%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GEO124+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 : n008.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 12:29:10 PM UTC 2026
% Result : Theorem 0.23s 0.67s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 136 ( 16 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 159 ( 54 ~; 57 |; 37 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-5 aty)
% Number of variables : 84 ( 4 sgn 58 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(start_point_defn,axiom,
! [X3,X9] :
( start_point(X3,X9)
<=> ( ! [X5] :
( ( incident_o(X5,X9)
& X3 != X5 )
=> ordered_by(X9,X3,X5) )
& incident_o(X3,X9) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',start_point_defn) ).
fof(corollary_4_10_1,conjecture,
! [X9,X3,X5] :
( ( start_point(X5,X9)
& start_point(X3,X9) )
=> X3 = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_4_10_1) ).
fof(between_o_defn,axiom,
! [X9,X3,X5,X7] :
( between_o(X9,X3,X5,X7)
<=> ( ( ordered_by(X9,X5,X3)
& ordered_by(X9,X7,X5) )
| ( ordered_by(X9,X5,X7)
& ordered_by(X9,X3,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',between_o_defn) ).
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(o3,axiom,
! [X3,X5,X7,X9] :
( between_o(X9,X3,X5,X7)
<=> ? [X1] :
( between_c(X1,X3,X5,X7)
& ! [X3] :
( incident_o(X3,X9)
<=> incident_c(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o3) ).
fof(c_0_5,plain,
! [X3,X9] :
( start_point(X3,X9)
<=> ( ! [X5] :
( ( incident_o(X5,X9)
& X3 != X5 )
=> ordered_by(X9,X3,X5) )
& incident_o(X3,X9) ) ),
inference(fof_simplification,[status(thm)],[start_point_defn]) ).
fof(c_0_6,negated_conjecture,
~ ! [X9,X3,X5] :
( ( start_point(X5,X9)
& start_point(X3,X9) )
=> X3 = X5 ),
inference(assume_negation,[status(cth)],[corollary_4_10_1]) ).
fof(c_0_7,plain,
! [X99,X100,X101,X102,X103] :
( ( start_point(X102,X103)
| ~ incident_o(X102,X103)
| ~ ordered_by(X103,X102,esk15_2(X102,X103)) )
& ( start_point(X102,X103)
| ~ incident_o(X102,X103)
| incident_o(esk15_2(X102,X103),X103) )
& ( start_point(X102,X103)
| ~ incident_o(X102,X103)
| X102 != esk15_2(X102,X103) )
& ( ~ start_point(X99,X100)
| ordered_by(X100,X99,X101)
| ~ incident_o(X101,X100)
| X99 = X101 )
& ( ~ start_point(X99,X100)
| incident_o(X99,X100) ) ),
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_8,negated_conjecture,
( esk26_0 != esk27_0
& start_point(esk27_0,esk25_0)
& start_point(esk26_0,esk25_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_9,plain,
( ~ start_point(X1,X3)
| ~ incident_o(X2,X3)
| ordered_by(X3,X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
start_point(esk26_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( ~ start_point(X1,X2)
| incident_o(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
start_point(esk27_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X95,X96,X97,X98] :
( ( between_o(X95,X96,X97,X98)
| ~ ordered_by(X95,X97,X96)
| ~ ordered_by(X95,X98,X97) )
& ( between_o(X95,X96,X97,X98)
| ~ ordered_by(X95,X97,X98)
| ~ ordered_by(X95,X96,X97) )
& ( ~ between_o(X95,X96,X97,X98)
| ordered_by(X95,X97,X98)
| ordered_by(X95,X97,X96) )
& ( ~ between_o(X95,X96,X97,X98)
| ordered_by(X95,X97,X98)
| ordered_by(X95,X98,X97) )
& ( ~ between_o(X95,X96,X97,X98)
| ordered_by(X95,X96,X97)
| ordered_by(X95,X97,X96) )
& ( ~ between_o(X95,X96,X97,X98)
| ordered_by(X95,X96,X97)
| ordered_by(X95,X98,X97) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[between_o_defn])])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ incident_o(X1,esk25_0)
| ordered_by(esk25_0,esk26_0,X1)
| esk26_0 = X1 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
incident_o(esk27_0,esk25_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
esk26_0 != esk27_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_17,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]) ).
cnf(c_0_18,plain,
( ~ ordered_by(X1,X3,X4)
| ~ ordered_by(X1,X2,X3)
| between_o(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
ordered_by(esk25_0,esk26_0,esk27_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( ~ incident_o(X1,esk25_0)
| ordered_by(esk25_0,esk27_0,X1)
| esk27_0 = X1 ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
incident_o(esk26_0,esk25_0),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
fof(c_0_22,plain,
! [X85,X86,X87,X88,X90,X91,X92,X93,X94] :
( ( between_c(X90,X91,X92,X93)
| ~ inner_point(X92,X94)
| ~ end_point(X93,X94)
| ~ end_point(X91,X94)
| ~ part_of(X94,X90)
| X91 = X93 )
& ( ~ between_c(X85,X86,X87,X88)
| inner_point(X87,esk14_4(X85,X86,X87,X88)) )
& ( ~ between_c(X85,X86,X87,X88)
| end_point(X88,esk14_4(X85,X86,X87,X88)) )
& ( ~ between_c(X85,X86,X87,X88)
| end_point(X86,esk14_4(X85,X86,X87,X88)) )
& ( ~ between_c(X85,X86,X87,X88)
| part_of(esk14_4(X85,X86,X87,X88),X85) )
& ( ~ between_c(X85,X86,X87,X88)
| X86 != X88 ) ),
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_17])])])])])])]) ).
fof(c_0_23,plain,
! [X118,X119,X120,X121,X123,X124,X125,X126,X127,X128,X129] :
( ( between_o(X128,X125,X126,X127)
| ~ between_c(X129,X125,X126,X127)
| incident_c(esk19_5(X125,X126,X127,X128,X129),X129)
| incident_o(esk19_5(X125,X126,X127,X128,X129),X128) )
& ( between_o(X128,X125,X126,X127)
| ~ between_c(X129,X125,X126,X127)
| ~ incident_c(esk19_5(X125,X126,X127,X128,X129),X129)
| ~ incident_o(esk19_5(X125,X126,X127,X128,X129),X128) )
& ( ~ between_o(X121,X118,X119,X120)
| between_c(esk18_4(X118,X119,X120,X121),X118,X119,X120) )
& ( ~ between_o(X121,X118,X119,X120)
| incident_o(X124,X121)
| ~ incident_c(X124,esk18_4(X118,X119,X120,X121)) )
& ( ~ between_o(X121,X118,X119,X120)
| incident_c(X123,esk18_4(X118,X119,X120,X121))
| ~ incident_o(X123,X121) ) ),
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)],[o3])])])])])])]) ).
cnf(c_0_24,negated_conjecture,
( ~ ordered_by(esk25_0,X1,esk26_0)
| between_o(esk25_0,X1,esk26_0,esk27_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
ordered_by(esk25_0,esk27_0,esk26_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_16]) ).
cnf(c_0_26,plain,
( ~ between_c(X3,X1,X4,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ between_o(X4,X1,X2,X3)
| between_c(esk18_4(X1,X2,X3,X4),X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
between_o(esk25_0,esk27_0,esk26_0,esk27_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
~ between_c(X1,X2,X3,X2),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 % Computer : n008.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Sun Sep 20 11:56:54 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.57 Running first-order theorem proving
% 0.23/0.57 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
% 0.23/0.67 % Version: 3.5.1
% 0.23/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.67 % Starting sh5l with 300s (1) cores
% 0.23/0.67 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2873334 completed with status 0
% 0.23/0.67 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.67 % No SInE strategy applied
% 0.23/0.67 % Search class: FGHSS-FFMF32-SFFFFFNN
% 0.23/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.67 % Starting G-E--_207_B07_F1_AE_CS_SP_PS_S0Y with 253s (1) cores
% 0.23/0.67 % Starting new_bool_3 with 248s (1) cores
% 0.23/0.67 % Starting new_bool_1 with 241s (1) cores
% 0.23/0.67 % new_bool_3 with pid 2873343 completed with status 0
% 0.23/0.67 % Result found by new_bool_3
% 0.23/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.67 % No SInE strategy applied
% 0.23/0.67 % Search class: FGHSS-FFMF32-SFFFFFNN
% 0.23/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.67 % Starting G-E--_207_B07_F1_AE_CS_SP_PS_S0Y with 253s (1) cores
% 0.23/0.67 % Starting new_bool_3 with 248s (1) cores
% 0.23/0.67 % Preprocessing time : 0.004 s
% 0.23/0.67 % Presaturation interreduction done
% 0.23/0.67
% 0.23/0.67 % Proof found!
% 0.23/0.67 % SZS status Theorem
% 0.23/0.67 % SZS output start CNFRefutation
% See solution above
% 0.23/0.67 % Parsed axioms : 28
% 0.23/0.67 % Removed by relevancy pruning/SinE : 0
% 0.23/0.67 % Initial clauses : 88
% 0.23/0.67 % Removed in clause preprocessing : 0
% 0.23/0.67 % Initial clauses in saturation : 88
% 0.23/0.67 % Processed clauses : 270
% 0.23/0.67 % ...of these trivial : 2
% 0.23/0.67 % ...subsumed : 7
% 0.23/0.67 % ...remaining for further processing : 261
% 0.23/0.67 % Other redundant clauses eliminated : 7
% 0.23/0.67 % Clauses deleted for lack of memory : 0
% 0.23/0.67 % Backward-subsumed : 0
% 0.23/0.67 % Backward-rewritten : 0
% 0.23/0.67 % Generated clauses : 596
% 0.23/0.67 % ...of the previous two non-redundant : 506
% 0.23/0.67 % ...aggressively subsumed : 0
% 0.23/0.67 % Contextual simplify-reflections : 2
% 0.23/0.67 % Paramodulations : 587
% 0.23/0.67 % Factorizations : 2
% 0.23/0.67 % NegExts : 0
% 0.23/0.67 % Equation resolutions : 7
% 0.23/0.67 % Disequality decompositions : 0
% 0.23/0.67 % Total rewrite steps : 83
% 0.23/0.67 % ...of those cached : 57
% 0.23/0.67 % Propositional unsat checks : 0
% 0.23/0.67 % Propositional check models : 0
% 0.23/0.67 % Propositional check unsatisfiable : 0
% 0.23/0.67 % Propositional clauses : 0
% 0.23/0.67 % Propositional clauses after purity: 0
% 0.23/0.67 % Propositional unsat core size : 0
% 0.23/0.67 % Propositional preprocessing time : 0.000
% 0.23/0.67 % Propositional encoding time : 0.000
% 0.23/0.67 % Propositional solver time : 0.000
% 0.23/0.67 % Success case prop preproc time : 0.000
% 0.23/0.67 % Success case prop encoding time : 0.000
% 0.23/0.67 % Success case prop solver time : 0.000
% 0.23/0.67 % Current number of processed clauses : 166
% 0.23/0.67 % Positive orientable unit clauses : 51
% 0.23/0.67 % Positive unorientable unit clauses: 0
% 0.23/0.67 % Negative unit clauses : 3
% 0.23/0.67 % Non-unit-clauses : 112
% 0.23/0.67 % Current number of unprocessed clauses: 412
% 0.23/0.67 % ...number of literals in the above : 946
% 0.23/0.67 % Current number of archived formulas : 0
% 0.23/0.67 % Current number of archived clauses : 88
% 0.23/0.67 % Clause-clause subsumption calls (NU) : 2958
% 0.23/0.67 % Rec. Clause-clause subsumption calls : 1662
% 0.23/0.67 % Non-unit clause-clause subsumptions : 9
% 0.23/0.67 % Unit Clause-clause subsumption calls : 485
% 0.23/0.67 % Rewrite failures with RHS unbound : 0
% 0.23/0.67 % BW rewrite match attempts : 10
% 0.23/0.67 % BW rewrite match successes : 0
% 0.23/0.67 % Condensation attempts : 0
% 0.23/0.67 % Condensation successes : 0
% 0.23/0.67 % Termbank termtop insertions : 15365
% 0.23/0.67 % Search garbage collected termcells : 1942
% 0.23/0.67
% 0.23/0.67 % -------------------------------------------------
% 0.23/0.67 % User time : 0.033 s
% 0.23/0.67 % System time : 0.008 s
% 0.23/0.67 % Total time : 0.041 s
% 0.23/0.67 % Maximum resident set size: 3676 pages
% 0.23/0.67
% 0.23/0.67 % -------------------------------------------------
% 0.23/0.67 % User time : 0.103 s
% 0.23/0.67 % System time : 0.025 s
% 0.23/0.67 % Total time : 0.128 s
% 0.23/0.67 % Maximum resident set size: 4864 pages
% 0.23/0.67 % E exiting
%------------------------------------------------------------------------------