%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO045-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:27:00 PM UTC 2026
% Result : Unsatisfiable 187.99s 38.24s
% Output : CNFRefutation 187.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 55 ( 28 unt; 5 nHn; 41 RR)
% Number of literals : 122 ( 24 equ; 68 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 159 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(identity_for_betweeness,axiom,
( ~ between(X1,X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(inner_pasch1,axiom,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X2,inner_pasch(X1,X2,X3,X5,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(transitivity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(inner_pasch2,axiom,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X5,inner_pasch(X1,X2,X3,X5,X4),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
cnf(outer_five_segment,axiom,
( ~ between(X3,X4,X6)
| ~ between(X1,X2,X5)
| ~ equidistant(X2,X7,X4,X8)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X7,X6,X8)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
cnf(w_between_v_and_x,hypothesis,
between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_v_and_x) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(v_not_w,hypothesis,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_not_w) ).
cnf(prove_v_between_u_and_x,negated_conjecture,
~ between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_between_u_and_x) ).
cnf(c_0_13,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
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,X5,X3)
| ~ between(X1,X2,X3)
| between(X2,inner_pasch(X1,X2,X3,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[inner_pasch1]) ).
cnf(c_0_16,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
c_0_13 ).
cnf(c_0_17,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_18,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
c_0_14 ).
cnf(c_0_19,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X2,inner_pasch(X1,X2,X3,X5,X4),X4) ),
c_0_15 ).
cnf(c_0_20,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_21,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[transitivity_for_equidistance]) ).
cnf(c_0_23,plain,
( ~ between(X1,X2,X3)
| ~ between(X2,X4,X3)
| inner_pasch(X1,X2,X3,X4,X2) = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
c_0_22 ).
cnf(c_0_26,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_27,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X5,inner_pasch(X1,X2,X3,X5,X4),X1) ),
inference(fof_simplification,[status(thm)],[inner_pasch2]) ).
cnf(c_0_28,plain,
( ~ between(X1,X2,X3)
| inner_pasch(X1,X2,X3,X3,X2) = X2 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ between(X3,X4,X6)
| ~ between(X1,X2,X5)
| ~ equidistant(X2,X7,X4,X8)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X7,X6,X8)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[outer_five_segment]) ).
cnf(c_0_30,plain,
( ~ equidistant(X4,X3,X1,X2)
| equidistant(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,hypothesis,
between(v,w,x),
w_between_v_and_x ).
cnf(c_0_32,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X5,inner_pasch(X1,X2,X3,X5,X4),X1) ),
c_0_27 ).
cnf(c_0_33,plain,
inner_pasch(X1,X2,extension(X1,X2,X3,X4),extension(X1,X2,X3,X4),X2) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_34,plain,
( ~ between(X3,X4,X6)
| ~ between(X1,X2,X5)
| ~ equidistant(X2,X7,X4,X8)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X7,X6,X8)
| X1 = X2 ),
c_0_29 ).
cnf(c_0_35,plain,
equidistant(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_36,hypothesis,
( ~ between(X1,v,x)
| inner_pasch(X1,v,x,w,v) = v ),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_37,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]),c_0_20])]) ).
cnf(c_0_38,plain,
( ~ between(X1,X2,X3)
| ~ between(X4,X1,X3)
| inner_pasch(X1,X2,X3,X1,X4) = X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_39,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_40,plain,
( ~ equidistant(X1,X2,X6,X2)
| ~ equidistant(X1,X4,X6,X4)
| ~ equidistant(X2,X3,X2,X5)
| ~ between(X1,X2,X3)
| ~ between(X6,X2,X5)
| equidistant(X3,X4,X5,X4)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
inner_pasch(extension(x,v,X1,X2),v,x,w,v) = v,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,hypothesis,
v != w,
inference(fof_simplification,[status(thm)],[v_not_w]) ).
cnf(c_0_43,hypothesis,
( ~ between(v,X1,w)
| inner_pasch(v,X1,w,v,u) = v ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( ~ equidistant(X1,X2,X6,X2)
| ~ equidistant(X1,X5,X6,X5)
| ~ between(X6,X2,X4)
| ~ between(X1,X2,extension(X3,X2,X2,X4))
| equidistant(extension(X3,X2,X2,X4),X5,X4,X5)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_40,c_0_17]) ).
cnf(c_0_45,hypothesis,
between(w,v,extension(x,v,X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_31]),c_0_37])]) ).
cnf(c_0_46,hypothesis,
v != w,
c_0_42 ).
cnf(c_0_47,hypothesis,
inner_pasch(v,w,w,v,u) = v,
inference(spm,[status(thm)],[c_0_43,c_0_24]) ).
cnf(c_0_48,hypothesis,
( ~ equidistant(w,X2,X3,X2)
| ~ equidistant(w,v,X3,v)
| ~ between(X3,v,X1)
| equidistant(extension(x,v,v,X1),X2,X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_49,hypothesis,
between(w,v,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_47]),c_0_39]),c_0_24])]) ).
cnf(c_0_50,hypothesis,
equidistant(extension(x,v,v,u),X1,u,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_35]),c_0_35])]) ).
cnf(c_0_51,negated_conjecture,
~ between(u,v,x),
inference(fof_simplification,[status(thm)],[prove_v_between_u_and_x]) ).
cnf(c_0_52,hypothesis,
extension(x,v,v,u) = u,
inference(spm,[status(thm)],[c_0_16,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
~ between(u,v,x),
c_0_51 ).
cnf(c_0_54,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO045-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 08:37:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 187.99/38.24 % Version: 3.5.1
% 187.99/38.24 % Preprocessing class: FSMSSMSSSSSNFFN.
% 187.99/38.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 187.99/38.24 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 187.99/38.24 % Starting new_bool_3 with 300s (1) cores
% 187.99/38.24 % Starting new_bool_1 with 300s (1) cores
% 187.99/38.24 % Starting sh5l with 300s (1) cores
% 187.99/38.24 % new_bool_1 with pid 3254224 completed with status 9
% 187.99/38.24 % new_bool_3 with pid 3254223 completed with status 9
% 187.99/38.24 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3254222 completed with status 0
% 187.99/38.24 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 187.99/38.24 % Preprocessing class: FSMSSMSSSSSNFFN.
% 187.99/38.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 187.99/38.24 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 187.99/38.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 187.99/38.24 % No SInE strategy applied
% 187.99/38.24 % Search class: FGUSS-FFMF33-SFFFFFNN
% 187.99/38.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 187.99/38.24 % Starting SubtermCWHack with 136s (1) cores
% 187.99/38.24 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 187.99/38.24 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 187.99/38.24 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 187.99/38.24 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 187.99/38.24 % 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 3254233 completed with status 0
% 187.99/38.24 % Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 187.99/38.24 % Preprocessing class: FSMSSMSSSSSNFFN.
% 187.99/38.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 187.99/38.24 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 187.99/38.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 187.99/38.24 % No SInE strategy applied
% 187.99/38.24 % Search class: FGUSS-FFMF33-SFFFFFNN
% 187.99/38.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 187.99/38.24 % Starting SubtermCWHack with 136s (1) cores
% 187.99/38.24 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 187.99/38.24 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 187.99/38.24 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 187.99/38.24 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 187.99/38.24 % Preprocessing time : 0.001 s
% 187.99/38.24 % Presaturation interreduction done
% 187.99/38.24
% 187.99/38.24 % Proof found!
% 187.99/38.24 % SZS status Unsatisfiable
% 187.99/38.24 % SZS output start CNFRefutation
% See solution above
% 187.99/38.25 % Parsed axioms : 22
% 187.99/38.25 % Removed by relevancy pruning/SinE : 0
% 187.99/38.25 % Initial clauses : 22
% 187.99/38.25 % Removed in clause preprocessing : 0
% 187.99/38.25 % Initial clauses in saturation : 22
% 187.99/38.25 % Processed clauses : 102928
% 187.99/38.25 % ...of these trivial : 2765
% 187.99/38.25 % ...subsumed : 86194
% 187.99/38.25 % ...remaining for further processing : 13969
% 187.99/38.25 % Other redundant clauses eliminated : 0
% 187.99/38.25 % Clauses deleted for lack of memory : 0
% 187.99/38.25 % Backward-subsumed : 704
% 187.99/38.25 % Backward-rewritten : 312
% 187.99/38.25 % Generated clauses : 1196845
% 187.99/38.25 % ...of the previous two non-redundant : 1113814
% 187.99/38.25 % ...aggressively subsumed : 0
% 187.99/38.25 % Contextual simplify-reflections : 12
% 187.99/38.25 % Paramodulations : 1196845
% 187.99/38.25 % Factorizations : 0
% 187.99/38.25 % NegExts : 0
% 187.99/38.25 % Equation resolutions : 0
% 187.99/38.25 % Disequality decompositions : 0
% 187.99/38.25 % Total rewrite steps : 300244
% 187.99/38.25 % ...of those cached : 295242
% 187.99/38.25 % Propositional unsat checks : 0
% 187.99/38.25 % Propositional check models : 0
% 187.99/38.25 % Propositional check unsatisfiable : 0
% 187.99/38.25 % Propositional clauses : 0
% 187.99/38.25 % Propositional clauses after purity: 0
% 187.99/38.25 % Propositional unsat core size : 0
% 187.99/38.25 % Propositional preprocessing time : 0.000
% 187.99/38.25 % Propositional encoding time : 0.000
% 187.99/38.25 % Propositional solver time : 0.000
% 187.99/38.25 % Success case prop preproc time : 0.000
% 187.99/38.25 % Success case prop encoding time : 0.000
% 187.99/38.25 % Success case prop solver time : 0.000
% 187.99/38.25 % Current number of processed clauses : 12931
% 187.99/38.25 % Positive orientable unit clauses : 1199
% 187.99/38.25 % Positive unorientable unit clauses: 0
% 187.99/38.25 % Negative unit clauses : 5
% 187.99/38.25 % Non-unit-clauses : 11727
% 187.99/38.25 % Current number of unprocessed clauses: 1009126
% 187.99/38.25 % ...number of literals in the above : 3185760
% 187.99/38.25 % Current number of archived formulas : 0
% 187.99/38.25 % Current number of archived clauses : 1038
% 187.99/38.25 % Clause-clause subsumption calls (NU) : 60916718
% 187.99/38.25 % Rec. Clause-clause subsumption calls : 46155407
% 187.99/38.25 % Non-unit clause-clause subsumptions : 86893
% 187.99/38.25 % Unit Clause-clause subsumption calls : 123821
% 187.99/38.25 % Rewrite failures with RHS unbound : 0
% 187.99/38.25 % BW rewrite match attempts : 194201
% 187.99/38.25 % BW rewrite match successes : 247
% 187.99/38.25 % Condensation attempts : 0
% 187.99/38.25 % Condensation successes : 0
% 187.99/38.25 % Termbank termtop insertions : 29491616
% 187.99/38.25 % Search garbage collected termcells : 77
% 187.99/38.25
% 187.99/38.25 % -------------------------------------------------
% 187.99/38.25 % User time : 36.537 s
% 187.99/38.25 % System time : 0.751 s
% 187.99/38.25 % Total time : 37.288 s
% 187.99/38.25 % Maximum resident set size: 3348 pages
% 187.99/38.25
% 187.99/38.25 % -------------------------------------------------
% 187.99/38.25 % User time : 182.470 s
% 187.99/38.25 % System time : 5.462 s
% 187.99/38.25 % Total time : 187.933 s
% 187.99/38.25 % Maximum resident set size: 4608 pages
% 187.99/38.25 % E exiting
%------------------------------------------------------------------------------