%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:26:58 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 37 ( 19 unt; 0 nHn; 22 RR)
% Number of literals : 61 ( 13 equ; 27 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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 : 118 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d4_4,axiom,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
cnf(d4_5,axiom,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(transitivity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(prove_lengthen,negated_conjecture,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lengthen) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(e1,axiom,
X1 = extension(X2,X1,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
cnf(e2_1,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
cnf(c_0_9,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X1,X2) ),
inference(fof_simplification,[status(thm)],[d4_4]) ).
cnf(c_0_10,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[d4_5]) ).
cnf(c_0_11,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X1,X2) ),
c_0_9 ).
cnf(c_0_12,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_13,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X4,X3,X2,X1) ),
c_0_10 ).
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,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
equidistant(X1,X2,extension(X3,X4,X2,X1),X4),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
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,plain,
equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_19,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
inference(fof_simplification,[status(thm)],[prove_lengthen]) ).
cnf(c_0_21,plain,
( ~ equidistant(extension(X5,X6,X4,X3),X6,X1,X2)
| equidistant(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
c_0_20 ).
cnf(c_0_24,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_25,plain,
equidistant(X1,extension(X2,X1,extension(X3,X4,X5,X6),X4),X6,X5),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_27,plain,
( ~ equidistant(X6,X5,X1,X2)
| equidistant(X1,X2,X3,extension(X4,X3,X5,X6)) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_28,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
cnf(c_0_29,plain,
equidistant(X1,X2,X3,extension(X4,X3,extension(X5,X6,X1,X2),X6)),
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_15])]) ).
cnf(c_0_31,axiom,
X1 = extension(X2,X1,X3,X3),
e1 ).
cnf(c_0_32,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(fof_simplification,[status(thm)],[e2_1]) ).
cnf(c_0_33,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
c_0_28 ).
cnf(c_0_34,negated_conjecture,
equidistant(lower_dimension_point_1,lower_dimension_point_2,X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_35,plain,
lower_dimension_point_1 != lower_dimension_point_2,
c_0_32 ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 08:34:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.46 % Version: 3.5.1
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1395112 completed with status 0
% 0.09/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGUSM-FFMF33-SFFFFFNN
% 0.09/0.46 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.46 % Starting G-E--_215_C46_F1_AE_CS_SP_PS_S2S with 901s (1) cores
% 0.09/0.46 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0a with 151s (1) cores
% 0.09/0.46 % Starting new_bool_3 with 151s (1) cores
% 0.09/0.46 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 146s (1) cores
% 0.09/0.46 % SubtermCWHack with pid 1395117 completed with status 0
% 0.09/0.46 % Result found by SubtermCWHack
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGUSM-FFMF33-SFFFFFNN
% 0.09/0.46 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.46 % Preprocessing time : 0.002 s
% 0.09/0.46
% 0.09/0.46 % Proof found!
% 0.09/0.46 % SZS status Unsatisfiable
% 0.09/0.46 % SZS output start CNFRefutation
% See solution above
% 0.09/0.46 % Parsed axioms : 61
% 0.09/0.46 % Removed by relevancy pruning/SinE : 0
% 0.09/0.46 % Initial clauses : 61
% 0.09/0.46 % Removed in clause preprocessing : 2
% 0.09/0.46 % Initial clauses in saturation : 59
% 0.09/0.46 % Processed clauses : 260
% 0.09/0.46 % ...of these trivial : 108
% 0.09/0.46 % ...subsumed : 31
% 0.09/0.46 % ...remaining for further processing : 121
% 0.09/0.46 % Other redundant clauses eliminated : 4
% 0.09/0.46 % Clauses deleted for lack of memory : 0
% 0.09/0.46 % Backward-subsumed : 0
% 0.09/0.46 % Backward-rewritten : 1
% 0.09/0.46 % Generated clauses : 1475
% 0.09/0.46 % ...of the previous two non-redundant : 867
% 0.09/0.46 % ...aggressively subsumed : 0
% 0.09/0.46 % Contextual simplify-reflections : 0
% 0.09/0.46 % Paramodulations : 1471
% 0.09/0.46 % Factorizations : 0
% 0.09/0.46 % NegExts : 0
% 0.09/0.46 % Equation resolutions : 4
% 0.09/0.46 % Disequality decompositions : 0
% 0.09/0.46 % Total rewrite steps : 837
% 0.09/0.46 % ...of those cached : 622
% 0.09/0.46 % Propositional unsat checks : 0
% 0.09/0.46 % Propositional check models : 0
% 0.09/0.46 % Propositional check unsatisfiable : 0
% 0.09/0.46 % Propositional clauses : 0
% 0.09/0.46 % Propositional clauses after purity: 0
% 0.09/0.46 % Propositional unsat core size : 0
% 0.09/0.46 % Propositional preprocessing time : 0.000
% 0.09/0.46 % Propositional encoding time : 0.000
% 0.09/0.46 % Propositional solver time : 0.000
% 0.09/0.46 % Success case prop preproc time : 0.000
% 0.09/0.46 % Success case prop encoding time : 0.000
% 0.09/0.46 % Success case prop solver time : 0.000
% 0.09/0.46 % Current number of processed clauses : 117
% 0.09/0.46 % Positive orientable unit clauses : 55
% 0.09/0.46 % Positive unorientable unit clauses: 0
% 0.09/0.46 % Negative unit clauses : 6
% 0.09/0.46 % Non-unit-clauses : 56
% 0.09/0.46 % Current number of unprocessed clauses: 660
% 0.09/0.46 % ...number of literals in the above : 2086
% 0.09/0.46 % Current number of archived formulas : 0
% 0.09/0.46 % Current number of archived clauses : 2
% 0.09/0.46 % Clause-clause subsumption calls (NU) : 1256
% 0.09/0.46 % Rec. Clause-clause subsumption calls : 950
% 0.09/0.46 % Non-unit clause-clause subsumptions : 31
% 0.09/0.46 % Unit Clause-clause subsumption calls : 23
% 0.09/0.46 % Rewrite failures with RHS unbound : 0
% 0.09/0.46 % BW rewrite match attempts : 573
% 0.09/0.46 % BW rewrite match successes : 1
% 0.09/0.46 % Condensation attempts : 0
% 0.09/0.46 % Condensation successes : 0
% 0.09/0.46 % Termbank termtop insertions : 12891
% 0.09/0.46 % Search garbage collected termcells : 143
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.024 s
% 0.09/0.46 % System time : 0.004 s
% 0.09/0.46 % Total time : 0.028 s
% 0.09/0.46 % Maximum resident set size: 3680 pages
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.107 s
% 0.09/0.46 % System time : 0.026 s
% 0.09/0.46 % Total time : 0.133 s
% 0.09/0.46 % Maximum resident set size: 4608 pages
% 0.09/0.46 % E exiting
%------------------------------------------------------------------------------