TSTP Solution File: GEO172+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO172+2 : 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 : n024.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 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 55 ( 20 unt; 9 typ; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 47 ~; 45 |; 9 &)
% ( 0 <=>; 8 =>; 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 : 77 ( 0 sgn; 45 !; 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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(apart6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).
fof(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
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/GEO008+0.ax',cu1) ).
fof(con2,axiom,
! [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/Axioms/GEO008+0.ax',con2) ).
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,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_11,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)],[apart6])]) ).
fof(c_0_12,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_13,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])]) ).
fof(c_0_14,plain,
! [X34,X35] :
( ~ convergent_lines(X34,X35)
| distinct_lines(X34,X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(c_0_15,plain,
! [X8] : ~ convergent_lines(X8,X8),
inference(variable_rename,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_19,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_23,plain,
! [X7] : ~ distinct_lines(X7,X7),
inference(variable_rename,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
convergent_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_27,plain,
! [X24,X25,X26,X27] :
( ~ distinct_points(X24,X25)
| ~ distinct_lines(X26,X27)
| apart_point_and_line(X24,X26)
| apart_point_and_line(X24,X27)
| apart_point_and_line(X25,X26)
| apart_point_and_line(X25,X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_28,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( distinct_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_30,plain,
! [X6] : ~ distinct_points(X6,X6),
inference(variable_rename,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
! [X21,X22,X23] :
( ( ~ apart_point_and_line(X23,X21)
| distinct_points(X23,intersection_point(X21,X22))
| ~ convergent_lines(X21,X22) )
& ( ~ apart_point_and_line(X23,X22)
| distinct_points(X23,intersection_point(X21,X22))
| ~ convergent_lines(X21,X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
cnf(c_0_32,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_27]) ).
cnf(c_0_33,negated_conjecture,
distinct_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,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_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,negated_conjecture,
~ apart_point_and_line(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_39,negated_conjecture,
~ apart_point_and_line(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_40,plain,
( distinct_points(X1,intersection_point(X3,X2))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,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_36,c_0_37]),c_0_38]),c_0_39]) ).
cnf(c_0_43,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_44,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_41,c_0_42]),c_0_17])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : GEO172+2 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.07 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.26 % Computer : n024.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Aug 29 21:20:07 EDT 2023
% 0.07/0.26 % CPUTime :
% 0.10/0.40 start to proof: theBenchmark
% 0.10/0.42 % Version : CSE_E---1.5
% 0.10/0.42 % Problem : theBenchmark.p
% 0.10/0.42 % Proof found
% 0.10/0.42 % SZS status Theorem for theBenchmark.p
% 0.10/0.42 % SZS output start Proof
% See solution above
% 0.10/0.43 % Total time : 0.013000 s
% 0.10/0.43 % SZS output end Proof
% 0.10/0.43 % Total time : 0.016000 s
%------------------------------------------------------------------------------