%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GEO001-2 : 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 : n011.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 12:28:43 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 15 unt; 0 nHn; 19 RR)
% Number of literals : 49 ( 8 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 76 ( 10 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(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
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_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
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(identity_for_betweeness,axiom,
( ~ between(X1,X2,X1)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(b_between_a_and_c,hypothesis,
between(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_between_a_and_c) ).
cnf(prove_b_between_c_and_a,negated_conjecture,
~ between(c,b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_between_c_and_a) ).
cnf(c_0_8,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
cnf(c_0_9,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
c_0_8 ).
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(X2,inner_pasch(X1,X2,X3,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[inner_pasch1]) ).
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(X5,inner_pasch(X1,X2,X3,X5,X4),X1) ),
inference(fof_simplification,[status(thm)],[inner_pasch2]) ).
cnf(c_0_15,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X2,inner_pasch(X1,X2,X3,X5,X4),X4) ),
c_0_11 ).
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(X5,inner_pasch(X1,X2,X3,X5,X4),X1) ),
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(X2,X1,X3)
| between(X1,inner_pasch(X2,X1,X3,X3,X4),X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,hypothesis,
between(a,b,c),
b_between_a_and_c ).
cnf(c_0_21,plain,
( ~ between(X2,X3,X1)
| between(X1,inner_pasch(X2,X3,X1,X1,X4),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_22,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
c_0_18 ).
cnf(c_0_23,hypothesis,
between(b,inner_pasch(a,b,c,c,X1),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
~ between(c,b,a),
inference(fof_simplification,[status(thm)],[prove_b_between_c_and_a]) ).
cnf(c_0_25,hypothesis,
between(c,inner_pasch(a,b,c,c,X1),a),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,hypothesis,
inner_pasch(a,b,c,c,b) = b,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
~ between(c,b,a),
c_0_24 ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n011.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 08:13:54 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43 % Version: 3.5.1
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.43 % Starting sh5l with 300s (1) cores
% 0.12/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3382071 completed with status 0
% 0.12/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.43 % No SInE strategy applied
% 0.12/0.43 % Search class: FGUSS-FFMF33-SFFFFFNN
% 0.12/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.43 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 0.12/0.43 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.12/0.43 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.12/0.43 % H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with pid 3382079 completed with status 0
% 0.12/0.43 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S4c
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.43 % No SInE strategy applied
% 0.12/0.43 % Search class: FGUSS-FFMF33-SFFFFFNN
% 0.12/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.43 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S4c with 136s (1) cores
% 0.12/0.43 % Preprocessing time : 0.001 s
% 0.12/0.43
% 0.12/0.43 % Proof found!
% 0.12/0.43 % SZS status Unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.43 % Parsed axioms : 20
% 0.12/0.43 % Removed by relevancy pruning/SinE : 0
% 0.12/0.43 % Initial clauses : 20
% 0.12/0.43 % Removed in clause preprocessing : 0
% 0.12/0.43 % Initial clauses in saturation : 20
% 0.12/0.43 % Processed clauses : 55
% 0.12/0.43 % ...of these trivial : 0
% 0.12/0.43 % ...subsumed : 3
% 0.12/0.43 % ...remaining for further processing : 52
% 0.12/0.43 % Other redundant clauses eliminated : 0
% 0.12/0.43 % Clauses deleted for lack of memory : 0
% 0.12/0.43 % Backward-subsumed : 0
% 0.12/0.43 % Backward-rewritten : 0
% 0.12/0.43 % Generated clauses : 211
% 0.12/0.43 % ...of the previous two non-redundant : 144
% 0.12/0.43 % ...aggressively subsumed : 0
% 0.12/0.43 % Contextual simplify-reflections : 0
% 0.12/0.43 % Paramodulations : 211
% 0.12/0.43 % Factorizations : 0
% 0.12/0.43 % NegExts : 0
% 0.12/0.43 % Equation resolutions : 0
% 0.12/0.43 % Disequality decompositions : 0
% 0.12/0.43 % Total rewrite steps : 75
% 0.12/0.43 % ...of those cached : 48
% 0.12/0.43 % Propositional unsat checks : 0
% 0.12/0.43 % Propositional check models : 0
% 0.12/0.43 % Propositional check unsatisfiable : 0
% 0.12/0.43 % Propositional clauses : 0
% 0.12/0.43 % Propositional clauses after purity: 0
% 0.12/0.43 % Propositional unsat core size : 0
% 0.12/0.43 % Propositional preprocessing time : 0.000
% 0.12/0.43 % Propositional encoding time : 0.000
% 0.12/0.43 % Propositional solver time : 0.000
% 0.12/0.43 % Success case prop preproc time : 0.000
% 0.12/0.43 % Success case prop encoding time : 0.000
% 0.12/0.43 % Success case prop solver time : 0.000
% 0.12/0.43 % Current number of processed clauses : 52
% 0.12/0.43 % Positive orientable unit clauses : 26
% 0.12/0.43 % Positive unorientable unit clauses: 0
% 0.12/0.43 % Negative unit clauses : 4
% 0.12/0.43 % Non-unit-clauses : 22
% 0.12/0.43 % Current number of unprocessed clauses: 109
% 0.12/0.43 % ...number of literals in the above : 304
% 0.12/0.43 % Current number of archived formulas : 0
% 0.12/0.43 % Current number of archived clauses : 0
% 0.12/0.43 % Clause-clause subsumption calls (NU) : 184
% 0.12/0.43 % Rec. Clause-clause subsumption calls : 98
% 0.12/0.43 % Non-unit clause-clause subsumptions : 3
% 0.12/0.43 % Unit Clause-clause subsumption calls : 42
% 0.12/0.43 % Rewrite failures with RHS unbound : 0
% 0.12/0.43 % BW rewrite match attempts : 247
% 0.12/0.43 % BW rewrite match successes : 0
% 0.12/0.43 % Condensation attempts : 0
% 0.12/0.43 % Condensation successes : 0
% 0.12/0.43 % Termbank termtop insertions : 2801
% 0.12/0.43 % Search garbage collected termcells : 75
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.004 s
% 0.12/0.43 % System time : 0.004 s
% 0.12/0.43 % Total time : 0.008 s
% 0.12/0.43 % Maximum resident set size: 3656 pages
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.023 s
% 0.12/0.43 % System time : 0.015 s
% 0.12/0.43 % Total time : 0.038 s
% 0.12/0.43 % Maximum resident set size: 4608 pages
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------