%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 43 ( 20 unt; 3 nHn; 37 RR)
% Number of literals : 76 ( 18 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 86 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_betweeness,axiom,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).
cnf(c_between_a_and_d,hypothesis,
between(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_d) ).
cnf(identity_for_betweeness,axiom,
( ~ between(X1,X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
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/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).
cnf(prove_not_between_others,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_between_others) ).
cnf(a_not_c,hypothesis,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
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/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).
cnf(c_not_d,hypothesis,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_d) ).
cnf(c_0_11,plain,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[transitivity_for_betweeness]) ).
cnf(c_0_12,plain,
( ~ between(X2,X4,X3)
| ~ between(X1,X2,X3)
| between(X1,X2,X4) ),
c_0_11 ).
cnf(c_0_13,hypothesis,
between(a,c,d),
c_between_a_and_d ).
cnf(c_0_14,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_betweeness]) ).
cnf(c_0_15,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_16,hypothesis,
( ~ between(X1,a,d)
| between(X1,a,c) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ),
prove_not_between_others ).
cnf(c_0_18,hypothesis,
a != c,
inference(fof_simplification,[status(thm)],[a_not_c]) ).
cnf(c_0_19,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
cnf(c_0_20,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
c_0_14 ).
cnf(c_0_21,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X1,outer_pasch(X2,X1,X4,X5,X3),X4) ),
c_0_15 ).
cnf(c_0_22,negated_conjecture,
( between(c,a,c)
| between(a,d,c) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,hypothesis,
a != c,
c_0_18 ).
cnf(c_0_24,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
c_0_19 ).
cnf(c_0_25,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_26,plain,
( ~ between(X2,X1,X4)
| ~ between(X2,X4,X3)
| outer_pasch(X1,X2,X2,X3,X4) = X2 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
between(a,d,c),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_22]),c_0_23]) ).
cnf(c_0_28,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_29,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,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_31,negated_conjecture,
( ~ between(a,X1,d)
| outer_pasch(X1,a,a,c,d) = a ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( ~ between(X4,X3,X5)
| ~ between(X1,X2,X3)
| between(X5,X2,outer_pasch(X2,X1,X4,X5,X3)) ),
c_0_30 ).
cnf(c_0_34,negated_conjecture,
outer_pasch(d,a,a,c,d) = a,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
between(c,d,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27]),c_0_32])]) ).
cnf(c_0_36,hypothesis,
c != d,
inference(fof_simplification,[status(thm)],[c_not_d]) ).
cnf(c_0_37,hypothesis,
( ~ between(a,X1,c)
| outer_pasch(X1,a,a,d,c) = a ),
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_38,negated_conjecture,
( ~ between(X1,c,a)
| between(X1,c,d) ),
inference(spm,[status(thm)],[c_0_12,c_0_35]) ).
cnf(c_0_39,hypothesis,
c != d,
c_0_36 ).
cnf(c_0_40,hypothesis,
outer_pasch(c,a,a,d,c) = a,
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
~ between(d,c,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_38]),c_0_39]) ).
cnf(c_0_42,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_13]),c_0_32])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 08:15:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 790185 completed with status 0
% 0.10/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FGUSS-FFMF33-SFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.45 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.10/0.45 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.10/0.45 % 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 790197 completed with status 0
% 0.10/0.45 % Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FGUSS-FFMF33-SFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.45 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.10/0.45 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.10/0.45 % Preprocessing time : 0.001 s
% 0.10/0.45 % Presaturation interreduction done
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 25
% 0.10/0.45 % Removed by relevancy pruning/SinE : 0
% 0.10/0.45 % Initial clauses : 25
% 0.10/0.45 % Removed in clause preprocessing : 0
% 0.10/0.45 % Initial clauses in saturation : 25
% 0.10/0.45 % Processed clauses : 93
% 0.10/0.45 % ...of these trivial : 1
% 0.10/0.45 % ...subsumed : 0
% 0.10/0.45 % ...remaining for further processing : 92
% 0.10/0.45 % Other redundant clauses eliminated : 0
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 0
% 0.10/0.45 % Backward-rewritten : 4
% 0.10/0.45 % Generated clauses : 146
% 0.10/0.45 % ...of the previous two non-redundant : 112
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 0
% 0.10/0.45 % Paramodulations : 146
% 0.10/0.45 % Factorizations : 0
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 0
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 46
% 0.10/0.45 % ...of those cached : 31
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 63
% 0.10/0.45 % Positive orientable unit clauses : 15
% 0.10/0.45 % Positive unorientable unit clauses: 0
% 0.10/0.45 % Negative unit clauses : 8
% 0.10/0.45 % Non-unit-clauses : 40
% 0.10/0.45 % Current number of unprocessed clauses: 67
% 0.10/0.45 % ...number of literals in the above : 289
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 29
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 640
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 308
% 0.10/0.45 % Non-unit clause-clause subsumptions : 0
% 0.10/0.45 % Unit Clause-clause subsumption calls : 82
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 102
% 0.10/0.45 % BW rewrite match successes : 3
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 3132
% 0.10/0.45 % Search garbage collected termcells : 84
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.012 s
% 0.10/0.45 % System time : 0.001 s
% 0.10/0.45 % Total time : 0.013 s
% 0.10/0.45 % Maximum resident set size: 3656 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.051 s
% 0.10/0.45 % System time : 0.014 s
% 0.10/0.45 % Total time : 0.065 s
% 0.10/0.45 % Maximum resident set size: 4608 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------