%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO173+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 : n026.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 04:19:40 PM UTC 2026
% Result : Theorem 2.13s 1.98s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 30 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 42 ~; 71 |; 9 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 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 : 129 ( 14 sgn 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& convergent_lines(X4,X5)
& distinct_lines(X4,line_connecting(X1,X2)) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
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(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
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(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
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(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(c_0_13,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& convergent_lines(X4,X5)
& distinct_lines(X4,line_connecting(X1,X2)) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X2,X4) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_14,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_15,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& convergent_lines(esk3_0,esk4_0)
& distinct_lines(esk3_0,line_connecting(esk1_0,esk2_0))
& ~ apart_point_and_line(esk1_0,esk3_0)
& ~ apart_point_and_line(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_17,plain,
! [X102,X103,X104] :
( ~ distinct_lines(X102,X103)
| distinct_lines(X102,X104)
| distinct_lines(X103,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
cnf(c_0_18,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
convergent_lines(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X97] : ~ distinct_lines(X97,X97),
inference(variable_rename,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( convergent_lines(esk3_0,X1)
| distinct_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_23,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_24,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( convergent_lines(esk3_0,X1)
| distinct_lines(esk4_0,X2)
| distinct_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_27,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_28,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( convergent_lines(esk3_0,X1)
| distinct_lines(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_30,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(c_0_31,plain,
! [X98] : ~ convergent_lines(X98,X98),
inference(variable_rename,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( convergent_lines(esk3_0,X1)
| convergent_lines(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_34,plain,
! [X131,X132] : ~ convergent_lines(parallel_through_point(X132,X131),X132),
inference(variable_rename,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( convergent_lines(X1,esk4_0)
| convergent_lines(esk3_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( convergent_lines(X1,esk3_0)
| convergent_lines(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
convergent_lines(parallel_through_point(esk4_0,X1),esk3_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_40,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_41,plain,
! [X99,X100,X101] :
( ~ distinct_points(X99,X100)
| distinct_points(X99,X101)
| distinct_points(X100,X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(c_0_42,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_43,negated_conjecture,
( convergent_lines(parallel_through_point(esk4_0,X1),X2)
| distinct_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_39]) ).
fof(c_0_44,plain,
! [X96] : ~ distinct_points(X96,X96),
inference(variable_rename,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_47,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_42]) ).
cnf(c_0_48,negated_conjecture,
distinct_lines(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_49,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_51,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])]) ).
cnf(c_0_52,negated_conjecture,
( apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk4_0)
| apart_point_and_line(X2,esk3_0)
| apart_point_and_line(X2,esk4_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
distinct_points(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
~ apart_point_and_line(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_55,negated_conjecture,
~ apart_point_and_line(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_56,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
cnf(c_0_57,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( apart_point_and_line(esk1_0,esk4_0)
| apart_point_and_line(esk2_0,esk4_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]) ).
fof(c_0_59,plain,
! [X133,X134] : ~ apart_point_and_line(X133,parallel_through_point(X134,X133)),
inference(variable_rename,[status(thm)],[c_0_56]) ).
cnf(c_0_60,negated_conjecture,
( apart_point_and_line(esk2_0,esk4_0)
| apart_point_and_line(esk1_0,X1)
| distinct_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( apart_point_and_line(esk2_0,esk4_0)
| apart_point_and_line(esk1_0,X1)
| convergent_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( apart_point_and_line(esk2_0,esk4_0)
| convergent_lines(esk4_0,parallel_through_point(X1,esk1_0)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_64,negated_conjecture,
( apart_point_and_line(esk2_0,esk4_0)
| convergent_lines(parallel_through_point(X1,esk1_0),X2)
| convergent_lines(esk4_0,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_63]) ).
cnf(c_0_65,negated_conjecture,
( apart_point_and_line(esk2_0,esk4_0)
| convergent_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_64]) ).
cnf(c_0_66,negated_conjecture,
( apart_point_and_line(esk2_0,X1)
| convergent_lines(esk4_0,X2)
| distinct_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_65]) ).
cnf(c_0_67,negated_conjecture,
( apart_point_and_line(esk2_0,X1)
| convergent_lines(esk4_0,X2)
| convergent_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_66]) ).
cnf(c_0_68,negated_conjecture,
( convergent_lines(esk4_0,parallel_through_point(X1,esk2_0))
| convergent_lines(esk4_0,X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_67]) ).
cnf(c_0_69,negated_conjecture,
convergent_lines(esk4_0,parallel_through_point(X1,esk2_0)),
inference(ef,[status(thm)],[c_0_68]) ).
cnf(c_0_70,negated_conjecture,
( convergent_lines(parallel_through_point(X1,esk2_0),X2)
| convergent_lines(esk4_0,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_69]) ).
cnf(c_0_71,negated_conjecture,
convergent_lines(esk4_0,X1),
inference(spm,[status(thm)],[c_0_37,c_0_70]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_35,c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO173+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
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:46:23 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 2.13/1.98 % Version : CSE_E---1.7
% 2.13/1.98 % Problem : theBenchmark.p
% 2.13/1.98 % SZS status Theorem for theBenchmark.p
% 2.13/1.98 % SZS output start CNFRefutation
% See solution above
% 2.13/1.98 % Total time : 1.371s
%------------------------------------------------------------------------------