TSTP Solution File: GEO172+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO172+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 22:46:39 EDT 2023
% Result : Theorem 0.49s 0.62s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 60 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 113 ( 42 ~; 53 |; 8 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 5 sgn; 50 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
distinct_points: ( $i * $i ) > $o ).
tff(decl_23,type,
distinct_lines: ( $i * $i ) > $o ).
tff(decl_24,type,
convergent_lines: ( $i * $i ) > $o ).
tff(decl_25,type,
line_connecting: ( $i * $i ) > $i ).
tff(decl_26,type,
apart_point_and_line: ( $i * $i ) > $o ).
tff(decl_27,type,
intersection_point: ( $i * $i ) > $i ).
tff(decl_28,type,
esk1_0: $i ).
tff(decl_29,type,
esk2_0: $i ).
tff(decl_30,type,
esk3_0: $i ).
fof(con,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ apart_point_and_line(X3,X1)
& ~ apart_point_and_line(X3,X2) )
=> ~ distinct_points(X3,intersection_point(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(cu1,axiom,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_lines(X4,X5) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X5)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X2,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ apart_point_and_line(X3,X1)
& ~ apart_point_and_line(X3,X2) )
=> ~ distinct_points(X3,intersection_point(X1,X2)) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_10,plain,
! [X15,X16,X17] :
( ~ convergent_lines(X15,X16)
| convergent_lines(X15,X17)
| convergent_lines(X16,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(c_0_11,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ apart_point_and_line(esk3_0,esk1_0)
& ~ apart_point_and_line(esk3_0,esk2_0)
& distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_12,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_13,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X8] : ~ convergent_lines(X8,X8),
inference(variable_rename,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk1_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_20,plain,
! [X36,X37,X38] :
( ~ convergent_lines(X36,X37)
| distinct_lines(X37,X38)
| convergent_lines(X36,X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_21,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(esk2_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_22,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
fof(c_0_24,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_25,plain,
! [X12,X13,X14] :
( ~ distinct_lines(X12,X13)
| distinct_lines(X12,X14)
| distinct_lines(X13,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
cnf(c_0_26,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,X2)
| distinct_lines(esk1_0,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X7] : ~ distinct_lines(X7,X7),
inference(variable_rename,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( convergent_lines(X1,esk2_0)
| distinct_lines(esk1_0,esk2_0) ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( convergent_lines(X1,esk2_0)
| distinct_lines(esk1_0,X2)
| distinct_lines(esk2_0,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( convergent_lines(X1,esk2_0)
| distinct_lines(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( convergent_lines(X1,X2)
| distinct_lines(esk2_0,esk1_0)
| distinct_lines(esk2_0,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
fof(c_0_34,plain,
! [X26,X27,X28,X29] :
( ~ distinct_points(X26,X27)
| ~ distinct_lines(X28,X29)
| apart_point_and_line(X26,X28)
| apart_point_and_line(X26,X29)
| apart_point_and_line(X27,X28)
| apart_point_and_line(X27,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_35,negated_conjecture,
( distinct_lines(esk2_0,esk1_0)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
fof(c_0_36,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
cnf(c_0_37,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X4)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X4)
| ~ distinct_points(X1,X2)
| ~ distinct_lines(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
distinct_lines(esk2_0,esk1_0),
inference(ef,[status(thm)],[c_0_35]) ).
fof(c_0_39,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(c_0_40,plain,
! [X22,X23] :
( ~ convergent_lines(X22,X23)
| ~ apart_point_and_line(intersection_point(X22,X23),X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
cnf(c_0_41,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X2,esk2_0)
| apart_point_and_line(X2,esk1_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_43,negated_conjecture,
~ apart_point_and_line(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_44,negated_conjecture,
~ apart_point_and_line(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_45,plain,
! [X24,X25] :
( ~ convergent_lines(X24,X25)
| ~ apart_point_and_line(intersection_point(X24,X25),X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
cnf(c_0_46,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_14])]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO172+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 20:46:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.22/0.59 start to proof: theBenchmark
% 0.49/0.62 % Version : CSE_E---1.5
% 0.49/0.62 % Problem : theBenchmark.p
% 0.49/0.62 % Proof found
% 0.49/0.62 % SZS status Theorem for theBenchmark.p
% 0.49/0.62 % SZS output start Proof
% See solution above
% 0.49/0.62 % Total time : 0.018000 s
% 0.49/0.62 % SZS output end Proof
% 0.49/0.62 % Total time : 0.021000 s
%------------------------------------------------------------------------------