%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO179+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /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 : Thu Sep 24 08:39:42 AM UTC 2026
% Result : Theorem 0.15s 10.76s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 63 ( 34 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 119 ( 51 ~; 43 |; 20 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 52 ( 0 sgn 33 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('GEO008+0.ax',apart1) ).
fof(con1,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('GEO008+0.ax',con1) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('GEO008+0.ax',ceq2) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ) ),
file('theBenchmark.p',con) ).
fof(f_1_1,plain,
! [X] : ~ distinct_points(X,X),
inference(fof_nnf,[status(thm)],[apart1]) ).
fof(f_1_2,plain,
! [U_0] : ~ distinct_points(U_0,U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
~ distinct_points(U_0,U_0),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_7_1,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con1]) ).
fof(f_7_2,plain,
! [U_14,U_13,U_12] :
( ( distinct_points(U_12,U_13)
& distinct_points(U_12,U_14) )
| ~ apart_point_and_line(U_12,line_connecting(U_14,U_13))
| ~ distinct_points(U_14,U_13) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_14,U_13] :
( ! [U_12] :
( ( distinct_points(U_12,U_13)
& distinct_points(U_12,U_14) )
| ~ apart_point_and_line(U_12,line_connecting(U_14,U_13)) )
| ~ distinct_points(U_14,U_13) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( distinct_points(U_12,U_14)
| ~ apart_point_and_line(U_12,line_connecting(U_14,U_13))
| ~ distinct_points(U_14,U_13) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( distinct_points(U_12,U_13)
| ~ apart_point_and_line(U_12,line_connecting(U_14,U_13))
| ~ distinct_points(U_14,U_13) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_11_1,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(fof_nnf,[status(thm)],[ceq2]) ).
fof(f_11_2,plain,
! [U_27,U_26,U_25] :
( apart_point_and_line(U_27,U_25)
| distinct_lines(U_26,U_25)
| ~ apart_point_and_line(U_27,U_26) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_27,U_26] :
( ! [U_25] :
( apart_point_and_line(U_27,U_25)
| distinct_lines(U_26,U_25) )
| ~ apart_point_and_line(U_27,U_26) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( apart_point_and_line(U_27,U_25)
| distinct_lines(U_26,U_25)
| ~ apart_point_and_line(U_27,U_26) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_13_1,negated_conjecture,
~ ! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ) ),
inference(negate,[status(cth)],[con]) ).
fof(f_13_2,negated_conjecture,
? [X,Y,Z] :
( ( ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
| ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) )
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_32,U_31,U_30] :
( ( ~ distinct_lines(line_connecting(U_32,U_31),line_connecting(U_30,U_31))
| ~ distinct_lines(line_connecting(U_32,U_31),line_connecting(U_30,U_32)) )
& apart_point_and_line(U_30,line_connecting(U_32,U_31))
& distinct_points(U_32,U_31) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_31,U_30] :
( ( ~ distinct_lines(line_connecting(sK1,U_31),line_connecting(U_30,U_31))
| ~ distinct_lines(line_connecting(sK1,U_31),line_connecting(U_30,sK1)) )
& apart_point_and_line(U_30,line_connecting(sK1,U_31))
& distinct_points(sK1,U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_32,sK1)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
? [U_30] :
( ( ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(U_30,sK2))
| ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(U_30,sK1)) )
& apart_point_and_line(U_30,line_connecting(sK1,sK2))
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_31,sK2)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ( ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK2))
| ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK1)) )
& apart_point_and_line(sK3,line_connecting(sK1,sK2))
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_30,sK3)],[f_13_5]) ).
fof(f_13_7,negated_conjecture,
( ( ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK2))
| ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK1)) )
& apart_point_and_line(sK3,line_connecting(sK1,sK2))
& distinct_points(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
distinct_points(sK1,sK2),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,negated_conjecture,
apart_point_and_line(sK3,line_connecting(sK1,sK2)),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_10,negated_conjecture,
( ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK2))
| ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK1)) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(t1,plain,
( ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK2))
| ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK1)) ),
inference(start,[status(thm),parent(0:0)],[f_13_10]) ).
cnf(t2,plain,
( apart_point_and_line(sK3,line_connecting(sK3,sK1))
| ~ apart_point_and_line(sK3,line_connecting(sK1,sK2))
| distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK1)) ),
inference(extension,[status(thm),parent(t1:1)],[f_11_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
apart_point_and_line(sK3,line_connecting(sK1,sK2)),
inference(extension,[status(thm),parent(t2:2)],[f_13_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(l2,lemma,
apart_point_and_line(sK3,line_connecting(sK1,sK2)),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t6,plain,
( distinct_points(sK3,sK1)
| ~ distinct_points(sK3,sK1)
| ~ apart_point_and_line(sK3,line_connecting(sK3,sK1)) ),
inference(extension,[status(thm),parent(t2:3)],[f_7_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK1,sK2))
| ~ distinct_points(sK1,sK2)
| distinct_points(sK3,sK1) ),
inference(extension,[status(thm),parent(t6:2)],[f_7_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
distinct_points(sK1,sK2),
inference(extension,[status(thm),parent(t8:2)],[f_13_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
apart_point_and_line(sK3,line_connecting(sK1,sK2)),
inference(lemma_extension,[status(thm),parent(t8:3)],[l2:1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK3,sK1))
| distinct_points(sK3,sK3)
| ~ distinct_points(sK3,sK1) ),
inference(extension,[status(thm),parent(t6:3)],[f_7_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
~ distinct_points(sK3,sK3),
inference(extension,[status(thm),parent(t14:2)],[f_1_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
$false,
inference(reduction,[status(thm),parent(t14:3)],[t14:3,t2:3]) ).
cnf(t19,plain,
( apart_point_and_line(sK3,line_connecting(sK3,sK2))
| ~ apart_point_and_line(sK3,line_connecting(sK1,sK2))
| distinct_lines(line_connecting(sK1,sK2),line_connecting(sK3,sK2)) ),
inference(extension,[status(thm),parent(t1:2)],[f_11_4]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t1:2]) ).
cnf(t21,plain,
apart_point_and_line(sK3,line_connecting(sK1,sK2)),
inference(extension,[status(thm),parent(t19:2)],[f_13_9]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(l10,lemma,
apart_point_and_line(sK3,line_connecting(sK1,sK2)),
inference(lemma,[status(cth),parent(t19:2),below(t1:2)],[t19:2]) ).
cnf(t23,plain,
( distinct_points(sK3,sK2)
| ~ distinct_points(sK3,sK2)
| ~ apart_point_and_line(sK3,line_connecting(sK3,sK2)) ),
inference(extension,[status(thm),parent(t19:3)],[f_7_5]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t19:3]) ).
cnf(t25,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK1,sK2))
| ~ distinct_points(sK1,sK2)
| distinct_points(sK3,sK2) ),
inference(extension,[status(thm),parent(t23:2)],[f_7_5]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
distinct_points(sK1,sK2),
inference(extension,[status(thm),parent(t25:2)],[f_13_8]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t25:2]) ).
cnf(t29,plain,
apart_point_and_line(sK3,line_connecting(sK1,sK2)),
inference(lemma_extension,[status(thm),parent(t25:3)],[l10:1]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t25:3]) ).
cnf(t31,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK3,sK2))
| distinct_points(sK3,sK3)
| ~ distinct_points(sK3,sK2) ),
inference(extension,[status(thm),parent(t23:3)],[f_7_4]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t23:3]) ).
cnf(t33,plain,
~ distinct_points(sK3,sK3),
inference(extension,[status(thm),parent(t31:2)],[f_1_3]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t31:2]) ).
cnf(t35,plain,
$false,
inference(reduction,[status(thm),parent(t31:3)],[t31:3,t19:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO179+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.59 % Computer : n004.cluster.edu
% 0.13/10.59 % Model : x86_64 x86_64
% 0.13/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.59 % Memory : 8046.5625MB
% 0.13/10.59 % OS : Linux 6.8.0-71-generic
% 0.13/10.59 % CPULimit : 300
% 0.13/10.59 % WCLimit : 300
% 0.13/10.59 % DateTime : Sat Sep 19 07:39:46 UTC 2026
% 0.15/10.60 % CPUTime :
% 0.15/10.76 % SZS status Theorem for theBenchmark
% 0.15/10.76 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------