%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO002-2 : 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 : n018.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 12:26:48 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 29 ( 15 unt; 0 nHn; 17 RR)
% Number of literals : 49 ( 8 equ; 23 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 : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 91 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
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(inner_pasch2,axiom,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X5,inner_pasch(X1,X2,X3,X5,X4),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
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(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
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/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
cnf(identity_for_betweeness,axiom,
( ~ between(X1,X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_between_a_and_b) ).
cnf(c_0_7,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
cnf(c_0_8,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_9,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
c_0_7 ).
cnf(c_0_10,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_11,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X5,inner_pasch(X1,X2,X3,X5,X4),X1) ),
c_0_8 ).
cnf(c_0_12,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_13,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,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_15,plain,
( ~ between(X2,X3,extension(X4,X1,X5,X6))
| between(X1,inner_pasch(X2,X3,extension(X4,X1,X5,X6),X1,X4),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X2,inner_pasch(X1,X2,X3,X5,X4),X4) ),
c_0_14 ).
cnf(c_0_18,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_betweeness]) ).
cnf(c_0_19,plain,
between(X1,inner_pasch(X2,extension(X3,X1,X4,X5),extension(X3,X1,X4,X5),X1,X3),X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( ~ between(X2,X1,X3)
| between(X1,inner_pasch(X2,X1,X3,X3,X4),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
c_0_18 ).
cnf(c_0_22,plain,
between(X1,inner_pasch(X2,X1,X1,X1,X3),X2),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_23,negated_conjecture,
~ between(a,a,b),
inference(fof_simplification,[status(thm)],[prove_a_between_a_and_b]) ).
cnf(c_0_24,plain,
between(X1,inner_pasch(X2,X1,X1,X1,X3),X3),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_25,plain,
inner_pasch(X1,X1,X1,X1,X2) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ between(a,a,b),
c_0_23 ).
cnf(c_0_27,plain,
between(X1,X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 08:16:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3406155 completed with status 0
% 0.14/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGUSS-FFMF33-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.45 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.14/0.45 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.14/0.45 % H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with pid 3406162 completed with status 0
% 0.14/0.45 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S4c
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.45 % No SInE strategy applied
% 0.14/0.45 % Search class: FGUSS-FFMF33-SFFFFFNN
% 0.14/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.45 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 0.14/0.45 % Preprocessing time : 0.001 s
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Unsatisfiable
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 19
% 0.14/0.45 % Removed by relevancy pruning/SinE : 0
% 0.14/0.45 % Initial clauses : 19
% 0.14/0.45 % Removed in clause preprocessing : 0
% 0.14/0.45 % Initial clauses in saturation : 19
% 0.14/0.45 % Processed clauses : 54
% 0.14/0.45 % ...of these trivial : 2
% 0.14/0.45 % ...subsumed : 3
% 0.14/0.45 % ...remaining for further processing : 49
% 0.14/0.45 % Other redundant clauses eliminated : 0
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 0
% 0.14/0.45 % Backward-rewritten : 3
% 0.14/0.45 % Generated clauses : 195
% 0.14/0.45 % ...of the previous two non-redundant : 139
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 0
% 0.14/0.45 % Paramodulations : 195
% 0.14/0.45 % Factorizations : 0
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 0
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 54
% 0.14/0.45 % ...of those cached : 30
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 46
% 0.14/0.45 % Positive orientable unit clauses : 21
% 0.14/0.45 % Positive unorientable unit clauses: 0
% 0.14/0.45 % Negative unit clauses : 3
% 0.14/0.45 % Non-unit-clauses : 22
% 0.14/0.45 % Current number of unprocessed clauses: 104
% 0.14/0.45 % ...number of literals in the above : 266
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 3
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 164
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 89
% 0.14/0.45 % Non-unit clause-clause subsumptions : 3
% 0.14/0.45 % Unit Clause-clause subsumption calls : 53
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 265
% 0.14/0.45 % BW rewrite match successes : 3
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 2449
% 0.14/0.45 % Search garbage collected termcells : 75
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.007 s
% 0.14/0.45 % System time : 0.003 s
% 0.14/0.45 % Total time : 0.010 s
% 0.14/0.45 % Maximum resident set size: 3604 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.039 s
% 0.14/0.45 % System time : 0.015 s
% 0.14/0.45 % Total time : 0.054 s
% 0.14/0.45 % Maximum resident set size: 4864 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------