%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:27:12 PM UTC 2026
% Result : Theorem 0.23s 0.64s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 9 unt; 0 def)
% Number of atoms : 170 ( 26 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 204 ( 77 ~; 70 |; 46 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 126 ( 14 sgn 53 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(between_c_defn,axiom,
! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
<=> ( ? [X8] :
( inner_point(X5,X8)
& end_point(X7,X8)
& end_point(X3,X8)
& part_of(X8,X1) )
& X3 != X7 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+1.ax',between_c_defn) ).
fof(inner_point_defn,axiom,
! [X3,X1] :
( inner_point(X3,X1)
<=> ( ~ end_point(X3,X1)
& incident_c(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).
fof(part_of_defn,axiom,
! [X1,X2] :
( part_of(X2,X1)
<=> ! [X3] :
( incident_c(X3,X2)
=> incident_c(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(end_point_defn,axiom,
! [X3,X1] :
( end_point(X3,X1)
<=> ( ! [X2,X4] :
( ( incident_c(X3,X4)
& incident_c(X3,X2)
& part_of(X4,X1)
& part_of(X2,X1) )
=> ( part_of(X4,X2)
| part_of(X2,X4) ) )
& incident_c(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).
fof(theorem_3_8_1,conjecture,
! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
=> ( X3 != X7
& X5 != X7
& X3 != X5
& incident_c(X7,X1)
& incident_c(X5,X1)
& incident_c(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_1) ).
fof(c_0_5,plain,
! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
<=> ( ? [X8] :
( inner_point(X5,X8)
& end_point(X7,X8)
& end_point(X3,X8)
& part_of(X8,X1) )
& X3 != X7 ) ),
inference(fof_simplification,[status(thm)],[between_c_defn]) ).
fof(c_0_6,plain,
! [X3,X1] :
( inner_point(X3,X1)
<=> ( ~ end_point(X3,X1)
& incident_c(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[inner_point_defn]) ).
fof(c_0_7,plain,
! [X13,X14,X15,X16,X17] :
( ( part_of(X17,X16)
| ~ incident_c(esk5_2(X16,X17),X16) )
& ( part_of(X17,X16)
| incident_c(esk5_2(X16,X17),X17) )
& ( incident_c(X15,X13)
| ~ incident_c(X15,X14)
| ~ part_of(X14,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[part_of_defn])])])])])])]) ).
fof(c_0_8,plain,
! [X30,X31,X32,X33,X35,X36,X37,X38,X39] :
( ( between_c(X35,X36,X37,X38)
| ~ inner_point(X37,X39)
| ~ end_point(X38,X39)
| ~ end_point(X36,X39)
| ~ part_of(X39,X35)
| X36 = X38 )
& ( ~ between_c(X30,X31,X32,X33)
| inner_point(X32,esk9_4(X30,X31,X32,X33)) )
& ( ~ between_c(X30,X31,X32,X33)
| end_point(X33,esk9_4(X30,X31,X32,X33)) )
& ( ~ between_c(X30,X31,X32,X33)
| end_point(X31,esk9_4(X30,X31,X32,X33)) )
& ( ~ between_c(X30,X31,X32,X33)
| part_of(esk9_4(X30,X31,X32,X33),X30) )
& ( ~ between_c(X30,X31,X32,X33)
| X31 != X33 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])]) ).
fof(c_0_9,plain,
! [X19,X20,X21,X22,X23,X24] :
( ( end_point(X23,X24)
| ~ incident_c(X23,X24)
| ~ part_of(esk7_2(X23,X24),esk6_2(X23,X24)) )
& ( end_point(X23,X24)
| ~ incident_c(X23,X24)
| ~ part_of(esk6_2(X23,X24),esk7_2(X23,X24)) )
& ( end_point(X23,X24)
| ~ incident_c(X23,X24)
| incident_c(X23,esk7_2(X23,X24)) )
& ( end_point(X23,X24)
| ~ incident_c(X23,X24)
| incident_c(X23,esk6_2(X23,X24)) )
& ( end_point(X23,X24)
| ~ incident_c(X23,X24)
| part_of(esk7_2(X23,X24),X24) )
& ( end_point(X23,X24)
| ~ incident_c(X23,X24)
| part_of(esk6_2(X23,X24),X24) )
& ( ~ end_point(X19,X20)
| part_of(X22,X21)
| part_of(X21,X22)
| ~ incident_c(X19,X22)
| ~ incident_c(X19,X21)
| ~ part_of(X22,X20)
| ~ part_of(X21,X20) )
& ( ~ end_point(X19,X20)
| incident_c(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[end_point_defn])])])])])])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
=> ( X3 != X7
& X5 != X7
& X3 != X5
& incident_c(X7,X1)
& incident_c(X5,X1)
& incident_c(X3,X1) ) ),
inference(assume_negation,[status(cth)],[theorem_3_8_1]) ).
fof(c_0_11,plain,
! [X52,X53] :
( ( inner_point(X52,X53)
| end_point(X52,X53)
| ~ incident_c(X52,X53) )
& ( ~ inner_point(X52,X53)
| ~ end_point(X52,X53) )
& ( ~ inner_point(X52,X53)
| incident_c(X52,X53) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_12,plain,
( ~ incident_c(X3,X1)
| ~ part_of(X1,X2)
| incident_c(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ between_c(X1,X2,X3,X4)
| part_of(esk9_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ end_point(X1,X2)
| incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ between_c(X2,X3,X4,X1)
| end_point(X1,esk9_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
=> ( X3 != X7
& X5 != X7
& X3 != X5
& incident_c(X7,X1)
& incident_c(X5,X1)
& incident_c(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ between_c(X2,X1,X3,X4)
| end_point(X1,esk9_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( ~ inner_point(X1,X2)
| incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ between_c(X2,X3,X1,X4)
| inner_point(X1,esk9_4(X2,X3,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( ~ incident_c(X1,esk9_4(X2,X3,X4,X5))
| ~ between_c(X2,X3,X4,X5)
| incident_c(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,plain,
( ~ between_c(X2,X3,X4,X1)
| incident_c(X1,esk9_4(X2,X3,X4,X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_22,negated_conjecture,
( ( esk2_0 = esk4_0
| esk3_0 = esk4_0
| esk2_0 = esk3_0
| ~ incident_c(esk4_0,esk1_0)
| ~ incident_c(esk3_0,esk1_0)
| ~ incident_c(esk2_0,esk1_0) )
& between_c(esk1_0,esk2_0,esk3_0,esk4_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_23,plain,
( ~ between_c(X2,X1,X3,X4)
| incident_c(X1,esk9_4(X2,X1,X3,X4)) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_24,plain,
( ~ between_c(X2,X3,X1,X4)
| incident_c(X1,esk9_4(X2,X3,X1,X4)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ between_c(X2,X3,X4,X1)
| incident_c(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
between_c(esk1_0,esk2_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ between_c(X2,X1,X3,X4)
| incident_c(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_28,plain,
( ~ between_c(X2,X3,X1,X4)
| incident_c(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_29,plain,
( ~ inner_point(X1,X2)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
( ~ incident_c(esk4_0,esk1_0)
| ~ incident_c(esk3_0,esk1_0)
| ~ incident_c(esk2_0,esk1_0)
| esk2_0 = esk4_0
| esk3_0 = esk4_0
| esk2_0 = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
incident_c(esk4_0,esk1_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
incident_c(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
incident_c(esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_34,plain,
( ~ end_point(X3,esk9_4(X1,X2,X3,X4))
| ~ between_c(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_35,negated_conjecture,
( esk4_0 = esk3_0
| esk4_0 = esk2_0
| esk3_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),c_0_32]),c_0_33])]) ).
cnf(c_0_36,plain,
~ between_c(X1,X2,X3,X3),
inference(spm,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_37,plain,
( ~ between_c(X3,X1,X4,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,negated_conjecture,
( esk3_0 = esk2_0
| esk4_0 = esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
~ between_c(X1,X2,X3,X2),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
esk3_0 = esk2_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_38]),c_0_39]) ).
cnf(c_0_41,plain,
~ between_c(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_34,c_0_17]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.46 % Computer : n020.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Sun Sep 20 11:26:49 UTC 2026
% 0.17/0.47 % CPUTime :
% 0.17/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.54 Running first-order theorem proving
% 0.23/0.54 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
% 0.23/0.64 % Version: 3.5.1
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.64 % Starting sh5l with 300s (1) cores
% 0.23/0.64 % new_bool_3 with pid 405806 completed with status 0
% 0.23/0.64 % Result found by new_bool_3
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.64 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.23/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.64 % SubtermCWHack with pid 405810 completed with status 0
% 0.23/0.64 % Result found by SubtermCWHack
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.64 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.23/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.64 % Preprocessing time : 0.003 s
% 0.23/0.64
% 0.23/0.64 % Proof found!
% 0.23/0.64 % SZS status Theorem
% 0.23/0.64 % SZS output start CNFRefutation
% See solution above
% 0.23/0.64 % Parsed axioms : 18
% 0.23/0.64 % Removed by relevancy pruning/SinE : 4
% 0.23/0.64 % Initial clauses : 45
% 0.23/0.64 % Removed in clause preprocessing : 0
% 0.23/0.64 % Initial clauses in saturation : 45
% 0.23/0.64 % Processed clauses : 151
% 0.23/0.64 % ...of these trivial : 1
% 0.23/0.64 % ...subsumed : 26
% 0.23/0.64 % ...remaining for further processing : 124
% 0.23/0.64 % Other redundant clauses eliminated : 4
% 0.23/0.64 % Clauses deleted for lack of memory : 0
% 0.23/0.64 % Backward-subsumed : 1
% 0.23/0.64 % Backward-rewritten : 4
% 0.23/0.64 % Generated clauses : 404
% 0.23/0.64 % ...of the previous two non-redundant : 390
% 0.23/0.64 % ...aggressively subsumed : 0
% 0.23/0.64 % Contextual simplify-reflections : 0
% 0.23/0.64 % Paramodulations : 389
% 0.23/0.64 % Factorizations : 11
% 0.23/0.64 % NegExts : 0
% 0.23/0.64 % Equation resolutions : 4
% 0.23/0.64 % Disequality decompositions : 0
% 0.23/0.64 % Total rewrite steps : 11
% 0.23/0.64 % ...of those cached : 5
% 0.23/0.64 % Propositional unsat checks : 0
% 0.23/0.64 % Propositional check models : 0
% 0.23/0.64 % Propositional check unsatisfiable : 0
% 0.23/0.64 % Propositional clauses : 0
% 0.23/0.64 % Propositional clauses after purity: 0
% 0.23/0.64 % Propositional unsat core size : 0
% 0.23/0.64 % Propositional preprocessing time : 0.000
% 0.23/0.64 % Propositional encoding time : 0.000
% 0.23/0.64 % Propositional solver time : 0.000
% 0.23/0.64 % Success case prop preproc time : 0.000
% 0.23/0.64 % Success case prop encoding time : 0.000
% 0.23/0.64 % Success case prop solver time : 0.000
% 0.23/0.64 % Current number of processed clauses : 115
% 0.23/0.64 % Positive orientable unit clauses : 9
% 0.23/0.64 % Positive unorientable unit clauses: 0
% 0.23/0.64 % Negative unit clauses : 4
% 0.23/0.64 % Non-unit-clauses : 102
% 0.23/0.64 % Current number of unprocessed clauses: 284
% 0.23/0.64 % ...number of literals in the above : 1135
% 0.23/0.64 % Current number of archived formulas : 0
% 0.23/0.64 % Current number of archived clauses : 5
% 0.23/0.64 % Clause-clause subsumption calls (NU) : 3848
% 0.23/0.64 % Rec. Clause-clause subsumption calls : 2426
% 0.23/0.64 % Non-unit clause-clause subsumptions : 27
% 0.23/0.64 % Unit Clause-clause subsumption calls : 161
% 0.23/0.64 % Rewrite failures with RHS unbound : 0
% 0.23/0.64 % BW rewrite match attempts : 9
% 0.23/0.64 % BW rewrite match successes : 2
% 0.23/0.64 % Condensation attempts : 0
% 0.23/0.64 % Condensation successes : 0
% 0.23/0.64 % Termbank termtop insertions : 9357
% 0.23/0.64 % Search garbage collected termcells : 1074
% 0.23/0.64
% 0.23/0.64 % -------------------------------------------------
% 0.23/0.64 % User time : 0.031 s
% 0.23/0.64 % System time : 0.005 s
% 0.23/0.64 % Total time : 0.036 s
% 0.23/0.64 % Maximum resident set size: 3664 pages
% 0.23/0.64
% 0.23/0.64 % -------------------------------------------------
% 0.23/0.64 % User time : 0.035 s
% 0.23/0.64 % System time : 0.011 s
% 0.23/0.64 % Total time : 0.046 s
% 0.23/0.64 % Maximum resident set size: 4864 pages
% 0.23/0.64 % E exiting
%------------------------------------------------------------------------------