%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO112+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 : n019.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 12:27:13 PM UTC 2026
% Result : Theorem 0.25s 0.77s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 64 ( 8 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 71 ( 29 ~; 24 |; 14 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 58 ( 4 sgn 25 !; 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(theorem_3_8_2,conjecture,
! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
=> between_c(X1,X7,X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_2) ).
fof(c_0_2,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_3,negated_conjecture,
~ ! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
=> between_c(X1,X7,X5,X3) ),
inference(assume_negation,[status(cth)],[theorem_3_8_2]) ).
fof(c_0_4,plain,
! [X82,X83,X84,X85,X87,X88,X89,X90,X91] :
( ( between_c(X87,X88,X89,X90)
| ~ inner_point(X89,X91)
| ~ end_point(X90,X91)
| ~ end_point(X88,X91)
| ~ part_of(X91,X87)
| X88 = X90 )
& ( ~ between_c(X82,X83,X84,X85)
| inner_point(X84,esk14_4(X82,X83,X84,X85)) )
& ( ~ between_c(X82,X83,X84,X85)
| end_point(X85,esk14_4(X82,X83,X84,X85)) )
& ( ~ between_c(X82,X83,X84,X85)
| end_point(X83,esk14_4(X82,X83,X84,X85)) )
& ( ~ between_c(X82,X83,X84,X85)
| part_of(esk14_4(X82,X83,X84,X85),X82) )
& ( ~ between_c(X82,X83,X84,X85)
| X83 != X85 ) ),
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_2])])])])])])]) ).
fof(c_0_5,negated_conjecture,
( ~ between_c(esk15_0,esk18_0,esk17_0,esk16_0)
& between_c(esk15_0,esk16_0,esk17_0,esk18_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_6,plain,
( ~ between_c(X2,X3,X1,X4)
| inner_point(X1,esk14_4(X2,X3,X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
between_c(esk15_0,esk16_0,esk17_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ inner_point(X5,X3)
| ~ end_point(X2,X3)
| ~ end_point(X1,X3)
| ~ part_of(X3,X4)
| between_c(X4,X1,X5,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
inner_point(esk17_0,esk14_4(esk15_0,esk16_0,esk17_0,esk18_0)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
( ~ between_c(X2,X1,X3,X4)
| end_point(X1,esk14_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,plain,
( ~ between_c(X2,X3,X4,X1)
| end_point(X1,esk14_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,plain,
( ~ between_c(X1,X2,X3,X4)
| part_of(esk14_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
~ between_c(esk15_0,esk18_0,esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( ~ part_of(esk14_4(esk15_0,esk16_0,esk17_0,esk18_0),X3)
| ~ end_point(X1,esk14_4(esk15_0,esk16_0,esk17_0,esk18_0))
| ~ end_point(X2,esk14_4(esk15_0,esk16_0,esk17_0,esk18_0))
| between_c(X3,X1,esk17_0,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
end_point(esk16_0,esk14_4(esk15_0,esk16_0,esk17_0,esk18_0)),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_16,negated_conjecture,
end_point(esk18_0,esk14_4(esk15_0,esk16_0,esk17_0,esk18_0)),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_17,negated_conjecture,
part_of(esk14_4(esk15_0,esk16_0,esk17_0,esk18_0),esk15_0),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_18,plain,
( ~ between_c(X3,X1,X4,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_19,negated_conjecture,
esk18_0 = esk16_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_20,plain,
~ between_c(X1,X2,X3,X2),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n019.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 11:27:08 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.55 Running first-order theorem proving
% 0.21/0.55 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
% 0.25/0.77 % Version: 3.5.1
% 0.25/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.77 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.77 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.77 % Starting sh5l with 300s (1) cores
% 0.25/0.77 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 97746 completed with status 0
% 0.25/0.77 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.25/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.77 % No SInE strategy applied
% 0.25/0.77 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.25/0.77 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.77 % Starting SubtermCWHack with 151s (1) cores
% 0.25/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 0.25/0.77 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 0.25/0.77 % Starting new_bool_3 with 151s (1) cores
% 0.25/0.77 % Starting new_bool_1 with 146s (1) cores
% 0.25/0.77 % G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with pid 97753 completed with status 0
% 0.25/0.77 % Result found by G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 0.25/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.77 % No SInE strategy applied
% 0.25/0.77 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.25/0.77 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.77 % Starting SubtermCWHack with 151s (1) cores
% 0.25/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 0.25/0.77 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 0.25/0.77 % Preprocessing time : 0.003 s
% 0.25/0.77 % Presaturation interreduction done
% 0.25/0.77
% 0.25/0.77 % Proof found!
% 0.25/0.77 % SZS status Theorem
% 0.25/0.77 % SZS output start CNFRefutation
% See solution above
% 0.25/0.77 % Parsed axioms : 18
% 0.25/0.77 % Removed by relevancy pruning/SinE : 0
% 0.25/0.77 % Initial clauses : 51
% 0.25/0.77 % Removed in clause preprocessing : 0
% 0.25/0.77 % Initial clauses in saturation : 51
% 0.25/0.77 % Processed clauses : 415
% 0.25/0.77 % ...of these trivial : 0
% 0.25/0.77 % ...subsumed : 132
% 0.25/0.77 % ...remaining for further processing : 283
% 0.25/0.77 % Other redundant clauses eliminated : 20
% 0.25/0.77 % Clauses deleted for lack of memory : 0
% 0.25/0.77 % Backward-subsumed : 2
% 0.25/0.77 % Backward-rewritten : 33
% 0.25/0.77 % Generated clauses : 1580
% 0.25/0.77 % ...of the previous two non-redundant : 1264
% 0.25/0.77 % ...aggressively subsumed : 0
% 0.25/0.77 % Contextual simplify-reflections : 5
% 0.25/0.77 % Paramodulations : 1525
% 0.25/0.77 % Factorizations : 30
% 0.25/0.77 % NegExts : 0
% 0.25/0.77 % Equation resolutions : 25
% 0.25/0.77 % Disequality decompositions : 0
% 0.25/0.77 % Total rewrite steps : 404
% 0.25/0.77 % ...of those cached : 378
% 0.25/0.77 % Propositional unsat checks : 0
% 0.25/0.77 % Propositional check models : 0
% 0.25/0.77 % Propositional check unsatisfiable : 0
% 0.25/0.77 % Propositional clauses : 0
% 0.25/0.77 % Propositional clauses after purity: 0
% 0.25/0.77 % Propositional unsat core size : 0
% 0.25/0.77 % Propositional preprocessing time : 0.000
% 0.25/0.77 % Propositional encoding time : 0.000
% 0.25/0.77 % Propositional solver time : 0.000
% 0.25/0.77 % Success case prop preproc time : 0.000
% 0.25/0.77 % Success case prop encoding time : 0.000
% 0.25/0.77 % Success case prop solver time : 0.000
% 0.25/0.77 % Current number of processed clauses : 196
% 0.25/0.77 % Positive orientable unit clauses : 22
% 0.25/0.77 % Positive unorientable unit clauses: 0
% 0.25/0.77 % Negative unit clauses : 4
% 0.25/0.77 % Non-unit-clauses : 170
% 0.25/0.77 % Current number of unprocessed clauses: 925
% 0.25/0.77 % ...number of literals in the above : 4544
% 0.25/0.77 % Current number of archived formulas : 0
% 0.25/0.77 % Current number of archived clauses : 86
% 0.25/0.77 % Clause-clause subsumption calls (NU) : 10169
% 0.25/0.77 % Rec. Clause-clause subsumption calls : 3829
% 0.25/0.77 % Non-unit clause-clause subsumptions : 134
% 0.25/0.77 % Unit Clause-clause subsumption calls : 434
% 0.25/0.77 % Rewrite failures with RHS unbound : 0
% 0.25/0.77 % BW rewrite match attempts : 19
% 0.25/0.77 % BW rewrite match successes : 1
% 0.25/0.77 % Condensation attempts : 0
% 0.25/0.77 % Condensation successes : 0
% 0.25/0.77 % Termbank termtop insertions : 30380
% 0.25/0.77 % Search garbage collected termcells : 1128
% 0.25/0.77
% 0.25/0.77 % -------------------------------------------------
% 0.25/0.77 % User time : 0.087 s
% 0.25/0.77 % System time : 0.009 s
% 0.25/0.77 % Total time : 0.096 s
% 0.25/0.77 % Maximum resident set size: 3408 pages
% 0.25/0.77
% 0.25/0.77 % -------------------------------------------------
% 0.25/0.77 % User time : 0.548 s
% 0.25/0.77 % System time : 0.049 s
% 0.25/0.77 % Total time : 0.597 s
% 0.25/0.77 % Maximum resident set size: 4864 pages
% 0.25/0.77 % E exiting
%------------------------------------------------------------------------------