%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO177+2 : 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 : n031.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 04:19:42 PM UTC 2026
% Result : Theorem 4.35s 3.31s
% Output : CNFRefutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 12 unt; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 142 ( 31 ~; 92 |; 9 &)
% ( 0 <=>; 10 =>; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 6 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/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/GEO008+0.ax',apart4) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
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/sandbox/benchmark/Axioms/GEO008+0.ax',ceq2) ).
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(con1,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con1) ).
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/GEO008+0.ax',ceq1) ).
fof(c_0_7,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(assume_negation,[status(cth)],[con]) ).
fof(c_0_8,plain,
! [X43,X44,X45] :
( ~ distinct_points(X43,X44)
| distinct_points(X43,X45)
| distinct_points(X44,X45) ),
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(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_7])])]) ).
fof(c_0_10,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
cnf(c_0_11,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
distinct_points(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X40] : ~ distinct_points(X40,X40),
inference(variable_rename,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( distinct_points(esk3_0,X1)
| distinct_points(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
( distinct_points(esk3_0,X1)
| distinct_points(esk4_0,X2)
| distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
fof(c_0_17,plain,
! [X65,X66,X67] :
( ~ apart_point_and_line(X65,X66)
| distinct_lines(X66,X67)
| apart_point_and_line(X65,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
cnf(c_0_18,negated_conjecture,
( distinct_points(X1,esk4_0)
| distinct_points(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,plain,
! [X58,X59,X60,X61] :
( ~ distinct_points(X58,X59)
| ~ distinct_lines(X60,X61)
| apart_point_and_line(X58,X60)
| apart_point_and_line(X58,X61)
| apart_point_and_line(X59,X60)
| apart_point_and_line(X59,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_20,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( distinct_points(X1,esk4_0)
| distinct_points(esk3_0,X2)
| distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_23,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_19]) ).
cnf(c_0_24,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,X1)
| distinct_lines(line_connecting(esk3_0,esk4_0),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( distinct_points(X1,esk3_0)
| distinct_points(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
fof(c_0_26,plain,
! [X52,X53,X54] :
( ( distinct_points(X54,X52)
| ~ apart_point_and_line(X54,line_connecting(X52,X53))
| ~ distinct_points(X52,X53) )
& ( distinct_points(X54,X53)
| ~ apart_point_and_line(X54,line_connecting(X52,X53))
| ~ distinct_points(X52,X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])])]) ).
cnf(c_0_27,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(X1,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(X2,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,X3)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
distinct_points(esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_29,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X3,X2))
| ~ distinct_points(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_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,X1)
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X2,X3))
| ~ distinct_points(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_12])]),c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk1_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_12])]),c_0_15]) ).
fof(c_0_34,plain,
! [X62,X63,X64] :
( ~ apart_point_and_line(X62,X63)
| distinct_points(X62,X64)
| apart_point_and_line(X64,X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
cnf(c_0_35,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_0,line_connecting(X1,X2))
| apart_point_and_line(esk3_0,line_connecting(X1,X2))
| distinct_points(esk1_0,X1)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_37,negated_conjecture,
~ apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,negated_conjecture,
~ apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_39,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
apart_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]),c_0_15]) ).
cnf(c_0_41,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk3_0,esk4_0))
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( apart_point_and_line(X1,X2)
| distinct_lines(line_connecting(esk3_0,esk4_0),X2)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( distinct_lines(line_connecting(esk3_0,esk4_0),line_connecting(X1,X2))
| distinct_points(esk2_0,X3)
| distinct_points(X3,X2)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
( distinct_lines(line_connecting(esk3_0,esk4_0),line_connecting(esk1_0,esk2_0))
| distinct_points(X1,esk2_0)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_36]) ).
cnf(c_0_45,negated_conjecture,
( distinct_lines(line_connecting(esk3_0,esk4_0),line_connecting(esk1_0,esk2_0))
| distinct_points(esk2_0,X1)
| distinct_points(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_44]),c_0_11]) ).
cnf(c_0_46,negated_conjecture,
( distinct_lines(line_connecting(esk3_0,esk4_0),line_connecting(esk1_0,esk2_0))
| distinct_points(esk2_0,X1) ),
inference(ef,[status(thm)],[c_0_45]) ).
cnf(c_0_47,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(esk2_0,X3)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| apart_point_and_line(esk4_0,line_connecting(esk3_0,esk4_0))
| distinct_points(esk2_0,X1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_28]),c_0_37]),c_0_38]) ).
cnf(c_0_49,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk3_0,esk4_0))
| distinct_points(esk2_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_48]),c_0_12])]),c_0_15]) ).
cnf(c_0_50,negated_conjecture,
distinct_points(esk2_0,X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_49]),c_0_12])]),c_0_15]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_15,c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO177+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:47:38 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.35/3.31 % Version : CSE_E---1.7
% 4.35/3.31 % Problem : theBenchmark.p
% 4.35/3.31 % SZS status Theorem for theBenchmark.p
% 4.35/3.31 % SZS output start CNFRefutation
% See solution above
% 4.35/3.32 % Total time : 2.370s
%------------------------------------------------------------------------------