%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO191+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n022.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 04:19:48 PM UTC 2026
% Result : Theorem 33.37s 20.17s
% Output : CNFRefutation 33.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 24 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 49 ~; 69 |; 9 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% 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 : 119 ( 6 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X4,X5] :
( ( convergent_lines(X1,X2)
& convergent_lines(X4,X5)
& ( apart_point_and_line(intersection_point(X1,X2),X4)
| apart_point_and_line(intersection_point(X1,X2),X5) ) )
=> ( apart_point_and_line(intersection_point(X4,X5),X1)
| apart_point_and_line(intersection_point(X4,X5),X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
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(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
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(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(cp2,axiom,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( convergent_lines(X1,X2)
& convergent_lines(X4,X5)
& ( apart_point_and_line(intersection_point(X1,X2),X4)
| apart_point_and_line(intersection_point(X1,X2),X5) ) )
=> ( apart_point_and_line(intersection_point(X4,X5),X1)
| apart_point_and_line(intersection_point(X4,X5),X2) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_14,plain,
! [X123,X124,X125] :
( ~ apart_point_and_line(X123,X124)
| distinct_lines(X124,X125)
| apart_point_and_line(X123,X125) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(c_0_15,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& convergent_lines(esk3_0,esk4_0)
& ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk4_0) )
& ~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0)
& ~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(c_0_17,plain,
! [X120,X121,X122] :
( ~ apart_point_and_line(X120,X121)
| distinct_points(X120,X122)
| apart_point_and_line(X122,X121) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
cnf(c_0_18,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X126,X127,X128] :
( ~ convergent_lines(X126,X127)
| distinct_lines(X127,X128)
| convergent_lines(X126,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(c_0_21,plain,
! [X114,X115] :
( ~ convergent_lines(X114,X115)
| ~ apart_point_and_line(intersection_point(X114,X115),X115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
cnf(c_0_22,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| distinct_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_25,plain,
! [X116,X117,X118,X119] :
( ~ distinct_points(X116,X117)
| ~ distinct_lines(X118,X119)
| apart_point_and_line(X116,X118)
| apart_point_and_line(X116,X119)
| apart_point_and_line(X117,X118)
| apart_point_and_line(X117,X119) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_26,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(X1,X2)
| distinct_lines(esk4_0,X2)
| distinct_points(intersection_point(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_30,plain,
! [X97] : ~ distinct_lines(X97,X97),
inference(variable_rename,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
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_25]) ).
cnf(c_0_33,negated_conjecture,
( convergent_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| distinct_lines(esk4_0,X1)
| distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(X2,X1))
| ~ convergent_lines(X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
convergent_lines(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_37,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_38,plain,
! [X112,X113] :
( ~ convergent_lines(X112,X113)
| ~ apart_point_and_line(intersection_point(X112,X113),X112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X2,esk2_0)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| convergent_lines(esk1_0,X3)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk3_0,esk4_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_42,plain,
! [X98] : ~ convergent_lines(X98,X98),
inference(variable_rename,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(intersection_point(esk3_0,esk4_0),X1)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| convergent_lines(esk1_0,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_45,negated_conjecture,
~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_46,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_47,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
cnf(c_0_48,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_27])]),c_0_45]),c_0_46]) ).
fof(c_0_49,plain,
! [X133,X134] : ~ apart_point_and_line(X133,parallel_through_point(X134,X133)),
inference(variable_rename,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_48]) ).
fof(c_0_51,plain,
! [X129,X130] :
( ~ distinct_lines(X129,X130)
| convergent_lines(X129,X130) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_52,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| distinct_lines(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_50]),c_0_27])]) ).
fof(c_0_54,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(c_0_55,plain,
! [X105,X106,X107] :
( ~ convergent_lines(X105,X106)
| convergent_lines(X105,X107)
| convergent_lines(X106,X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
cnf(c_0_56,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,negated_conjecture,
distinct_lines(esk3_0,parallel_through_point(X1,intersection_point(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_58,plain,
! [X131,X132] : ~ convergent_lines(parallel_through_point(X132,X131),X132),
inference(variable_rename,[status(thm)],[c_0_54]) ).
cnf(c_0_59,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,negated_conjecture,
convergent_lines(esk3_0,parallel_through_point(X1,intersection_point(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( convergent_lines(parallel_through_point(X1,intersection_point(esk1_0,esk2_0)),X2)
| convergent_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
convergent_lines(esk3_0,X1),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_46,c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO191+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n022.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 17:47:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 33.37/20.17 % Version : CSE_E---1.7
% 33.37/20.17 % Problem : theBenchmark.p
% 33.37/20.17 % SZS status Theorem for theBenchmark.p
% 33.37/20.17 % SZS output start CNFRefutation
% See solution above
% 33.55/20.30 % Total time : 14.395s
%------------------------------------------------------------------------------