
inference(resolve,[status(thm)],[c_66,c_33]) ).
cnf(c_67,plain,
( apart_point_and_line(A,line_connecting(sK2,sK3))
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_28,c_47]) ).
cnf(c_57,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_67,c_39]) ).
cnf(c_68,plain,
( apart_point_and_line(A,line_connecting(sK2,sK3))
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_28,c_47]) ).
cnf(c_58,plain,
~ apart_point_and_line(sK3,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_68,c_38]) ).
cnf(c_69,negated_conjecture,
apart_point_and_line(sK3,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_57,c_34]) ).
cnf(c_62,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_58,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 13:03:14 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1654983 was started by sandbox on n009,
% 0.17/0.44 % Fri Sep 25 13:03:14 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 22.
% 0.17/0.46 % Level of proof is 5.
% 0.17/0.46 % Maximum clause weight is 23.000.
% 0.17/0.46 % Given clauses 26.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------