%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:27:52 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 20 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 108 ( 42 ~; 49 |; 9 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 101 ( 8 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(couo1,axiom,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X8)
& ~ unorthogonal_lines(X6,X7) )
=> ~ convergent_lines(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(occu1,axiom,
! [X6,X7] :
( unorthogonal_lines(X6,X7)
| convergent_lines(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(con,conjecture,
! [X9,X6] : parallel_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
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(oac1,axiom,
! [X6,X7,X8] :
( ( unorthogonal_lines(X6,X7)
& convergent_lines(X6,X7) )
=> ( ( unorthogonal_lines(X7,X8)
& convergent_lines(X7,X8) )
| ( unorthogonal_lines(X6,X8)
& convergent_lines(X6,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(c_0_10,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(c_0_11,plain,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X8)
& ~ unorthogonal_lines(X6,X7) )
=> ~ convergent_lines(X7,X8) ),
inference(fof_simplification,[status(thm)],[couo1]) ).
fof(c_0_12,plain,
! [X15,X16] : ~ unorthogonal_lines(orthogonal_through_point(X16,X15),X16),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_10])]) ).
fof(c_0_13,plain,
! [X25,X26] :
( unorthogonal_lines(X25,X26)
| convergent_lines(X25,X26) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(c_0_14,plain,
! [X39,X40,X41] :
( ~ convergent_lines(X40,X41)
| unorthogonal_lines(X39,X41)
| unorthogonal_lines(X39,X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_15,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,negated_conjecture,
~ ! [X9,X6] : parallel_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_18,plain,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a3]) ).
cnf(c_0_19,plain,
( ~ convergent_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_21,negated_conjecture,
~ parallel_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_22,plain,
! [X13,X14] :
( ( parallel_lines(X13,X14)
| convergent_lines(X13,X14) )
& ( ~ convergent_lines(X13,X14)
| ~ parallel_lines(X13,X14) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_23,plain,
! [X27,X28,X29] :
( ( ~ unorthogonal_lines(X27,X28)
| ~ convergent_lines(X27,X28)
| unorthogonal_lines(X27,X29)
| unorthogonal_lines(X28,X29) )
& ( ~ unorthogonal_lines(X27,X28)
| ~ convergent_lines(X27,X28)
| unorthogonal_lines(X27,X29)
| convergent_lines(X28,X29) )
& ( ~ unorthogonal_lines(X27,X28)
| ~ convergent_lines(X27,X28)
| convergent_lines(X27,X29)
| unorthogonal_lines(X28,X29) )
& ( ~ unorthogonal_lines(X27,X28)
| ~ convergent_lines(X27,X28)
| convergent_lines(X27,X29)
| convergent_lines(X28,X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])])]) ).
cnf(c_0_24,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,orthogonal_through_point(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_25,plain,
! [X22,X23,X24] :
( convergent_lines(X23,X24)
| convergent_lines(X22,X24)
| ~ convergent_lines(X22,X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])]) ).
cnf(c_0_26,negated_conjecture,
~ parallel_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( parallel_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_29,plain,
( ~ unorthogonal_lines(X3,X1)
| ~ convergent_lines(X3,X1)
| convergent_lines(X3,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_31,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_33,plain,
! [X21] : ~ convergent_lines(X21,X21),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
cnf(c_0_34,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(X1,X3),X4),X1)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(X1,X3),X4),X2)
| unorthogonal_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,plain,
! [X65,X66,X67] :
( convergent_lines(X65,X67)
| distinct_lines(X66,X67)
| ~ convergent_lines(X65,X66) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])])]) ).
cnf(c_0_38,negated_conjecture,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| unorthogonal_lines(esk2_0,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,plain,
( ~ unorthogonal_lines(X3,X1)
| ~ convergent_lines(X3,X1)
| unorthogonal_lines(X3,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_41,negated_conjecture,
unorthogonal_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(spm,[status(thm)],[c_0_36,c_0_38]) ).
fof(c_0_42,plain,
! [X68,X69] :
( convergent_lines(X68,X69)
| ~ distinct_lines(X68,X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_43,plain,
( distinct_lines(X1,X3)
| convergent_lines(orthogonal_through_point(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_44,negated_conjecture,
( unorthogonal_lines(esk2_0,X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_32])]) ).
cnf(c_0_45,plain,
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,plain,
distinct_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_15,c_0_44]) ).
cnf(c_0_48,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( convergent_lines(esk2_0,X1)
| unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_47]),c_0_48])]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_49]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 % Computer : n003.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 20 13:55:31 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.44 Running first-order theorem proving
% 0.09/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % Version: 3.5.1
% 0.17/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.48 % Starting sh5l with 300s (1) cores
% 0.17/0.48 % new_bool_3 with pid 1954638 completed with status 0
% 0.17/0.48 % Result found by new_bool_3
% 0.17/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.48 % Search class: FGHNF-FFMF22-SFFFFFNN
% 0.17/0.48 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.48 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.48 % SubtermCWHack with pid 1954643 completed with status 0
% 0.17/0.48 % Result found by SubtermCWHack
% 0.17/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.48 % Search class: FGHNF-FFMF22-SFFFFFNN
% 0.17/0.48 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.48 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.48 % Preprocessing time : 0.001 s
% 0.17/0.48
% 0.17/0.48 % Proof found!
% 0.17/0.48 % SZS status Theorem
% 0.17/0.48 % SZS output start CNFRefutation
% See solution above
% 0.17/0.48 % Parsed axioms : 36
% 0.17/0.48 % Removed by relevancy pruning/SinE : 4
% 0.17/0.48 % Initial clauses : 39
% 0.17/0.48 % Removed in clause preprocessing : 0
% 0.17/0.48 % Initial clauses in saturation : 39
% 0.17/0.48 % Processed clauses : 391
% 0.17/0.48 % ...of these trivial : 0
% 0.17/0.48 % ...subsumed : 196
% 0.17/0.48 % ...remaining for further processing : 195
% 0.17/0.48 % Other redundant clauses eliminated : 0
% 0.17/0.48 % Clauses deleted for lack of memory : 0
% 0.17/0.48 % Backward-subsumed : 0
% 0.17/0.48 % Backward-rewritten : 2
% 0.17/0.48 % Generated clauses : 1606
% 0.17/0.48 % ...of the previous two non-redundant : 1430
% 0.17/0.48 % ...aggressively subsumed : 0
% 0.17/0.48 % Contextual simplify-reflections : 0
% 0.17/0.48 % Paramodulations : 1494
% 0.17/0.48 % Factorizations : 112
% 0.17/0.48 % NegExts : 0
% 0.17/0.48 % Equation resolutions : 0
% 0.17/0.48 % Disequality decompositions : 0
% 0.17/0.48 % Total rewrite steps : 185
% 0.17/0.48 % ...of those cached : 101
% 0.17/0.48 % Propositional unsat checks : 0
% 0.17/0.48 % Propositional check models : 0
% 0.17/0.48 % Propositional check unsatisfiable : 0
% 0.17/0.48 % Propositional clauses : 0
% 0.17/0.48 % Propositional clauses after purity: 0
% 0.17/0.48 % Propositional unsat core size : 0
% 0.17/0.48 % Propositional preprocessing time : 0.000
% 0.17/0.48 % Propositional encoding time : 0.000
% 0.17/0.48 % Propositional solver time : 0.000
% 0.17/0.48 % Success case prop preproc time : 0.000
% 0.17/0.48 % Success case prop encoding time : 0.000
% 0.17/0.48 % Success case prop solver time : 0.000
% 0.17/0.48 % Current number of processed clauses : 193
% 0.17/0.48 % Positive orientable unit clauses : 37
% 0.17/0.48 % Positive unorientable unit clauses: 0
% 0.17/0.48 % Negative unit clauses : 8
% 0.17/0.48 % Non-unit-clauses : 148
% 0.17/0.48 % Current number of unprocessed clauses: 1072
% 0.17/0.48 % ...number of literals in the above : 4649
% 0.17/0.48 % Current number of archived formulas : 0
% 0.17/0.48 % Current number of archived clauses : 2
% 0.17/0.48 % Clause-clause subsumption calls (NU) : 6584
% 0.17/0.48 % Rec. Clause-clause subsumption calls : 3351
% 0.17/0.48 % Non-unit clause-clause subsumptions : 196
% 0.17/0.48 % Unit Clause-clause subsumption calls : 954
% 0.17/0.48 % Rewrite failures with RHS unbound : 0
% 0.17/0.48 % BW rewrite match attempts : 41
% 0.17/0.48 % BW rewrite match successes : 2
% 0.17/0.48 % Condensation attempts : 0
% 0.17/0.48 % Condensation successes : 0
% 0.17/0.48 % Termbank termtop insertions : 21561
% 0.17/0.48 % Search garbage collected termcells : 438
% 0.17/0.48
% 0.17/0.48 % -------------------------------------------------
% 0.17/0.48 % User time : 0.020 s
% 0.17/0.48 % System time : 0.005 s
% 0.17/0.48 % Total time : 0.025 s
% 0.17/0.48 % Maximum resident set size: 3680 pages
% 0.17/0.48
% 0.17/0.48 % -------------------------------------------------
% 0.17/0.48 % User time : 0.023 s
% 0.17/0.48 % System time : 0.010 s
% 0.17/0.48 % Total time : 0.033 s
% 0.17/0.48 % Maximum resident set size: 4864 pages
% 0.17/0.48 % E exiting
%------------------------------------------------------------------------------