%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO049-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:27:01 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.98s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 67 ( 32 unt; 10 nHn; 52 RR)
% Number of literals : 133 ( 20 equ; 59 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 178 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d4_5,axiom,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
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(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(d4_3,axiom,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
cnf(d8,axiom,
( ~ between(X3,X4,X6)
| ~ between(X1,X2,X5)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X1,X5,X3,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
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(t1,axiom,
( ~ between(X1,X2,X3)
| between(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
cnf(u_to_w_equals_u1_to_w1,hypothesis,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(d5,axiom,
( ~ equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X1,X2,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(d3,axiom,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
cnf(d10_2,axiom,
( ~ equidistant(X1,X2,X3,X4)
| X5 = X6
| extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).
cnf(d11,axiom,
( ~ equidistant(X2,X3,X2,X4)
| ~ equidistant(X1,X3,X1,X4)
| ~ between(X1,X2,X3)
| X3 = X4
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(prove_v1_between_u1_and_w1,negated_conjecture,
~ between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v1_between_u1_and_w1) ).
cnf(t2,axiom,
between(X1,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
cnf(c_0_18,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[d4_5]) ).
cnf(c_0_19,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_20,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
c_0_18 ).
cnf(c_0_21,hypothesis,
equidistant(v,w,v1,w1),
v_to_w_equals_v1_to_w1 ).
cnf(c_0_22,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X2,X1) ),
inference(fof_simplification,[status(thm)],[d4_3]) ).
cnf(c_0_23,plain,
( ~ between(X3,X4,X6)
| ~ between(X1,X2,X5)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X1,X5,X3,X6) ),
inference(fof_simplification,[status(thm)],[d8]) ).
cnf(c_0_24,hypothesis,
equidistant(u,v,u1,v1),
u_to_v_equals_u1_to_v1 ).
cnf(c_0_25,plain,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
c_0_19 ).
cnf(c_0_26,hypothesis,
equidistant(w1,v1,w,v),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X2,X1) ),
c_0_22 ).
cnf(c_0_28,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_29,plain,
( ~ between(X1,X2,X3)
| between(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[t1]) ).
cnf(c_0_30,hypothesis,
equidistant(u,w,u1,w1),
u_to_w_equals_u1_to_w1 ).
cnf(c_0_31,plain,
( ~ between(X3,X4,X6)
| ~ between(X1,X2,X5)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X1,X5,X3,X6) ),
c_0_23 ).
cnf(c_0_32,hypothesis,
equidistant(v1,u1,v,u),
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_33,hypothesis,
( ~ equidistant(w1,v1,X1,X2)
| equidistant(X1,X2,w,v) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
( ~ between(X1,X2,X3)
| between(X3,X2,X1) ),
c_0_29 ).
cnf(c_0_36,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_37,plain,
( ~ equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X1,X2,X5,X6) ),
inference(fof_simplification,[status(thm)],[d5]) ).
cnf(c_0_38,hypothesis,
equidistant(w1,u1,w,u),
inference(spm,[status(thm)],[c_0_20,c_0_30]) ).
cnf(c_0_39,hypothesis,
( ~ equidistant(X1,v1,X2,v)
| ~ between(X1,v1,u1)
| ~ between(X2,v,u)
| equidistant(X1,u1,X2,u) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,hypothesis,
equidistant(extension(X1,X2,w1,v1),X2,w,v),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,hypothesis,
between(w,v,u),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_43,plain,
( ~ equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X1,X2,X5,X6) ),
c_0_37 ).
cnf(c_0_44,hypothesis,
equidistant(w,u,u1,w1),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_45,hypothesis,
( ~ between(extension(X1,v1,w1,v1),v1,u1)
| equidistant(extension(X1,v1,w1,v1),u1,w,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_46,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_47,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(fof_simplification,[status(thm)],[d3]) ).
cnf(c_0_48,hypothesis,
( ~ equidistant(X1,X2,w,u)
| equidistant(X1,X2,u1,w1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,hypothesis,
equidistant(extension(u1,v1,w1,v1),u1,w,u),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
( ~ equidistant(X1,X2,X3,X4)
| X5 = X6
| extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4) ),
inference(fof_simplification,[status(thm)],[d10_2]) ).
cnf(c_0_51,plain,
( ~ equidistant(X2,X3,X2,X4)
| ~ equidistant(X1,X3,X1,X4)
| ~ between(X1,X2,X3)
| X3 = X4
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[d11]) ).
cnf(c_0_52,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
c_0_47 ).
cnf(c_0_53,hypothesis,
equidistant(extension(u1,v1,w1,v1),u1,u1,w1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( ~ equidistant(X1,X2,X3,X4)
| X5 = X6
| extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4) ),
c_0_50 ).
cnf(c_0_55,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_56,plain,
( ~ equidistant(X2,X3,X2,X4)
| ~ equidistant(X1,X3,X1,X4)
| ~ between(X1,X2,X3)
| X3 = X4
| X1 = X2 ),
c_0_51 ).
cnf(c_0_57,hypothesis,
equidistant(u1,extension(u1,v1,w1,v1),u1,w1),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
( X1 = X2
| extension(X1,X2,X3,X4) = extension(X1,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
( ~ equidistant(X4,extension(X1,X2,X2,X3),X4,X3)
| ~ between(X4,X2,extension(X1,X2,X2,X3))
| X4 = X2
| extension(X1,X2,X2,X3) = X3 ),
inference(spm,[status(thm)],[c_0_56,c_0_28]) ).
cnf(c_0_60,hypothesis,
( equidistant(u1,extension(u1,v1,v1,w1),u1,w1)
| v1 = u1 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
~ between(u1,v1,w1),
inference(fof_simplification,[status(thm)],[prove_v1_between_u1_and_w1]) ).
cnf(c_0_62,hypothesis,
( v1 = u1
| extension(u1,v1,v1,w1) = w1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_42])]) ).
cnf(c_0_63,negated_conjecture,
~ between(u1,v1,w1),
c_0_61 ).
cnf(c_0_64,hypothesis,
v1 = u1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_62]),c_0_63]) ).
cnf(c_0_65,axiom,
between(X1,X1,X2),
t2 ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO049-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n010.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 08:44:40 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.54 Running first-order theorem proving
% 0.23/0.54 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
% 0.27/0.98 % Version: 3.5.1
% 0.27/0.98 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.27/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.98 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.27/0.98 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.98 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.98 % Starting sh5l with 300s (1) cores
% 0.27/0.98 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2614595 completed with status 0
% 0.27/0.98 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.27/0.98 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.27/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.98 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.27/0.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.98 % No SInE strategy applied
% 0.27/0.98 % Search class: FGUSM-FFMS33-SFFFFFNN
% 0.27/0.98 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.98 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.98 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.27/0.98 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.27/0.98 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.98 % Starting new_bool_1 with 136s (1) cores
% 0.27/0.98 % new_bool_3 with pid 2614603 completed with status 0
% 0.27/0.98 % Result found by new_bool_3
% 0.27/0.98 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.27/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.98 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.27/0.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.98 % No SInE strategy applied
% 0.27/0.98 % Search class: FGUSM-FFMS33-SFFFFFNN
% 0.27/0.98 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.98 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.98 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.27/0.98 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.27/0.98 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.98 % Preprocessing time : 0.003 s
% 0.27/0.98 % Presaturation interreduction done
% 0.27/0.98
% 0.27/0.98 % Proof found!
% 0.27/0.98 % SZS status Unsatisfiable
% 0.27/0.98 % SZS output start CNFRefutation
% See solution above
% 0.27/0.98 % Parsed axioms : 80
% 0.27/0.98 % Removed by relevancy pruning/SinE : 0
% 0.27/0.98 % Initial clauses : 80
% 0.27/0.98 % Removed in clause preprocessing : 3
% 0.27/0.98 % Initial clauses in saturation : 77
% 0.27/0.98 % Processed clauses : 1713
% 0.27/0.98 % ...of these trivial : 146
% 0.27/0.98 % ...subsumed : 776
% 0.27/0.98 % ...remaining for further processing : 791
% 0.27/0.98 % Other redundant clauses eliminated : 5
% 0.27/0.98 % Clauses deleted for lack of memory : 0
% 0.27/0.98 % Backward-subsumed : 35
% 0.27/0.98 % Backward-rewritten : 236
% 0.27/0.98 % Generated clauses : 9875
% 0.27/0.98 % ...of the previous two non-redundant : 7342
% 0.27/0.98 % ...aggressively subsumed : 0
% 0.27/0.98 % Contextual simplify-reflections : 0
% 0.27/0.98 % Paramodulations : 9870
% 0.27/0.98 % Factorizations : 0
% 0.27/0.98 % NegExts : 0
% 0.27/0.98 % Equation resolutions : 5
% 0.27/0.98 % Disequality decompositions : 0
% 0.27/0.98 % Total rewrite steps : 3694
% 0.27/0.98 % ...of those cached : 2928
% 0.27/0.98 % Propositional unsat checks : 0
% 0.27/0.98 % Propositional check models : 0
% 0.27/0.98 % Propositional check unsatisfiable : 0
% 0.27/0.98 % Propositional clauses : 0
% 0.27/0.98 % Propositional clauses after purity: 0
% 0.27/0.98 % Propositional unsat core size : 0
% 0.27/0.98 % Propositional preprocessing time : 0.000
% 0.27/0.98 % Propositional encoding time : 0.000
% 0.27/0.98 % Propositional solver time : 0.000
% 0.27/0.98 % Success case prop preproc time : 0.000
% 0.27/0.98 % Success case prop encoding time : 0.000
% 0.27/0.98 % Success case prop solver time : 0.000
% 0.27/0.98 % Current number of processed clauses : 449
% 0.27/0.98 % Positive orientable unit clauses : 96
% 0.27/0.98 % Positive unorientable unit clauses: 0
% 0.27/0.98 % Negative unit clauses : 35
% 0.27/0.98 % Non-unit-clauses : 318
% 0.27/0.98 % Current number of unprocessed clauses: 5467
% 0.27/0.98 % ...number of literals in the above : 14439
% 0.27/0.98 % Current number of archived formulas : 0
% 0.27/0.98 % Current number of archived clauses : 341
% 0.27/0.98 % Clause-clause subsumption calls (NU) : 48545
% 0.27/0.98 % Rec. Clause-clause subsumption calls : 41430
% 0.27/0.98 % Non-unit clause-clause subsumptions : 605
% 0.27/0.98 % Unit Clause-clause subsumption calls : 2010
% 0.27/0.98 % Rewrite failures with RHS unbound : 0
% 0.27/0.98 % BW rewrite match attempts : 1260
% 0.27/0.98 % BW rewrite match successes : 27
% 0.27/0.98 % Condensation attempts : 0
% 0.27/0.98 % Condensation successes : 0
% 0.27/0.98 % Termbank termtop insertions : 148345
% 0.27/0.98 % Search garbage collected termcells : 187
% 0.27/0.98
% 0.27/0.98 % -------------------------------------------------
% 0.27/0.98 % User time : 0.330 s
% 0.27/0.98 % System time : 0.019 s
% 0.27/0.98 % Total time : 0.349 s
% 0.27/0.98 % Maximum resident set size: 3440 pages
% 0.27/0.98
% 0.27/0.98 % -------------------------------------------------
% 0.27/0.98 % User time : 1.169 s
% 0.27/0.98 % System time : 0.069 s
% 0.27/0.98 % Total time : 1.238 s
% 0.27/0.98 % Maximum resident set size: 4608 pages
% 0.27/0.98 % E exiting
%------------------------------------------------------------------------------