%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:26:49 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 38 ( 16 unt; 0 nHn; 22 RR)
% Number of literals : 72 ( 0 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 129 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X3,X3)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
cnf(transitivity_for_betweeness,axiom,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
cnf(between_substitution3,axiom,
( ~ between(X3,X4,X1)
| ~ equalish(X1,X2)
| between(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_substitution3) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
cnf(outer_pasch1,axiom,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X1,outer_pasch(X2,X1,X4,X5,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch1) ).
cnf(outer_pasch2,axiom,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch2) ).
cnf(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
cnf(c_0_8,plain,
( ~ equidistant(X1,X2,X3,X3)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
cnf(c_0_9,plain,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[transitivity_for_betweeness]) ).
cnf(c_0_10,plain,
( ~ between(X3,X4,X1)
| ~ equalish(X1,X2)
| between(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[between_substitution3]) ).
cnf(c_0_11,plain,
( ~ equidistant(X1,X2,X3,X3)
| equalish(X1,X2) ),
c_0_8 ).
cnf(c_0_12,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_13,plain,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
c_0_9 ).
cnf(c_0_14,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_15,plain,
( ~ between(X3,X4,X1)
| ~ equalish(X1,X2)
| between(X3,X4,X2) ),
c_0_10 ).
cnf(c_0_16,plain,
equalish(X1,extension(X2,X1,X3,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( ~ between(X1,X2,extension(X2,X3,X4,X5))
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( ~ between(X1,X2,X4)
| between(X1,X2,extension(X3,X4,X5,X5)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
between(X1,X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_20,plain,
between(X1,X1,extension(X2,X1,X3,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X1,outer_pasch(X2,X1,X4,X5,X3),X4) ),
inference(fof_simplification,[status(thm)],[outer_pasch1]) ).
cnf(c_0_22,plain,
( ~ between(X1,X2,extension(X3,X2,X4,X4))
| between(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_23,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X1,outer_pasch(X2,X1,X4,X5,X3),X4) ),
c_0_21 ).
cnf(c_0_24,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_25,plain,
( ~ between(X1,X2,X4)
| between(X1,outer_pasch(X2,X1,X3,X4,X4),X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
between(X1,outer_pasch(X2,X1,X3,X2,X2),X3),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_27,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)) ),
inference(fof_simplification,[status(thm)],[outer_pasch2]) ).
cnf(c_0_28,plain,
( ~ between(X1,X2,X4)
| between(X1,X2,outer_pasch(X3,X2,X4,X3,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_29,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)) ),
c_0_27 ).
cnf(c_0_30,plain,
between(X1,X2,outer_pasch(X3,X2,X2,X3,X3)),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_31,plain,
( ~ between(X3,X2,X1)
| between(X1,X2,outer_pasch(X2,X3,X4,X1,X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
~ between(a,a,b),
inference(fof_simplification,[status(thm)],[prove_a_between_a_and_b]) ).
cnf(c_0_33,plain,
( ~ between(X1,X2,outer_pasch(X4,X3,X3,X4,X4))
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_30]) ).
cnf(c_0_34,plain,
between(X1,X1,outer_pasch(X1,X2,X3,X1,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_35,negated_conjecture,
~ between(a,a,b),
c_0_32 ).
cnf(c_0_36,plain,
between(X1,X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 20 08:14:27 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 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
% 0.17/0.46 % Version: 3.5.1
% 0.17/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.46 % Starting sh5l with 300s (1) cores
% 0.17/0.46 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3233036 completed with status 0
% 0.17/0.46 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.17/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.46 % No SInE strategy applied
% 0.17/0.46 % Search class: FHUNS-FFSF33-SFFFFFNN
% 0.17/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.17/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 169s (1) cores
% 0.17/0.46 % Starting new_bool_3 with 169s (1) cores
% 0.17/0.46 % Starting new_bool_1 with 169s (1) cores
% 0.17/0.46 % new_bool_3 with pid 3233046 completed with status 0
% 0.17/0.46 % Result found by new_bool_3
% 0.17/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.46 % No SInE strategy applied
% 0.17/0.46 % Search class: FHUNS-FFSF33-SFFFFFNN
% 0.17/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.17/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 169s (1) cores
% 0.17/0.46 % Starting new_bool_3 with 169s (1) cores
% 0.17/0.46 % Preprocessing time : 0.001 s
% 0.17/0.46 % Presaturation interreduction done
% 0.17/0.46
% 0.17/0.46 % Proof found!
% 0.17/0.46 % SZS status Unsatisfiable
% 0.17/0.46 % SZS output start CNFRefutation
% See solution above
% 0.17/0.46 % Parsed axioms : 8
% 0.17/0.46 % Removed by relevancy pruning/SinE : 0
% 0.17/0.46 % Initial clauses : 8
% 0.17/0.46 % Removed in clause preprocessing : 0
% 0.17/0.46 % Initial clauses in saturation : 8
% 0.17/0.46 % Processed clauses : 38
% 0.17/0.46 % ...of these trivial : 0
% 0.17/0.46 % ...subsumed : 1
% 0.17/0.46 % ...remaining for further processing : 37
% 0.17/0.46 % Other redundant clauses eliminated : 0
% 0.17/0.46 % Clauses deleted for lack of memory : 0
% 0.17/0.46 % Backward-subsumed : 2
% 0.17/0.46 % Backward-rewritten : 5
% 0.17/0.46 % Generated clauses : 104
% 0.17/0.46 % ...of the previous two non-redundant : 84
% 0.17/0.46 % ...aggressively subsumed : 0
% 0.17/0.46 % Contextual simplify-reflections : 0
% 0.17/0.46 % Paramodulations : 104
% 0.17/0.46 % Factorizations : 0
% 0.17/0.46 % NegExts : 0
% 0.17/0.46 % Equation resolutions : 0
% 0.17/0.46 % Disequality decompositions : 0
% 0.17/0.46 % Total rewrite steps : 12
% 0.17/0.46 % ...of those cached : 6
% 0.17/0.46 % Propositional unsat checks : 0
% 0.17/0.46 % Propositional check models : 0
% 0.17/0.46 % Propositional check unsatisfiable : 0
% 0.17/0.46 % Propositional clauses : 0
% 0.17/0.46 % Propositional clauses after purity: 0
% 0.17/0.46 % Propositional unsat core size : 0
% 0.17/0.46 % Propositional preprocessing time : 0.000
% 0.17/0.46 % Propositional encoding time : 0.000
% 0.17/0.46 % Propositional solver time : 0.000
% 0.17/0.46 % Success case prop preproc time : 0.000
% 0.17/0.46 % Success case prop encoding time : 0.000
% 0.17/0.46 % Success case prop solver time : 0.000
% 0.17/0.46 % Current number of processed clauses : 22
% 0.17/0.46 % Positive orientable unit clauses : 9
% 0.17/0.46 % Positive unorientable unit clauses: 0
% 0.17/0.46 % Negative unit clauses : 0
% 0.17/0.46 % Non-unit-clauses : 13
% 0.17/0.46 % Current number of unprocessed clauses: 58
% 0.17/0.46 % ...number of literals in the above : 71
% 0.17/0.46 % Current number of archived formulas : 0
% 0.17/0.46 % Current number of archived clauses : 15
% 0.17/0.46 % Clause-clause subsumption calls (NU) : 91
% 0.17/0.46 % Rec. Clause-clause subsumption calls : 88
% 0.17/0.46 % Non-unit clause-clause subsumptions : 3
% 0.17/0.46 % Unit Clause-clause subsumption calls : 43
% 0.17/0.46 % Rewrite failures with RHS unbound : 0
% 0.17/0.46 % BW rewrite match attempts : 141
% 0.17/0.46 % BW rewrite match successes : 5
% 0.17/0.46 % Condensation attempts : 0
% 0.17/0.46 % Condensation successes : 0
% 0.17/0.46 % Termbank termtop insertions : 1118
% 0.17/0.46 % Search garbage collected termcells : 22
% 0.17/0.46
% 0.17/0.46 % -------------------------------------------------
% 0.17/0.46 % User time : 0.004 s
% 0.17/0.46 % System time : 0.004 s
% 0.17/0.46 % Total time : 0.008 s
% 0.17/0.46 % Maximum resident set size: 3376 pages
% 0.17/0.46
% 0.17/0.46 % -------------------------------------------------
% 0.17/0.46 % User time : 0.025 s
% 0.17/0.46 % System time : 0.014 s
% 0.17/0.46 % Total time : 0.039 s
% 0.17/0.46 % Maximum resident set size: 4608 pages
% 0.17/0.46 % E exiting
%------------------------------------------------------------------------------