%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO204+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 : Tue May 5 04:19:53 PM UTC 2026
% Result : Theorem 1.19s 1.64s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 11 unt; 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 predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
! [X45,X46,X47] :
( ~ distinct_points(X45,X46)
| distinct_points(X45,X47)
| distinct_points(X46,X47) ),
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,
! [X42] : ~ distinct_points(X42,X42),
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,
! [X62,X63,X64,X65] :
( ~ distinct_points(X62,X63)
| ~ distinct_lines(X64,X65)
| apart_point_and_line(X62,X64)
| apart_point_and_line(X62,X65)
| apart_point_and_line(X63,X64)
| apart_point_and_line(X63,X65) ),
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,
! [X56,X57] :
( ~ distinct_points(X56,X57)
| ~ apart_point_and_line(X57,line_connecting(X56,X57)) ),
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,
! [X66,X67,X68] :
( ~ apart_point_and_line(X66,X67)
| distinct_points(X66,X68)
| apart_point_and_line(X68,X67) ),
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,
! [X54,X55] :
( ~ distinct_points(X54,X55)
| ~ apart_point_and_line(X54,line_connecting(X54,X55)) ),
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
% 0.00/0.06 % Problem : GEO204+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 17:48:01 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.19/1.64 % Version : CSE_E---1.7
% 1.19/1.64 % Problem : theBenchmark.p
% 1.19/1.64 % SZS status Theorem for theBenchmark.p
% 1.19/1.64 % SZS output start CNFRefutation
% See solution above
% 1.19/1.64 % Total time : 1.361s
%------------------------------------------------------------------------------