%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO187+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 : n027.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 04:19:46 PM UTC 2026
% Result : Theorem 1.58s 1.80s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 15 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 28 ~; 34 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 4 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_points(X4,X5)
& incident_point_and_line(X1,line_connecting(X4,X5))
& incident_point_and_line(X2,line_connecting(X4,X5)) )
=> ( incident_point_and_line(X4,line_connecting(X1,X2))
& incident_point_and_line(X5,line_connecting(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(a4,axiom,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a4) ).
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(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(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
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_8,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_points(X4,X5)
& incident_point_and_line(X1,line_connecting(X4,X5))
& incident_point_and_line(X2,line_connecting(X4,X5)) )
=> ( incident_point_and_line(X4,line_connecting(X1,X2))
& incident_point_and_line(X5,line_connecting(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_9,plain,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4]) ).
fof(c_0_10,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& distinct_points(esk3_0,esk4_0)
& incident_point_and_line(esk1_0,line_connecting(esk3_0,esk4_0))
& incident_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
& ( ~ incident_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| ~ incident_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_8])])]) ).
fof(c_0_11,plain,
! [X173,X174] :
( ( ~ incident_point_and_line(X173,X174)
| ~ apart_point_and_line(X173,X174) )
& ( apart_point_and_line(X173,X174)
| incident_point_and_line(X173,X174) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
cnf(c_0_12,negated_conjecture,
( ~ incident_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| ~ incident_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( apart_point_and_line(X1,X2)
| incident_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
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])]) ).
cnf(c_0_15,negated_conjecture,
( apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0))
| ~ incident_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_12,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)
| 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(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
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,
( 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_18,c_0_19]) ).
fof(c_0_23,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(c_0_24,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_25,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,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),X2)
| distinct_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_27,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(c_0_28,plain,
! [X131,X132] : ~ convergent_lines(parallel_through_point(X132,X131),X132),
inference(variable_rename,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X1)
| distinct_lines(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_31,plain,
! [X133,X134] : ~ apart_point_and_line(X133,parallel_through_point(X134,X133)),
inference(variable_rename,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X1)
| convergent_lines(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( apart_point_and_line(esk4_0,parallel_through_point(line_connecting(esk1_0,esk2_0),X1))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( apart_point_and_line(esk3_0,X1)
| distinct_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( apart_point_and_line(esk3_0,X1)
| distinct_lines(line_connecting(esk1_0,esk2_0),X2)
| distinct_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( apart_point_and_line(esk3_0,X1)
| distinct_lines(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( apart_point_and_line(esk3_0,X1)
| convergent_lines(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
apart_point_and_line(esk3_0,parallel_through_point(line_connecting(esk1_0,esk2_0),X1)),
inference(spm,[status(thm)],[c_0_32,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_34,c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO187+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
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:46:50 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.58/1.80 % Version : CSE_E---1.7
% 1.58/1.80 % Problem : theBenchmark.p
% 1.58/1.80 % SZS status Theorem for theBenchmark.p
% 1.58/1.80 % SZS output start CNFRefutation
% See solution above
% 1.58/1.80 % Total time : 1.367s
%------------------------------------------------------------------------------