TSTP Solution File: GEO187+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO187+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 22:46:50 EDT 2023
% Result : Theorem 0.21s 0.66s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 68 ( 16 unt; 10 typ; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 149 ( 49 ~; 76 |; 13 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn; 58 !; 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 ).
tff(decl_31,type,
esk4_0: $i ).
fof(con,conjecture,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_points(X4,X5)
& ~ apart_point_and_line(X1,line_connecting(X4,X5))
& ~ apart_point_and_line(X2,line_connecting(X4,X5)) )
=> ( ~ apart_point_and_line(X4,line_connecting(X1,X2))
& ~ apart_point_and_line(X5,line_connecting(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(ceq2,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
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/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(ci1,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_points(X4,X5)
& ~ apart_point_and_line(X1,line_connecting(X4,X5))
& ~ apart_point_and_line(X2,line_connecting(X4,X5)) )
=> ( ~ apart_point_and_line(X4,line_connecting(X1,X2))
& ~ apart_point_and_line(X5,line_connecting(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_11,plain,
! [X33,X34,X35] :
( ~ apart_point_and_line(X33,X34)
| distinct_lines(X34,X35)
| apart_point_and_line(X33,X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(c_0_12,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& distinct_points(esk3_0,esk4_0)
& ~ apart_point_and_line(esk1_0,line_connecting(esk3_0,esk4_0))
& ~ apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
& ( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_13,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_14,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_15,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_16,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X6] : ~ distinct_points(X6,X6),
inference(variable_rename,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,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_22,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_15]) ).
cnf(c_0_23,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X1)
| distinct_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,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_21])]) ).
cnf(c_0_27,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X3)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
distinct_points(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_29,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_30,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_32,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_29])]) ).
cnf(c_0_33,negated_conjecture,
~ apart_point_and_line(esk1_0,line_connecting(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_20])]) ).
cnf(c_0_35,negated_conjecture,
~ apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_36,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_37,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( apart_point_and_line(esk4_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
distinct_points(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_40,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_42,negated_conjecture,
( apart_point_and_line(esk2_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_40,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_42]),c_0_20])]) ).
fof(c_0_44,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_45,negated_conjecture,
( apart_point_and_line(X1,X2)
| distinct_lines(line_connecting(esk1_0,esk2_0),X2)
| distinct_points(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_43]) ).
fof(c_0_46,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_47,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(X1,X2))
| distinct_points(esk3_0,X1)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
fof(c_0_49,plain,
! [X7] : ~ distinct_lines(X7,X7),
inference(variable_rename,[status(thm)],[c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
| distinct_lines(line_connecting(X2,X3),X1)
| distinct_points(esk3_0,X2)
| ~ distinct_points(X2,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( distinct_lines(line_connecting(esk3_0,esk4_0),X1)
| distinct_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_39]),c_0_24]) ).
cnf(c_0_53,negated_conjecture,
distinct_lines(line_connecting(esk3_0,esk4_0),line_connecting(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X2,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_53]) ).
cnf(c_0_55,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_28]),c_0_35]),c_0_33]) ).
cnf(c_0_56,negated_conjecture,
apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_55]),c_0_20])]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_56]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO187+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 19:56:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.66 % Version : CSE_E---1.5
% 0.21/0.66 % Problem : theBenchmark.p
% 0.21/0.66 % Proof found
% 0.21/0.66 % SZS status Theorem for theBenchmark.p
% 0.21/0.66 % SZS output start Proof
% See solution above
% 0.21/0.67 % Total time : 0.075000 s
% 0.21/0.67 % SZS output end Proof
% 0.21/0.67 % Total time : 0.078000 s
%------------------------------------------------------------------------------