%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% 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 : n020.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 08:39:45 AM UTC 2026
% Result : Theorem 9.66s 10.02s
% Output : Proof 9.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 40 unt; 0 def)
% Number of atoms : 224 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 215 ( 85 ~; 78 |; 42 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 136 ( 4 sgn 94 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('GEO006+0.ax',apart1) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('GEO006+0.ax',apart4) ).
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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('GEO006+0.ax',ceq3) ).
fof(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('GEO006+3.ax',ooc1) ).
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('GEO006+4.ax',couo1) ).
fof(ax1,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('GEO006+6.ax',ax1) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('GEO006+6.ax',a4) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_points(X,intersection_point(U,V)) ),
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_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_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_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_21_1,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(fof_nnf,[status(thm)],[ooc1]) ).
fof(f_21_2,plain,
! [U_48,U_47] : ~ unorthogonal_lines(orthogonal_through_point(U_47,U_48),U_47),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
~ unorthogonal_lines(orthogonal_through_point(U_47,U_48),U_47),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_26_1,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[couo1]) ).
fof(f_26_2,plain,
! [U_62,U_61,U_60] :
( ~ convergent_lines(U_61,U_60)
| unorthogonal_lines(U_62,U_60)
| unorthogonal_lines(U_62,U_61) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ~ convergent_lines(U_61,U_60)
| unorthogonal_lines(U_62,U_60)
| unorthogonal_lines(U_62,U_61) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_31_1,plain,
! [X,Y] :
( ( equal_points(X,Y)
| distinct_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(fof_nnf,[status(thm)],[ax1]) ).
fof(f_31_2,plain,
! [U_72,U_71] :
( ( equal_points(U_72,U_71)
| distinct_points(U_72,U_71) )
& ( ~ distinct_points(U_72,U_71)
| ~ equal_points(U_72,U_71) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_76,U_74] :
( equal_points(U_76,U_74)
| distinct_points(U_76,U_74) )
& ! [U_75,U_73] :
( ~ distinct_points(U_75,U_73)
| ~ equal_points(U_75,U_73) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_5,plain,
( equal_points(U_76,U_74)
| distinct_points(U_76,U_74) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_34_1,plain,
! [X,Y] :
( ( incident_point_and_line(X,Y)
| apart_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a4]) ).
fof(f_34_2,plain,
! [U_90,U_89] :
( ( incident_point_and_line(U_90,U_89)
| apart_point_and_line(U_90,U_89) )
& ( ~ apart_point_and_line(U_90,U_89)
| ~ incident_point_and_line(U_90,U_89) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_94,U_92] :
( incident_point_and_line(U_94,U_92)
| apart_point_and_line(U_94,U_92) )
& ! [U_93,U_91] :
( ~ apart_point_and_line(U_93,U_91)
| ~ incident_point_and_line(U_93,U_91) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ apart_point_and_line(U_93,U_91)
| ~ incident_point_and_line(U_93,U_91) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_36_1,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_points(X,intersection_point(U,V)) ),
inference(negate,[status(cth)],[con]) ).
fof(f_36_2,negated_conjecture,
? [X,Y,U,V] :
( ~ equal_points(X,intersection_point(U,V))
& incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[f_36_1]) ).
fof(f_36_3,negated_conjecture,
? [U_104,U_103,U_102,U_101] :
( ~ equal_points(U_104,intersection_point(U_102,U_101))
& incident_point_and_line(U_104,U_101)
& incident_point_and_line(U_104,U_102)
& convergent_lines(U_102,U_101)
& distinct_points(U_104,U_103) ),
inference(variable_rename,[status(thm)],[f_36_2]) ).
fof(f_36_4,negated_conjecture,
? [U_103,U_102,U_101] :
( ~ equal_points(sK1,intersection_point(U_102,U_101))
& incident_point_and_line(sK1,U_101)
& incident_point_and_line(sK1,U_102)
& convergent_lines(U_102,U_101)
& distinct_points(sK1,U_103) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_104,sK1)],[f_36_3]) ).
fof(f_36_5,negated_conjecture,
? [U_102,U_101] :
( ~ equal_points(sK1,intersection_point(U_102,U_101))
& incident_point_and_line(sK1,U_101)
& incident_point_and_line(sK1,U_102)
& convergent_lines(U_102,U_101)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_103,sK2)],[f_36_4]) ).
fof(f_36_6,negated_conjecture,
? [U_101] :
( ~ equal_points(sK1,intersection_point(sK3,U_101))
& incident_point_and_line(sK1,U_101)
& incident_point_and_line(sK1,sK3)
& convergent_lines(sK3,U_101)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_102,sK3)],[f_36_5]) ).
fof(f_36_7,negated_conjecture,
( ~ equal_points(sK1,intersection_point(sK3,sK4))
& incident_point_and_line(sK1,sK4)
& incident_point_and_line(sK1,sK3)
& convergent_lines(sK3,sK4)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_101,sK4)],[f_36_6]) ).
fof(f_36_8,negated_conjecture,
( ~ equal_points(sK1,intersection_point(sK3,sK4))
& incident_point_and_line(sK1,sK4)
& incident_point_and_line(sK1,sK3)
& convergent_lines(sK3,sK4)
& distinct_points(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_36_7]) ).
cnf(f_36_10,negated_conjecture,
convergent_lines(sK3,sK4),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_11,negated_conjecture,
incident_point_and_line(sK1,sK3),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_12,negated_conjecture,
incident_point_and_line(sK1,sK4),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_13,negated_conjecture,
~ equal_points(sK1,intersection_point(sK3,sK4)),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(t1,plain,
( ~ apart_point_and_line(intersection_point(sK3,sK4),sK3)
| ~ convergent_lines(sK3,sK4) ),
inference(start,[status(thm),parent(0:0)],[f_9_3]) ).
cnf(t2,plain,
convergent_lines(sK3,sK4),
inference(extension,[status(thm),parent(t1:1)],[f_36_10]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(l1,lemma,
convergent_lines(sK3,sK4),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t4,plain,
( ~ distinct_lines(sK4,sK3)
| apart_point_and_line(intersection_point(sK3,sK4),sK4)
| apart_point_and_line(sK1,sK3)
| apart_point_and_line(sK1,sK4)
| ~ distinct_points(intersection_point(sK3,sK4),sK1)
| apart_point_and_line(intersection_point(sK3,sK4),sK3) ),
inference(extension,[status(thm),parent(t1:2)],[f_11_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
( distinct_points(sK1,sK1)
| ~ distinct_points(sK1,intersection_point(sK3,sK4))
| distinct_points(intersection_point(sK3,sK4),sK1) ),
inference(extension,[status(thm),parent(t4:2)],[f_4_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( equal_points(sK1,intersection_point(sK3,sK4))
| distinct_points(sK1,intersection_point(sK3,sK4)) ),
inference(extension,[status(thm),parent(t6:2)],[f_31_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
~ equal_points(sK1,intersection_point(sK3,sK4)),
inference(extension,[status(thm),parent(t8:2)],[f_36_13]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
~ distinct_points(sK1,sK1),
inference(extension,[status(thm),parent(t6:3)],[f_1_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:3]) ).
cnf(t14,plain,
( ~ incident_point_and_line(sK1,sK4)
| ~ apart_point_and_line(sK1,sK4) ),
inference(extension,[status(thm),parent(t4:3)],[f_34_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:3]) ).
cnf(t16,plain,
incident_point_and_line(sK1,sK4),
inference(extension,[status(thm),parent(t14:2)],[f_36_12]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ incident_point_and_line(sK1,sK3)
| ~ apart_point_and_line(sK1,sK3) ),
inference(extension,[status(thm),parent(t4:4)],[f_34_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:4]) ).
cnf(t20,plain,
incident_point_and_line(sK1,sK3),
inference(extension,[status(thm),parent(t18:2)],[f_36_11]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ convergent_lines(sK3,sK4)
| ~ apart_point_and_line(intersection_point(sK3,sK4),sK4) ),
inference(extension,[status(thm),parent(t4:5)],[f_10_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t4:5]) ).
cnf(t24,plain,
convergent_lines(sK3,sK4),
inference(lemma_extension,[status(thm),parent(t22:2)],[l1:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( convergent_lines(sK3,sK3)
| ~ convergent_lines(sK3,sK4)
| distinct_lines(sK4,sK3) ),
inference(extension,[status(thm),parent(t4:6)],[f_14_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t4:6]) ).
cnf(t28,plain,
convergent_lines(sK3,sK4),
inference(extension,[status(thm),parent(t26:2)],[f_36_10]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( unorthogonal_lines(orthogonal_through_point(sK3,U_679),sK3)
| unorthogonal_lines(orthogonal_through_point(sK3,U_679),sK3)
| ~ convergent_lines(sK3,sK3) ),
inference(extension,[status(thm),parent(t26:3)],[f_26_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
~ unorthogonal_lines(orthogonal_through_point(sK3,U_679),sK3),
inference(extension,[status(thm),parent(t30:2)],[f_21_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(l15,lemma,
~ unorthogonal_lines(orthogonal_through_point(sK3,U_679),sK3),
inference(lemma,[status(cth),parent(t30:2),below(t26:3)],[t30:2]) ).
cnf(t34,plain,
~ unorthogonal_lines(orthogonal_through_point(sK3,U_679),sK3),
inference(lemma_extension,[status(thm),parent(t30:3)],[l15:1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 07:41:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 9.66/10.02 % SZS status Theorem for theBenchmark
% 9.66/10.02 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------