%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO221+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 : n011.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 12:27:51 PM UTC 2026
% Result : Theorem 0.22s 0.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 40 |; 10 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 3 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X9,X10,X6] :
( incident_point_and_line(X10,orthogonal_through_point(X6,X9))
=> equal_lines(orthogonal_through_point(X6,X9),orthogonal_through_point(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(ax2,axiom,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(occu1,axiom,
! [X6,X7] :
( unorthogonal_lines(X6,X7)
| convergent_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
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(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
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/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(c_0_9,negated_conjecture,
~ ! [X9,X10,X6] :
( incident_point_and_line(X10,orthogonal_through_point(X6,X9))
=> equal_lines(orthogonal_through_point(X6,X9),orthogonal_through_point(X6,X10)) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_10,plain,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax2]) ).
fof(c_0_11,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(c_0_12,negated_conjecture,
( ~ equal_lines(orthogonal_through_point(esk3_0,esk1_0),orthogonal_through_point(esk3_0,esk2_0))
& incident_point_and_line(esk2_0,orthogonal_through_point(esk3_0,esk1_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_13,plain,
! [X84,X85] :
( ( equal_lines(X84,X85)
| distinct_lines(X84,X85) )
& ( ~ distinct_lines(X84,X85)
| ~ equal_lines(X84,X85) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_14,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_15,plain,
! [X58,X59] : ~ unorthogonal_lines(orthogonal_through_point(X59,X58),X59),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_11])]) ).
fof(c_0_16,plain,
! [X53,X54] :
( unorthogonal_lines(X53,X54)
| convergent_lines(X53,X54) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(c_0_17,plain,
! [X17,X18,X19] :
( distinct_lines(X18,X19)
| distinct_lines(X17,X19)
| ~ distinct_lines(X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])])]) ).
cnf(c_0_18,negated_conjecture,
~ equal_lines(orthogonal_through_point(esk3_0,esk1_0),orthogonal_through_point(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( equal_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X71,X72,X73] :
( ~ convergent_lines(X72,X73)
| unorthogonal_lines(X71,X73)
| unorthogonal_lines(X71,X72) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_21,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_24,plain,
! [X44,X45] :
( convergent_lines(X44,X45)
| ~ distinct_lines(X44,X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_25,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X2,X3)
| distinct_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
distinct_lines(orthogonal_through_point(esk3_0,esk1_0),orthogonal_through_point(esk3_0,esk2_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_27,plain,
! [X55,X56,X57] :
( ( ~ unorthogonal_lines(X55,X56)
| ~ convergent_lines(X55,X56)
| unorthogonal_lines(X55,X57)
| unorthogonal_lines(X56,X57) )
& ( ~ unorthogonal_lines(X55,X56)
| ~ convergent_lines(X55,X56)
| unorthogonal_lines(X55,X57)
| convergent_lines(X56,X57) )
& ( ~ unorthogonal_lines(X55,X56)
| ~ convergent_lines(X55,X56)
| convergent_lines(X55,X57)
| unorthogonal_lines(X56,X57) )
& ( ~ unorthogonal_lines(X55,X56)
| ~ convergent_lines(X55,X56)
| convergent_lines(X55,X57)
| convergent_lines(X56,X57) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])])]) ).
cnf(c_0_28,plain,
( ~ convergent_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_30,plain,
! [X12] : ~ distinct_lines(X12,X12),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
cnf(c_0_31,plain,
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( distinct_lines(orthogonal_through_point(esk3_0,esk2_0),X1)
| distinct_lines(orthogonal_through_point(esk3_0,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( ~ unorthogonal_lines(X3,X1)
| ~ convergent_lines(X3,X1)
| unorthogonal_lines(X3,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,orthogonal_through_point(X2,X3)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( distinct_lines(orthogonal_through_point(esk3_0,esk1_0),X1)
| convergent_lines(orthogonal_through_point(esk3_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( ~ convergent_lines(X4,orthogonal_through_point(X1,X2))
| unorthogonal_lines(X4,X3)
| unorthogonal_lines(X4,X1)
| unorthogonal_lines(orthogonal_through_point(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
convergent_lines(orthogonal_through_point(esk3_0,esk2_0),orthogonal_through_point(esk3_0,esk1_0)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk3_0,esk1_0),X1)
| unorthogonal_lines(orthogonal_through_point(esk3_0,esk2_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_21]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_39]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO221+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n011.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 20 13:48:09 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 0.22/0.50 % Version: 3.5.1
% 0.22/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.50 % Starting sh5l with 300s (1) cores
% 0.22/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3754606 completed with status 0
% 0.22/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.50 % No SInE strategy applied
% 0.22/0.50 % Search class: FGHNF-FFMF22-SFFFFFNN
% 0.22/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/0.50 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.22/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.22/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3754614 completed with status 0
% 0.22/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.50 % No SInE strategy applied
% 0.22/0.50 % Search class: FGHNF-FFMF22-SFFFFFNN
% 0.22/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/0.50 % Preprocessing time : 0.001 s
% 0.22/0.50 % Presaturation interreduction done
% 0.22/0.50
% 0.22/0.50 % Proof found!
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 % SZS output start CNFRefutation
% See solution above
% 0.22/0.50 % Parsed axioms : 36
% 0.22/0.50 % Removed by relevancy pruning/SinE : 0
% 0.22/0.50 % Initial clauses : 48
% 0.22/0.50 % Removed in clause preprocessing : 0
% 0.22/0.50 % Initial clauses in saturation : 48
% 0.22/0.50 % Processed clauses : 146
% 0.22/0.50 % ...of these trivial : 0
% 0.22/0.50 % ...subsumed : 17
% 0.22/0.50 % ...remaining for further processing : 129
% 0.22/0.50 % Other redundant clauses eliminated : 0
% 0.22/0.50 % Clauses deleted for lack of memory : 0
% 0.22/0.50 % Backward-subsumed : 0
% 0.22/0.50 % Backward-rewritten : 6
% 0.22/0.50 % Generated clauses : 237
% 0.22/0.50 % ...of the previous two non-redundant : 197
% 0.22/0.50 % ...aggressively subsumed : 0
% 0.22/0.50 % Contextual simplify-reflections : 0
% 0.22/0.50 % Paramodulations : 235
% 0.22/0.50 % Factorizations : 2
% 0.22/0.50 % NegExts : 0
% 0.22/0.50 % Equation resolutions : 0
% 0.22/0.50 % Disequality decompositions : 0
% 0.22/0.50 % Total rewrite steps : 40
% 0.22/0.50 % ...of those cached : 24
% 0.22/0.50 % Propositional unsat checks : 0
% 0.22/0.50 % Propositional check models : 0
% 0.22/0.50 % Propositional check unsatisfiable : 0
% 0.22/0.50 % Propositional clauses : 0
% 0.22/0.50 % Propositional clauses after purity: 0
% 0.22/0.50 % Propositional unsat core size : 0
% 0.22/0.50 % Propositional preprocessing time : 0.000
% 0.22/0.50 % Propositional encoding time : 0.000
% 0.22/0.50 % Propositional solver time : 0.000
% 0.22/0.50 % Success case prop preproc time : 0.000
% 0.22/0.50 % Success case prop encoding time : 0.000
% 0.22/0.50 % Success case prop solver time : 0.000
% 0.22/0.50 % Current number of processed clauses : 79
% 0.22/0.50 % Positive orientable unit clauses : 12
% 0.22/0.50 % Positive unorientable unit clauses: 0
% 0.22/0.50 % Negative unit clauses : 9
% 0.22/0.50 % Non-unit-clauses : 58
% 0.22/0.50 % Current number of unprocessed clauses: 137
% 0.22/0.50 % ...number of literals in the above : 500
% 0.22/0.50 % Current number of archived formulas : 0
% 0.22/0.50 % Current number of archived clauses : 50
% 0.22/0.50 % Clause-clause subsumption calls (NU) : 980
% 0.22/0.50 % Rec. Clause-clause subsumption calls : 647
% 0.22/0.50 % Non-unit clause-clause subsumptions : 17
% 0.22/0.50 % Unit Clause-clause subsumption calls : 77
% 0.22/0.50 % Rewrite failures with RHS unbound : 0
% 0.22/0.50 % BW rewrite match attempts : 8
% 0.22/0.50 % BW rewrite match successes : 2
% 0.22/0.50 % Condensation attempts : 0
% 0.22/0.50 % Condensation successes : 0
% 0.22/0.50 % Termbank termtop insertions : 7397
% 0.22/0.50 % Search garbage collected termcells : 490
% 0.22/0.50
% 0.22/0.50 % -------------------------------------------------
% 0.22/0.50 % User time : 0.018 s
% 0.22/0.50 % System time : 0.003 s
% 0.22/0.50 % Total time : 0.021 s
% 0.22/0.50 % Maximum resident set size: 3680 pages
% 0.22/0.50
% 0.22/0.50 % -------------------------------------------------
% 0.22/0.50 % User time : 0.062 s
% 0.22/0.50 % System time : 0.017 s
% 0.22/0.50 % Total time : 0.079 s
% 0.22/0.50 % Maximum resident set size: 4608 pages
% 0.22/0.50 % E exiting
%------------------------------------------------------------------------------