%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO220+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.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 04:19:59 PM UTC 2026
% Result : Theorem 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 50 ( 23 ~; 11 |; 8 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X6,X7,X8] :
( ( orthogonal_lines(X6,X7)
& orthogonal_lines(X6,X8) )
=> parallel_lines(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(a3,axiom,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a3) ).
fof(a5,axiom,
! [X1,X2] :
( orthogonal_lines(X1,X2)
<=> ~ unorthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a5) ).
fof(couo1,axiom,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X7,X8] :
( ( orthogonal_lines(X6,X7)
& orthogonal_lines(X6,X8) )
=> parallel_lines(X7,X8) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_5,plain,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(c_0_6,plain,
! [X1,X2] :
( orthogonal_lines(X1,X2)
<=> ~ unorthogonal_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a5]) ).
fof(c_0_7,plain,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
inference(fof_simplification,[status(thm)],[couo1]) ).
fof(c_0_8,negated_conjecture,
( orthogonal_lines(esk1_0,esk2_0)
& orthogonal_lines(esk1_0,esk3_0)
& ~ parallel_lines(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_9,plain,
! [X170,X171] :
( ( ~ parallel_lines(X170,X171)
| ~ convergent_lines(X170,X171) )
& ( convergent_lines(X170,X171)
| parallel_lines(X170,X171) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
fof(c_0_10,plain,
! [X174,X175] :
( ( ~ orthogonal_lines(X174,X175)
| ~ unorthogonal_lines(X174,X175) )
& ( unorthogonal_lines(X174,X175)
| orthogonal_lines(X174,X175) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
fof(c_0_11,plain,
! [X155,X156,X157] :
( unorthogonal_lines(X155,X156)
| unorthogonal_lines(X155,X157)
| ~ convergent_lines(X156,X157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,negated_conjecture,
~ parallel_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( convergent_lines(X1,X2)
| parallel_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ orthogonal_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
orthogonal_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
convergent_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
orthogonal_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( unorthogonal_lines(X1,esk2_0)
| unorthogonal_lines(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO220+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n023.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 17:49:38 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Theorem for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------