TSTP Solution File: GEO204+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO204+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 : n001.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 22:47:02 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 53 ( 11 unt; 9 typ; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 34 ~; 52 |; 7 &)
% ( 0 <=>; 9 =>; 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 : 67 ( 0 sgn; 41 !; 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] :
( ( distinct_points(X1,X2)
& ~ distinct_points(X2,X3) )
=> ( distinct_points(X1,X3)
& ~ distinct_lines(line_connecting(X1,X2),line_connecting(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+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/GEO006+0.ax',cu1) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(ceq1,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_points(X1,X3)
| apart_point_and_line(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(ci1,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( distinct_points(X1,X2)
& ~ distinct_points(X2,X3) )
=> ( distinct_points(X1,X3)
& ~ distinct_lines(line_connecting(X1,X2),line_connecting(X1,X3)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_8,plain,
! [X9,X10,X11] :
( ~ distinct_points(X9,X10)
| distinct_points(X9,X11)
| distinct_points(X10,X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(c_0_9,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& ~ distinct_points(esk2_0,esk3_0)
& ( ~ distinct_points(esk1_0,esk3_0)
| distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_10,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_13,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
cnf(c_0_14,negated_conjecture,
~ distinct_points(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk2_0,X2)
| distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
fof(c_0_16,plain,
! [X6] : ~ distinct_points(X6,X6),
inference(variable_rename,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( distinct_points(X1,esk3_0)
| distinct_points(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,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_19,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))
| ~ distinct_points(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
distinct_points(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_21,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( distinct_points(X1,esk3_0)
| distinct_points(esk1_0,X2)
| distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
fof(c_0_23,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
cnf(c_0_24,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_18]) ).
cnf(c_0_25,negated_conjecture,
distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_26,negated_conjecture,
( distinct_points(X1,esk1_0)
| distinct_points(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_27,plain,
! [X20,X21] :
( ~ distinct_points(X20,X21)
| ~ apart_point_and_line(X21,line_connecting(X20,X21)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk3_0))
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
distinct_points(esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
fof(c_0_30,plain,
! [X30,X31,X32] :
( ~ apart_point_and_line(X30,X31)
| distinct_points(X30,X32)
| apart_point_and_line(X32,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
cnf(c_0_31,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci1]) ).
cnf(c_0_34,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20])]) ).
fof(c_0_36,plain,
! [X18,X19] :
( ~ distinct_points(X18,X19)
| ~ apart_point_and_line(X18,line_connecting(X18,X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_37,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| distinct_points(esk3_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_37]),c_0_11])]) ).
cnf(c_0_40,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_20])]) ).
cnf(c_0_41,negated_conjecture,
distinct_points(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_40]),c_0_11])]) ).
cnf(c_0_42,negated_conjecture,
( distinct_points(esk3_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_42]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEO204+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.35 % Computer : n001.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Aug 29 22:46:38 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.61 % Version : CSE_E---1.5
% 0.19/0.61 % Problem : theBenchmark.p
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark.p
% 0.19/0.61 % SZS output start Proof
% See solution above
% 0.19/0.62 % Total time : 0.032000 s
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time : 0.035000 s
%------------------------------------------------------------------------------