%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO025-2 : 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 : n015.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 12:26:55 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 57 ( 32 unt; 4 nHn; 48 RR)
% Number of literals : 119 ( 15 equ; 62 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-5 aty)
% Number of variables : 134 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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(identity_for_betweeness,axiom,
( ~ between(X1,X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
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(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
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(identity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
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(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
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(v_to_w_equals_v1_to_w1,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
cnf(prove_equal_sums,negated_conjecture,
~ equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_sums) ).
cnf(v1_between_u1_and_w1,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(c_0_14,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_15,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_betweeness]) ).
cnf(c_0_16,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_17,plain,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
c_0_14 ).
cnf(c_0_18,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_19,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_20,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
c_0_15 ).
cnf(c_0_21,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X5,inner_pasch(X1,X2,X3,X5,X4),X1) ),
c_0_16 ).
cnf(c_0_22,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
cnf(c_0_23,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_24,plain,
( ~ equidistant(X4,X3,X1,X2)
| equidistant(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,hypothesis,
equidistant(u,v,u1,v1),
u_to_v_equals_u1_to_v1 ).
cnf(c_0_26,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X2,inner_pasch(X1,X2,X3,X5,X4),X4) ),
c_0_19 ).
cnf(c_0_27,plain,
( ~ between(X1,X2,X3)
| ~ between(X4,X1,X3)
| inner_pasch(X1,X2,X3,X1,X4) = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
c_0_22 ).
cnf(c_0_29,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_30,hypothesis,
equidistant(v,w,v1,w1),
v_to_w_equals_v1_to_w1 ).
cnf(c_0_31,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_23 ).
cnf(c_0_32,hypothesis,
equidistant(u1,v1,v,u),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
~ equidistant(u,w,u1,w1),
inference(fof_simplification,[status(thm)],[prove_equal_sums]) ).
cnf(c_0_34,plain,
( ~ between(X2,X1,X4)
| ~ between(X3,X2,X4)
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,hypothesis,
between(u1,v1,w1),
v1_between_u1_and_w1 ).
cnf(c_0_36,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_37,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_39,hypothesis,
equidistant(v1,w1,w,v),
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
cnf(c_0_40,hypothesis,
( ~ equidistant(X1,v,X4,v1)
| ~ equidistant(X1,w,X4,w1)
| ~ equidistant(v,X2,v1,X3)
| ~ between(X1,v,X2)
| ~ between(X4,v1,X3)
| equidistant(X2,w,X3,w1)
| X1 = v ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_41,hypothesis,
equidistant(v,u,v1,u1),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_42,negated_conjecture,
~ equidistant(u,w,u1,w1),
c_0_33 ).
cnf(c_0_43,hypothesis,
( ~ between(v1,X1,w1)
| between(X1,v1,u1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,hypothesis,
( ~ between(v,X1,w)
| between(X1,v,u) ),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_46,hypothesis,
equidistant(w,v,w1,v1),
inference(spm,[status(thm)],[c_0_24,c_0_39]) ).
cnf(c_0_47,hypothesis,
( ~ equidistant(X1,v,X2,v1)
| ~ equidistant(X1,w,X2,w1)
| ~ between(X1,v,u)
| ~ between(X2,v1,u1)
| X1 = v ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_48,plain,
equidistant(X1,X1,X2,X2),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_49,hypothesis,
between(w1,v1,u1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,hypothesis,
between(w,v,u),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_51,hypothesis,
equidistant(w1,v1,v,w),
inference(spm,[status(thm)],[c_0_24,c_0_46]) ).
cnf(c_0_52,hypothesis,
w = v,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]),c_0_46])]) ).
cnf(c_0_53,hypothesis,
equidistant(w1,v1,v,v),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
~ equidistant(u,v,u1,w1),
inference(rw,[status(thm)],[c_0_42,c_0_52]) ).
cnf(c_0_55,hypothesis,
w1 = v1,
inference(spm,[status(thm)],[c_0_28,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO025-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.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 08:26:06 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
% 0.10/0.46 % Version: 3.5.1
% 0.10/0.46 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % Starting sh5l with 300s (1) cores
% 0.10/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2979400 completed with status 0
% 0.10/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.10/0.46 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.46 % No SInE strategy applied
% 0.10/0.46 % Search class: FGUSS-FFMS33-SFFFFFNN
% 0.10/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S0Y with 193s (1) cores
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S0Y with 161s (1) cores
% 0.10/0.46 % Starting new_bool_3 with 161s (1) cores
% 0.10/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S0Y with pid 2979409 completed with status 0
% 0.10/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S0Y
% 0.10/0.46 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.46 % No SInE strategy applied
% 0.10/0.46 % Search class: FGUSS-FFMS33-SFFFFFNN
% 0.10/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S0Y with 193s (1) cores
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S0Y with 161s (1) cores
% 0.10/0.46 % Preprocessing time : 0.001 s
% 0.10/0.46 % Presaturation interreduction done
% 0.10/0.46
% 0.10/0.46 % Proof found!
% 0.10/0.46 % SZS status Unsatisfiable
% 0.10/0.46 % SZS output start CNFRefutation
% See solution above
% 0.10/0.46 % Parsed axioms : 23
% 0.10/0.46 % Removed by relevancy pruning/SinE : 0
% 0.10/0.46 % Initial clauses : 23
% 0.10/0.46 % Removed in clause preprocessing : 0
% 0.10/0.46 % Initial clauses in saturation : 23
% 0.10/0.46 % Processed clauses : 167
% 0.10/0.46 % ...of these trivial : 1
% 0.10/0.46 % ...subsumed : 6
% 0.10/0.46 % ...remaining for further processing : 160
% 0.10/0.46 % Other redundant clauses eliminated : 0
% 0.10/0.46 % Clauses deleted for lack of memory : 0
% 0.10/0.46 % Backward-subsumed : 2
% 0.10/0.46 % Backward-rewritten : 63
% 0.10/0.46 % Generated clauses : 607
% 0.10/0.46 % ...of the previous two non-redundant : 469
% 0.10/0.46 % ...aggressively subsumed : 0
% 0.10/0.46 % Contextual simplify-reflections : 0
% 0.10/0.46 % Paramodulations : 607
% 0.10/0.46 % Factorizations : 0
% 0.10/0.46 % NegExts : 0
% 0.10/0.46 % Equation resolutions : 0
% 0.10/0.46 % Disequality decompositions : 0
% 0.10/0.46 % Total rewrite steps : 251
% 0.10/0.46 % ...of those cached : 169
% 0.10/0.46 % Propositional unsat checks : 0
% 0.10/0.46 % Propositional check models : 0
% 0.10/0.46 % Propositional check unsatisfiable : 0
% 0.10/0.46 % Propositional clauses : 0
% 0.10/0.46 % Propositional clauses after purity: 0
% 0.10/0.46 % Propositional unsat core size : 0
% 0.10/0.46 % Propositional preprocessing time : 0.000
% 0.10/0.46 % Propositional encoding time : 0.000
% 0.10/0.46 % Propositional solver time : 0.000
% 0.10/0.46 % Success case prop preproc time : 0.000
% 0.10/0.46 % Success case prop encoding time : 0.000
% 0.10/0.46 % Success case prop solver time : 0.000
% 0.10/0.46 % Current number of processed clauses : 72
% 0.10/0.46 % Positive orientable unit clauses : 28
% 0.10/0.46 % Positive unorientable unit clauses: 0
% 0.10/0.46 % Negative unit clauses : 3
% 0.10/0.46 % Non-unit-clauses : 41
% 0.10/0.46 % Current number of unprocessed clauses: 348
% 0.10/0.46 % ...number of literals in the above : 1329
% 0.10/0.46 % Current number of archived formulas : 0
% 0.10/0.46 % Current number of archived clauses : 88
% 0.10/0.46 % Clause-clause subsumption calls (NU) : 1376
% 0.10/0.46 % Rec. Clause-clause subsumption calls : 604
% 0.10/0.46 % Non-unit clause-clause subsumptions : 8
% 0.10/0.46 % Unit Clause-clause subsumption calls : 62
% 0.10/0.46 % Rewrite failures with RHS unbound : 0
% 0.10/0.46 % BW rewrite match attempts : 440
% 0.10/0.46 % BW rewrite match successes : 4
% 0.10/0.46 % Condensation attempts : 0
% 0.10/0.46 % Condensation successes : 0
% 0.10/0.46 % Termbank termtop insertions : 9352
% 0.10/0.46 % Search garbage collected termcells : 75
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.019 s
% 0.10/0.46 % System time : 0.005 s
% 0.10/0.46 % Total time : 0.025 s
% 0.10/0.46 % Maximum resident set size: 3656 pages
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.088 s
% 0.10/0.46 % System time : 0.023 s
% 0.10/0.46 % Total time : 0.111 s
% 0.10/0.46 % Maximum resident set size: 4864 pages
% 0.10/0.46 % E exiting
%------------------------------------------------------------------------------