%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% 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 08:39:55 AM UTC 2026
% Result : Theorem 1.88s 12.16s
% Output : Proof 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 24 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 129 ( 53 ~; 47 |; 23 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 2 sgn 64 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('GEO006+3.ax',ooc1) ).
fof(ooc2,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('GEO006+3.ax',ooc2) ).
fof(ouo1,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('GEO006+3.ax',ouo1) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('GEO006+6.ax',ax2) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('GEO006+6.ax',a4) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('GEO006+6.ax',a5) ).
fof(con,conjecture,
! [A,L,M] :
( ( orthogonal_lines(L,M)
& incident_point_and_line(A,L) )
=> equal_lines(L,orthogonal_through_point(M,A)) ),
file('theBenchmark.p',con) ).
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_22_1,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(fof_nnf,[status(thm)],[ooc2]) ).
fof(f_22_2,plain,
! [U_50,U_49] : ~ apart_point_and_line(U_50,orthogonal_through_point(U_49,U_50)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
~ apart_point_and_line(U_50,orthogonal_through_point(U_49,U_50)),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ouo1]) ).
fof(f_23_2,plain,
! [U_54,U_53,U_52,U_51] :
( unorthogonal_lines(U_52,U_51)
| unorthogonal_lines(U_53,U_51)
| apart_point_and_line(U_54,U_52)
| apart_point_and_line(U_54,U_53)
| ~ distinct_lines(U_53,U_52) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_54,U_53,U_52] :
( ! [U_51] :
( unorthogonal_lines(U_52,U_51)
| unorthogonal_lines(U_53,U_51) )
| apart_point_and_line(U_54,U_52)
| apart_point_and_line(U_54,U_53)
| ~ distinct_lines(U_53,U_52) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( unorthogonal_lines(U_52,U_51)
| unorthogonal_lines(U_53,U_51)
| apart_point_and_line(U_54,U_52)
| apart_point_and_line(U_54,U_53)
| ~ distinct_lines(U_53,U_52) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_32_1,plain,
! [X,Y] :
( ( equal_lines(X,Y)
| distinct_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[ax2]) ).
fof(f_32_2,plain,
! [U_78,U_77] :
( ( equal_lines(U_78,U_77)
| distinct_lines(U_78,U_77) )
& ( ~ distinct_lines(U_78,U_77)
| ~ equal_lines(U_78,U_77) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_82,U_80] :
( equal_lines(U_82,U_80)
| distinct_lines(U_82,U_80) )
& ! [U_81,U_79] :
( ~ distinct_lines(U_81,U_79)
| ~ equal_lines(U_81,U_79) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_5,plain,
( equal_lines(U_82,U_80)
| distinct_lines(U_82,U_80) ),
inference(clausify,[status(thm)],[f_32_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_35_1,plain,
! [X,Y] :
( ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a5]) ).
fof(f_35_2,plain,
! [U_96,U_95] :
( ( orthogonal_lines(U_96,U_95)
| unorthogonal_lines(U_96,U_95) )
& ( ~ unorthogonal_lines(U_96,U_95)
| ~ orthogonal_lines(U_96,U_95) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_100,U_98] :
( orthogonal_lines(U_100,U_98)
| unorthogonal_lines(U_100,U_98) )
& ! [U_99,U_97] :
( ~ unorthogonal_lines(U_99,U_97)
| ~ orthogonal_lines(U_99,U_97) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( ~ unorthogonal_lines(U_99,U_97)
| ~ orthogonal_lines(U_99,U_97) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,negated_conjecture,
~ ! [A,L,M] :
( ( orthogonal_lines(L,M)
& incident_point_and_line(A,L) )
=> equal_lines(L,orthogonal_through_point(M,A)) ),
inference(negate,[status(cth)],[con]) ).
fof(f_36_2,negated_conjecture,
? [A,L,M] :
( ~ equal_lines(L,orthogonal_through_point(M,A))
& orthogonal_lines(L,M)
& incident_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[f_36_1]) ).
fof(f_36_3,negated_conjecture,
? [U_103,U_102,U_101] :
( ~ equal_lines(U_102,orthogonal_through_point(U_101,U_103))
& orthogonal_lines(U_102,U_101)
& incident_point_and_line(U_103,U_102) ),
inference(variable_rename,[status(thm)],[f_36_2]) ).
fof(f_36_4,negated_conjecture,
? [U_102,U_101] :
( ~ equal_lines(U_102,orthogonal_through_point(U_101,sK1))
& orthogonal_lines(U_102,U_101)
& incident_point_and_line(sK1,U_102) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_103,sK1)],[f_36_3]) ).
fof(f_36_5,negated_conjecture,
? [U_101] :
( ~ equal_lines(sK2,orthogonal_through_point(U_101,sK1))
& orthogonal_lines(sK2,U_101)
& incident_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_102,sK2)],[f_36_4]) ).
fof(f_36_6,negated_conjecture,
( ~ equal_lines(sK2,orthogonal_through_point(sK3,sK1))
& orthogonal_lines(sK2,sK3)
& incident_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_101,sK3)],[f_36_5]) ).
fof(f_36_7,negated_conjecture,
( ~ equal_lines(sK2,orthogonal_through_point(sK3,sK1))
& orthogonal_lines(sK2,sK3)
& incident_point_and_line(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_36_6]) ).
cnf(f_36_8,negated_conjecture,
incident_point_and_line(sK1,sK2),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_9,negated_conjecture,
orthogonal_lines(sK2,sK3),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_10,negated_conjecture,
~ equal_lines(sK2,orthogonal_through_point(sK3,sK1)),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(t1,plain,
~ unorthogonal_lines(orthogonal_through_point(sK3,sK1),sK3),
inference(start,[status(thm),parent(0:0)],[f_21_3]) ).
cnf(t2,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK1,orthogonal_through_point(sK3,sK1))
| unorthogonal_lines(sK2,sK3)
| ~ distinct_lines(sK2,orthogonal_through_point(sK3,sK1))
| unorthogonal_lines(orthogonal_through_point(sK3,sK1),sK3) ),
inference(extension,[status(thm),parent(t1:1)],[f_23_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( equal_lines(sK2,orthogonal_through_point(sK3,sK1))
| distinct_lines(sK2,orthogonal_through_point(sK3,sK1)) ),
inference(extension,[status(thm),parent(t2:2)],[f_32_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ equal_lines(sK2,orthogonal_through_point(sK3,sK1)),
inference(extension,[status(thm),parent(t4:2)],[f_36_10]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ orthogonal_lines(sK2,sK3)
| ~ unorthogonal_lines(sK2,sK3) ),
inference(extension,[status(thm),parent(t2:3)],[f_35_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
orthogonal_lines(sK2,sK3),
inference(extension,[status(thm),parent(t8:2)],[f_36_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(sK3,sK1)),
inference(extension,[status(thm),parent(t2:4)],[f_22_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
( ~ incident_point_and_line(sK1,sK2)
| ~ apart_point_and_line(sK1,sK2) ),
inference(extension,[status(thm),parent(t2:5)],[f_34_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:5]) ).
cnf(t16,plain,
incident_point_and_line(sK1,sK2),
inference(extension,[status(thm),parent(t14:2)],[f_36_8]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO210+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n004.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Sat Sep 19 07:41:31 UTC 2026
% 0.10/10.37 % CPUTime :
% 1.88/12.16 % SZS status Theorem for theBenchmark
% 1.88/12.16 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------