%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO191+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:39:47 AM UTC 2026
% Result : Theorem 1.89s 2.31s
% Output : Proof 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 137 ( 72 unt; 0 def)
% Number of atoms : 298 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 266 ( 105 ~; 118 |; 33 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 101 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('GEO006+0.ax',apart1) ).
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('GEO006+0.ax',apart2) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('GEO006+0.ax',apart3) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('GEO006+0.ax',apart4) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('GEO006+0.ax',apart5) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('GEO006+0.ax',ci3) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('GEO006+0.ax',ci4) ).
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('GEO006+0.ax',cu1) ).
fof(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('GEO006+0.ax',ceq1) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('GEO006+0.ax',ceq2) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('GEO006+0.ax',ceq3) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( ( apart_point_and_line(intersection_point(X,Y),V)
| apart_point_and_line(intersection_point(X,Y),U) )
& convergent_lines(U,V)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(U,V),Y)
| apart_point_and_line(intersection_point(U,V),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_2_1,plain,
! [X] : ~ distinct_lines(X,X),
inference(fof_nnf,[status(thm)],[apart2]) ).
fof(f_2_2,plain,
! [U_1] : ~ distinct_lines(U_1,U_1),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
~ distinct_lines(U_1,U_1),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [X] : ~ convergent_lines(X,X),
inference(fof_nnf,[status(thm)],[apart3]) ).
fof(f_3_2,plain,
! [U_2] : ~ convergent_lines(U_2,U_2),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
~ convergent_lines(U_2,U_2),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[apart4]) ).
fof(f_4_2,plain,
! [U_5,U_4,U_3] :
( distinct_points(U_4,U_3)
| distinct_points(U_5,U_3)
| ~ distinct_points(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_4] :
( ! [U_3] :
( distinct_points(U_4,U_3)
| distinct_points(U_5,U_3) )
| ~ distinct_points(U_5,U_4) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( distinct_points(U_4,U_3)
| distinct_points(U_5,U_3)
| ~ distinct_points(U_5,U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[apart5]) ).
fof(f_5_2,plain,
! [U_8,U_7,U_6] :
( distinct_lines(U_7,U_6)
| distinct_lines(U_8,U_6)
| ~ distinct_lines(U_8,U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_8,U_7] :
( ! [U_6] :
( distinct_lines(U_7,U_6)
| distinct_lines(U_8,U_6) )
| ~ distinct_lines(U_8,U_7) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( distinct_lines(U_7,U_6)
| distinct_lines(U_8,U_6)
| ~ distinct_lines(U_8,U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_9_1,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[ci3]) ).
fof(f_9_2,plain,
! [U_17,U_16] :
( ~ apart_point_and_line(intersection_point(U_17,U_16),U_17)
| ~ convergent_lines(U_17,U_16) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ~ apart_point_and_line(intersection_point(U_17,U_16),U_17)
| ~ convergent_lines(U_17,U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[ci4]) ).
fof(f_10_2,plain,
! [U_19,U_18] :
( ~ apart_point_and_line(intersection_point(U_19,U_18),U_18)
| ~ convergent_lines(U_19,U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ~ apart_point_and_line(intersection_point(U_19,U_18),U_18)
| ~ convergent_lines(U_19,U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[cu1]) ).
fof(f_11_2,plain,
! [U_23,U_22,U_21,U_20] :
( apart_point_and_line(U_22,U_20)
| apart_point_and_line(U_22,U_21)
| apart_point_and_line(U_23,U_20)
| apart_point_and_line(U_23,U_21)
| ~ distinct_lines(U_21,U_20)
| ~ distinct_points(U_23,U_22) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( apart_point_and_line(U_22,U_20)
| apart_point_and_line(U_22,U_21)
| apart_point_and_line(U_23,U_20)
| apart_point_and_line(U_23,U_21)
| ~ distinct_lines(U_21,U_20)
| ~ distinct_points(U_23,U_22) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(fof_nnf,[status(thm)],[ceq1]) ).
fof(f_12_2,plain,
! [U_26,U_25,U_24] :
( apart_point_and_line(U_24,U_25)
| distinct_points(U_26,U_24)
| ~ apart_point_and_line(U_26,U_25) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_26,U_25] :
( ! [U_24] :
( apart_point_and_line(U_24,U_25)
| distinct_points(U_26,U_24) )
| ~ apart_point_and_line(U_26,U_25) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( apart_point_and_line(U_24,U_25)
| distinct_points(U_26,U_24)
| ~ apart_point_and_line(U_26,U_25) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_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_13_2,plain,
! [U_29,U_28,U_27] :
( apart_point_and_line(U_29,U_27)
| distinct_lines(U_28,U_27)
| ~ apart_point_and_line(U_29,U_28) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_29,U_28] :
( ! [U_27] :
( apart_point_and_line(U_29,U_27)
| distinct_lines(U_28,U_27) )
| ~ apart_point_and_line(U_29,U_28) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( apart_point_and_line(U_29,U_27)
| distinct_lines(U_28,U_27)
| ~ apart_point_and_line(U_29,U_28) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[ceq3]) ).
fof(f_14_2,plain,
! [U_32,U_31,U_30] :
( convergent_lines(U_32,U_30)
| distinct_lines(U_31,U_30)
| ~ convergent_lines(U_32,U_31) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_32,U_31] :
( ! [U_30] :
( convergent_lines(U_32,U_30)
| distinct_lines(U_31,U_30) )
| ~ convergent_lines(U_32,U_31) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( convergent_lines(U_32,U_30)
| distinct_lines(U_31,U_30)
| ~ convergent_lines(U_32,U_31) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ( apart_point_and_line(intersection_point(X,Y),V)
| apart_point_and_line(intersection_point(X,Y),U) )
& convergent_lines(U,V)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(U,V),Y)
| apart_point_and_line(intersection_point(U,V),X) ) ),
inference(negate,[status(cth)],[con]) ).
fof(f_15_2,negated_conjecture,
? [X,Y,U,V] :
( ~ apart_point_and_line(intersection_point(U,V),Y)
& ~ apart_point_and_line(intersection_point(U,V),X)
& ( apart_point_and_line(intersection_point(X,Y),V)
| apart_point_and_line(intersection_point(X,Y),U) )
& convergent_lines(U,V)
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[f_15_1]) ).
fof(f_15_3,negated_conjecture,
? [U_36,U_35,U_34,U_33] :
( ~ apart_point_and_line(intersection_point(U_34,U_33),U_35)
& ~ apart_point_and_line(intersection_point(U_34,U_33),U_36)
& ( apart_point_and_line(intersection_point(U_36,U_35),U_33)
| apart_point_and_line(intersection_point(U_36,U_35),U_34) )
& convergent_lines(U_34,U_33)
& convergent_lines(U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_15_2]) ).
fof(f_15_4,negated_conjecture,
? [U_35,U_34,U_33] :
( ~ apart_point_and_line(intersection_point(U_34,U_33),U_35)
& ~ apart_point_and_line(intersection_point(U_34,U_33),sK1)
& ( apart_point_and_line(intersection_point(sK1,U_35),U_33)
| apart_point_and_line(intersection_point(sK1,U_35),U_34) )
& convergent_lines(U_34,U_33)
& convergent_lines(sK1,U_35) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_36,sK1)],[f_15_3]) ).
fof(f_15_5,negated_conjecture,
? [U_34,U_33] :
( ~ apart_point_and_line(intersection_point(U_34,U_33),sK2)
& ~ apart_point_and_line(intersection_point(U_34,U_33),sK1)
& ( apart_point_and_line(intersection_point(sK1,sK2),U_33)
| apart_point_and_line(intersection_point(sK1,sK2),U_34) )
& convergent_lines(U_34,U_33)
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_35,sK2)],[f_15_4]) ).
fof(f_15_6,negated_conjecture,
? [U_33] :
( ~ apart_point_and_line(intersection_point(sK3,U_33),sK2)
& ~ apart_point_and_line(intersection_point(sK3,U_33),sK1)
& ( apart_point_and_line(intersection_point(sK1,sK2),U_33)
| apart_point_and_line(intersection_point(sK1,sK2),sK3) )
& convergent_lines(sK3,U_33)
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3)],[f_15_5]) ).
fof(f_15_7,negated_conjecture,
( ~ apart_point_and_line(intersection_point(sK3,sK4),sK2)
& ~ apart_point_and_line(intersection_point(sK3,sK4),sK1)
& ( apart_point_and_line(intersection_point(sK1,sK2),sK4)
| apart_point_and_line(intersection_point(sK1,sK2),sK3) )
& convergent_lines(sK3,sK4)
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4)],[f_15_6]) ).
fof(f_15_8,negated_conjecture,
( ~ apart_point_and_line(intersection_point(sK3,sK4),sK2)
& ~ apart_point_and_line(intersection_point(sK3,sK4),sK1)
& ( apart_point_and_line(intersection_point(sK1,sK2),sK4)
| apart_point_and_line(intersection_point(sK1,sK2),sK3) )
& convergent_lines(sK3,sK4)
& convergent_lines(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_15_7]) ).
cnf(f_15_9,negated_conjecture,
convergent_lines(sK1,sK2),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_10,negated_conjecture,
convergent_lines(sK3,sK4),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_11,negated_conjecture,
( apart_point_and_line(intersection_point(sK1,sK2),sK4)
| apart_point_and_line(intersection_point(sK1,sK2),sK3) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_12,negated_conjecture,
~ apart_point_and_line(intersection_point(sK3,sK4),sK1),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_13,negated_conjecture,
~ apart_point_and_line(intersection_point(sK3,sK4),sK2),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(t1,plain,
~ distinct_points(intersection_point(sK3,sK4),intersection_point(sK3,sK4)),
inference(start,[status(thm),parent(0:0)],[f_1_3]) ).
cnf(t2,plain,
( distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK4))
| ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK4))
| distinct_points(intersection_point(sK3,sK4),intersection_point(sK3,sK4)) ),
inference(extension,[status(thm),parent(t1:1)],[f_4_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( apart_point_and_line(intersection_point(sK3,sK4),sK4)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK4)
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK4)) ),
inference(extension,[status(thm),parent(t2:2)],[f_12_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( apart_point_and_line(intersection_point(sK1,sK2),sK3)
| apart_point_and_line(intersection_point(sK1,sK2),sK4) ),
inference(extension,[status(thm),parent(t4:2)],[f_15_11]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK4))
| apart_point_and_line(intersection_point(sK3,sK4),sK3)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK3) ),
inference(extension,[status(thm),parent(t6:2)],[f_12_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ convergent_lines(sK3,sK4)
| ~ apart_point_and_line(intersection_point(sK3,sK4),sK3) ),
inference(extension,[status(thm),parent(t8:2)],[f_9_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
convergent_lines(sK3,sK4),
inference(extension,[status(thm),parent(t10:2)],[f_15_10]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
$false,
inference(reduction,[status(thm),parent(t8:3)],[t8:3,t2:2]) ).
cnf(t15,plain,
( distinct_points(intersection_point(sK3,sK4),intersection_point(sK1,sK2))
| apart_point_and_line(intersection_point(sK1,sK2),sK4)
| ~ apart_point_and_line(intersection_point(sK3,sK4),sK4) ),
inference(extension,[status(thm),parent(t4:3)],[f_12_4]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t4:3]) ).
cnf(t17,plain,
( distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK4))
| apart_point_and_line(intersection_point(sK3,sK4),sK4)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK4) ),
inference(extension,[status(thm),parent(t15:2)],[f_12_4]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
( ~ convergent_lines(sK3,sK4)
| ~ apart_point_and_line(intersection_point(sK3,sK4),sK4) ),
inference(extension,[status(thm),parent(t17:2)],[f_10_3]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
convergent_lines(sK3,sK4),
inference(extension,[status(thm),parent(t19:2)],[f_15_10]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
$false,
inference(reduction,[status(thm),parent(t17:3)],[t17:3,t2:2]) ).
cnf(t24,plain,
( distinct_points(intersection_point(sK3,sK4),intersection_point(sK3,sK4))
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK4))
| ~ distinct_points(intersection_point(sK3,sK4),intersection_point(sK1,sK2)) ),
inference(extension,[status(thm),parent(t15:3)],[f_4_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t15:3]) ).
cnf(t26,plain,
$false,
inference(reduction,[status(thm),parent(t24:2)],[t24:2,t2:2]) ).
cnf(t27,plain,
$false,
inference(reduction,[status(thm),parent(t24:3)],[t24:3,t1:1]) ).
cnf(t28,plain,
( ~ distinct_lines(sK2,sK2)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| apart_point_and_line(intersection_point(sK3,sK4),sK2)
| apart_point_and_line(intersection_point(sK3,sK4),sK2)
| ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK4)) ),
inference(extension,[status(thm),parent(t2:3)],[f_11_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t2:3]) ).
cnf(t30,plain,
~ apart_point_and_line(intersection_point(sK3,sK4),sK2),
inference(extension,[status(thm),parent(t28:2)],[f_15_13]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
~ apart_point_and_line(intersection_point(sK3,sK4),sK2),
inference(extension,[status(thm),parent(t28:3)],[f_15_13]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(l18,lemma,
~ apart_point_and_line(intersection_point(sK3,sK4),sK2),
inference(lemma,[status(cth),parent(t28:3),below(t2:3)],[t28:3]) ).
cnf(t34,plain,
( distinct_lines(sK2,sK2)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK2) ),
inference(extension,[status(thm),parent(t28:4)],[f_13_4]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:4]) ).
cnf(t36,plain,
( distinct_lines(sK2,sK2)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK2) ),
inference(extension,[status(thm),parent(t34:2)],[f_13_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK2) ),
inference(extension,[status(thm),parent(t36:2)],[f_10_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
convergent_lines(sK1,sK2),
inference(extension,[status(thm),parent(t38:2)],[f_15_9]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
~ distinct_lines(sK2,sK2),
inference(extension,[status(thm),parent(t36:3)],[f_2_3]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t36:3]) ).
cnf(t44,plain,
~ distinct_lines(sK2,sK2),
inference(extension,[status(thm),parent(t34:3)],[f_2_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t34:3]) ).
cnf(l19,lemma,
~ apart_point_and_line(intersection_point(sK1,sK2),sK2),
inference(lemma,[status(cth),parent(t28:4),below(t2:3)],[t28:4]) ).
cnf(t46,plain,
~ apart_point_and_line(intersection_point(sK1,sK2),sK2),
inference(lemma_extension,[status(thm),parent(t28:5)],[l19:1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t28:5]) ).
cnf(t48,plain,
( distinct_lines(sK1,sK2)
| ~ distinct_lines(sK2,sK1)
| distinct_lines(sK2,sK2) ),
inference(extension,[status(thm),parent(t28:6)],[f_5_4]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t28:6]) ).
cnf(t50,plain,
( convergent_lines(sK1,sK1)
| ~ convergent_lines(sK1,sK2)
| distinct_lines(sK2,sK1) ),
inference(extension,[status(thm),parent(t48:2)],[f_14_4]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
convergent_lines(sK1,sK2),
inference(extension,[status(thm),parent(t50:2)],[f_15_9]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
( distinct_lines(sK1,sK1)
| convergent_lines(sK1,sK1)
| ~ convergent_lines(sK1,sK1) ),
inference(extension,[status(thm),parent(t50:3)],[f_14_4]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
cnf(t56,plain,
~ convergent_lines(sK1,sK1),
inference(extension,[status(thm),parent(t54:2)],[f_3_3]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
~ distinct_lines(sK1,sK1),
inference(extension,[status(thm),parent(t54:3)],[f_2_3]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
( apart_point_and_line(intersection_point(sK3,sK4),sK2)
| apart_point_and_line(intersection_point(sK1,sK2),sK1)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| apart_point_and_line(intersection_point(sK3,sK4),sK1)
| ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK4))
| ~ distinct_lines(sK1,sK2) ),
inference(extension,[status(thm),parent(t48:3)],[f_11_3]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t48:3]) ).
cnf(t62,plain,
$false,
inference(reduction,[status(thm),parent(t60:2)],[t60:2,t2:3]) ).
cnf(t63,plain,
~ apart_point_and_line(intersection_point(sK3,sK4),sK1),
inference(extension,[status(thm),parent(t60:3)],[f_15_12]) ).
cnf(t64,plain,
$false,
inference(connection,[status(thm),parent(t63:1)],[t63:1,t60:3]) ).
cnf(t65,plain,
~ apart_point_and_line(intersection_point(sK1,sK2),sK2),
inference(lemma_extension,[status(thm),parent(t60:4)],[l19:1]) ).
cnf(t66,plain,
$false,
inference(connection,[status(thm),parent(t65:1)],[t65:1,t60:4]) ).
cnf(t67,plain,
( ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK1) ),
inference(extension,[status(thm),parent(t60:5)],[f_9_3]) ).
cnf(t68,plain,
$false,
inference(connection,[status(thm),parent(t67:1)],[t67:1,t60:5]) ).
cnf(t69,plain,
convergent_lines(sK1,sK2),
inference(extension,[status(thm),parent(t67:2)],[f_15_9]) ).
cnf(t70,plain,
$false,
inference(connection,[status(thm),parent(t69:1)],[t69:1,t67:2]) ).
cnf(t71,plain,
~ apart_point_and_line(intersection_point(sK3,sK4),sK2),
inference(lemma_extension,[status(thm),parent(t60:6)],[l18:1]) ).
cnf(t72,plain,
$false,
inference(connection,[status(thm),parent(t71:1)],[t71:1,t60:6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO191+1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n008.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Sat Sep 19 07:41:10 UTC 2026
% 0.09/0.53 % CPUTime :
% 1.89/2.31 % SZS status Theorem for theBenchmark
% 1.89/2.31 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------