%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO219+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:27:50 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 17 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 135 ( 55 ~; 57 |; 11 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 92 ( 0 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a5,axiom,
! [X1,X2] :
( orthogonal_lines(X1,X2)
<=> ~ unorthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a5) ).
fof(con,conjecture,
! [X6,X7,X8] :
( ( parallel_lines(X6,X8)
& orthogonal_lines(X6,X7) )
=> orthogonal_lines(X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(occu1,axiom,
! [X6,X7] :
( unorthogonal_lines(X6,X7)
| convergent_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| distinct_lines(X2,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(X2,X3)
| distinct_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(a3,axiom,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a3) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(cotno1,axiom,
! [X6,X7,X8] :
( ( ( ~ unorthogonal_lines(X6,X8)
| ~ convergent_lines(X6,X8) )
& ( ~ unorthogonal_lines(X6,X7)
| ~ convergent_lines(X6,X7) ) )
=> ( ~ unorthogonal_lines(X7,X8)
| ~ convergent_lines(X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',cotno1) ).
fof(c_0_11,plain,
! [X1,X2] :
( orthogonal_lines(X1,X2)
<=> ~ unorthogonal_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a5]) ).
fof(c_0_12,negated_conjecture,
~ ! [X6,X7,X8] :
( ( parallel_lines(X6,X8)
& orthogonal_lines(X6,X7) )
=> orthogonal_lines(X7,X8) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_13,plain,
! [X14,X15] :
( ( orthogonal_lines(X14,X15)
| unorthogonal_lines(X14,X15) )
& ( ~ unorthogonal_lines(X14,X15)
| ~ orthogonal_lines(X14,X15) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,negated_conjecture,
( ~ orthogonal_lines(esk2_0,esk3_0)
& parallel_lines(esk1_0,esk3_0)
& orthogonal_lines(esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_15,plain,
( ~ unorthogonal_lines(X1,X2)
| ~ orthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
orthogonal_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X18,X19] :
( unorthogonal_lines(X18,X19)
| convergent_lines(X18,X19) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(c_0_18,plain,
! [X56,X57,X58] :
( convergent_lines(X56,X58)
| distinct_lines(X57,X58)
| ~ convergent_lines(X56,X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])])]) ).
cnf(c_0_19,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_22,plain,
! [X53,X54,X55] :
( distinct_lines(X54,X55)
| distinct_lines(X53,X55)
| ~ distinct_lines(X53,X54) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])])]) ).
cnf(c_0_23,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_25,plain,
! [X52] : ~ distinct_lines(X52,X52),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_21])]) ).
cnf(c_0_26,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X2,X3)
| distinct_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( distinct_lines(esk2_0,X1)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(c_0_29,plain,
! [X59,X60] :
( convergent_lines(X59,X60)
| ~ distinct_lines(X59,X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_30,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( distinct_lines(X1,X2)
| distinct_lines(esk2_0,X2)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_32,plain,
! [X16,X17] :
( ( parallel_lines(X16,X17)
| convergent_lines(X16,X17) )
& ( ~ convergent_lines(X16,X17)
| ~ parallel_lines(X16,X17) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_33,plain,
! [X36,X37,X38] :
( convergent_lines(X37,X38)
| convergent_lines(X36,X38)
| ~ convergent_lines(X36,X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])]) ).
cnf(c_0_34,plain,
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( distinct_lines(X1,esk2_0)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_36,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_37,plain,
( ~ convergent_lines(X1,X2)
| ~ parallel_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
parallel_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_39,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_41,plain,
! [X6,X7,X8] :
( ( ( ~ unorthogonal_lines(X6,X8)
| ~ convergent_lines(X6,X8) )
& ( ~ unorthogonal_lines(X6,X7)
| ~ convergent_lines(X6,X7) ) )
=> ( ~ unorthogonal_lines(X7,X8)
| ~ convergent_lines(X7,X8) ) ),
inference(fof_simplification,[status(thm)],[cotno1]) ).
fof(c_0_42,plain,
! [X35] : ~ convergent_lines(X35,X35),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_36])]) ).
cnf(c_0_43,negated_conjecture,
~ convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(esk1_0,X2)
| convergent_lines(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_45,plain,
! [X29,X30,X31] :
( ( ~ unorthogonal_lines(X30,X31)
| ~ convergent_lines(X30,X31)
| unorthogonal_lines(X29,X30)
| unorthogonal_lines(X29,X31) )
& ( ~ unorthogonal_lines(X30,X31)
| ~ convergent_lines(X30,X31)
| unorthogonal_lines(X29,X30)
| convergent_lines(X29,X31) )
& ( ~ unorthogonal_lines(X30,X31)
| ~ convergent_lines(X30,X31)
| convergent_lines(X29,X30)
| unorthogonal_lines(X29,X31) )
& ( ~ unorthogonal_lines(X30,X31)
| ~ convergent_lines(X30,X31)
| convergent_lines(X29,X30)
| convergent_lines(X29,X31) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
cnf(c_0_46,negated_conjecture,
~ orthogonal_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_47,plain,
( orthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_48,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
( ~ unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X2)
| unorthogonal_lines(X1,X3)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,negated_conjecture,
unorthogonal_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
convergent_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( convergent_lines(X1,esk3_0)
| unorthogonal_lines(X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_53]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO219+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 20 13:38:33 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 % Version: 3.5.1
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.45 % Starting sh5l with 300s (1) cores
% 0.09/0.45 % new_bool_3 with pid 1156195 completed with status 0
% 0.09/0.45 % Result found by new_bool_3
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.45 % Search class: FGHNF-FFMF00-SFFFFFNN
% 0.09/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.45 % SubtermCWHack with pid 1156198 completed with status 0
% 0.09/0.45 % Result found by SubtermCWHack
% 0.09/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.45 % Search class: FGHNF-FFMF00-SFFFFFNN
% 0.09/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.45 % Preprocessing time : 0.001 s
% 0.09/0.45
% 0.09/0.45 % Proof found!
% 0.09/0.45 % SZS status Theorem
% 0.09/0.45 % SZS output start CNFRefutation
% See solution above
% 0.09/0.45 % Parsed axioms : 36
% 0.09/0.45 % Removed by relevancy pruning/SinE : 17
% 0.09/0.45 % Initial clauses : 29
% 0.09/0.45 % Removed in clause preprocessing : 0
% 0.09/0.45 % Initial clauses in saturation : 29
% 0.09/0.45 % Processed clauses : 104
% 0.09/0.45 % ...of these trivial : 0
% 0.09/0.45 % ...subsumed : 39
% 0.09/0.45 % ...remaining for further processing : 65
% 0.09/0.45 % Other redundant clauses eliminated : 0
% 0.09/0.45 % Clauses deleted for lack of memory : 0
% 0.09/0.45 % Backward-subsumed : 0
% 0.09/0.45 % Backward-rewritten : 0
% 0.09/0.45 % Generated clauses : 265
% 0.09/0.45 % ...of the previous two non-redundant : 218
% 0.09/0.45 % ...aggressively subsumed : 0
% 0.09/0.45 % Contextual simplify-reflections : 0
% 0.09/0.45 % Paramodulations : 243
% 0.09/0.45 % Factorizations : 22
% 0.09/0.45 % NegExts : 0
% 0.09/0.45 % Equation resolutions : 0
% 0.09/0.45 % Disequality decompositions : 0
% 0.09/0.45 % Total rewrite steps : 39
% 0.09/0.45 % ...of those cached : 34
% 0.09/0.45 % Propositional unsat checks : 0
% 0.09/0.45 % Propositional check models : 0
% 0.09/0.45 % Propositional check unsatisfiable : 0
% 0.09/0.45 % Propositional clauses : 0
% 0.09/0.45 % Propositional clauses after purity: 0
% 0.09/0.45 % Propositional unsat core size : 0
% 0.09/0.45 % Propositional preprocessing time : 0.000
% 0.09/0.45 % Propositional encoding time : 0.000
% 0.09/0.45 % Propositional solver time : 0.000
% 0.09/0.45 % Success case prop preproc time : 0.000
% 0.09/0.45 % Success case prop encoding time : 0.000
% 0.09/0.45 % Success case prop solver time : 0.000
% 0.09/0.45 % Current number of processed clauses : 65
% 0.09/0.45 % Positive orientable unit clauses : 9
% 0.09/0.45 % Positive unorientable unit clauses: 0
% 0.09/0.45 % Negative unit clauses : 5
% 0.09/0.45 % Non-unit-clauses : 51
% 0.09/0.45 % Current number of unprocessed clauses: 143
% 0.09/0.45 % ...number of literals in the above : 573
% 0.09/0.45 % Current number of archived formulas : 0
% 0.09/0.45 % Current number of archived clauses : 0
% 0.09/0.45 % Clause-clause subsumption calls (NU) : 362
% 0.09/0.45 % Rec. Clause-clause subsumption calls : 253
% 0.09/0.45 % Non-unit clause-clause subsumptions : 36
% 0.09/0.45 % Unit Clause-clause subsumption calls : 25
% 0.09/0.45 % Rewrite failures with RHS unbound : 0
% 0.09/0.45 % BW rewrite match attempts : 0
% 0.09/0.45 % BW rewrite match successes : 0
% 0.09/0.45 % Condensation attempts : 0
% 0.09/0.45 % Condensation successes : 0
% 0.09/0.45 % Termbank termtop insertions : 4591
% 0.09/0.45 % Search garbage collected termcells : 410
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.005 s
% 0.09/0.45 % System time : 0.004 s
% 0.09/0.45 % Total time : 0.009 s
% 0.09/0.45 % Maximum resident set size: 3680 pages
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.007 s
% 0.09/0.45 % System time : 0.009 s
% 0.09/0.45 % Total time : 0.016 s
% 0.09/0.45 % Maximum resident set size: 4608 pages
% 0.09/0.45 % E exiting
%------------------------------------------------------------------------------