%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO010-2 : 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 : n004.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 12:26:51 PM UTC 2026
% Result : Unsatisfiable 0.14s 10.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 59 ( 13 unt; 7 nHn; 53 RR)
% Number of literals : 140 ( 8 equ; 87 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 113 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_colinear_in_all_orders,negated_conjecture,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_colinear_in_all_orders) ).
cnf(colinearity2,axiom,
( ~ between(X1,X2,X3)
| colinear(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
cnf(colinearity3,axiom,
( ~ between(X1,X2,X3)
| colinear(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
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(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(colinearity4,axiom,
( ~ colinear(X1,X2,X3)
| between(X3,X1,X2)
| between(X2,X3,X1)
| between(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
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(colinearity1,axiom,
( ~ between(X1,X2,X3)
| colinear(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
cnf(abc_colinear,hypothesis,
colinear(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abc_colinear) ).
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(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(c_0_12,negated_conjecture,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(fof_simplification,[status(thm)],[prove_colinear_in_all_orders]) ).
cnf(c_0_13,plain,
( ~ between(X1,X2,X3)
| colinear(X3,X1,X2) ),
inference(fof_simplification,[status(thm)],[colinearity2]) ).
cnf(c_0_14,plain,
( ~ between(X1,X2,X3)
| colinear(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[colinearity3]) ).
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,negated_conjecture,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
c_0_12 ).
cnf(c_0_18,plain,
( ~ between(X1,X2,X3)
| colinear(X3,X1,X2) ),
c_0_13 ).
cnf(c_0_19,plain,
( ~ between(X1,X2,X3)
| colinear(X2,X3,X1) ),
c_0_14 ).
cnf(c_0_20,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_21,plain,
( ~ between(X1,X2,X1)
| X1 = X2 ),
c_0_15 ).
cnf(c_0_22,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_23,plain,
( ~ colinear(X1,X2,X3)
| between(X3,X1,X2)
| between(X2,X3,X1)
| between(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[colinearity4]) ).
cnf(c_0_24,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[identity_for_equidistance]) ).
cnf(c_0_25,plain,
( ~ between(X1,X2,X3)
| colinear(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[colinearity1]) ).
cnf(c_0_26,negated_conjecture,
( ~ between(b,a,c)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_27,plain,
( ~ between(X4,X5,X3)
| ~ between(X1,X2,X3)
| between(X2,inner_pasch(X1,X2,X3,X5,X4),X4) ),
c_0_20 ).
cnf(c_0_28,plain,
( ~ between(X1,X2,X3)
| ~ between(X4,X1,X3)
| inner_pasch(X1,X2,X3,X1,X4) = X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( ~ colinear(X1,X2,X3)
| between(X3,X1,X2)
| between(X2,X3,X1)
| between(X1,X2,X3) ),
c_0_23 ).
cnf(c_0_30,hypothesis,
colinear(a,b,c),
abc_colinear ).
cnf(c_0_31,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
c_0_24 ).
cnf(c_0_32,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_33,plain,
( ~ between(X1,X2,X3)
| colinear(X1,X2,X3) ),
c_0_25 ).
cnf(c_0_34,negated_conjecture,
( ~ between(b,c,a)
| ~ between(b,a,c)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_35,negated_conjecture,
( ~ between(a,b,c)
| ~ between(b,a,c)
| ~ colinear(b,a,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_19]) ).
cnf(c_0_36,plain,
( ~ between(X2,X1,X4)
| ~ between(X3,X2,X4)
| between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,hypothesis,
( between(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_39,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( ~ between(c,a,b)
| ~ between(b,a,c) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_18]),c_0_33]) ).
cnf(c_0_41,negated_conjecture,
( ~ between(b,c,a)
| ~ between(b,a,c) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( ~ between(a,b,c)
| ~ between(b,a,c) ),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_43,hypothesis,
( ~ between(a,X1,b)
| between(X1,a,c)
| between(a,b,c)
| between(b,c,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
~ between(b,a,c),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_41]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( ~ between(a,c,b)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(a,c,b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_18]) ).
cnf(c_0_47,hypothesis,
( between(b,c,a)
| between(a,b,c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( ~ between(c,a,b)
| ~ between(a,c,b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_33]),c_0_18]),c_0_33]) ).
cnf(c_0_49,negated_conjecture,
( ~ between(b,c,a)
| ~ between(a,c,b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_19]),c_0_33]),c_0_33]) ).
cnf(c_0_50,negated_conjecture,
( ~ between(a,b,c)
| ~ between(a,c,b) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_18]),c_0_19]),c_0_33]) ).
cnf(c_0_51,hypothesis,
( ~ between(c,X1,a)
| between(X1,c,b)
| between(a,b,c) ),
inference(spm,[status(thm)],[c_0_36,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
~ between(a,c,b),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_37]),c_0_49]),c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( ~ between(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_33]),c_0_19]),c_0_18]) ).
cnf(c_0_54,hypothesis,
between(a,b,c),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_44]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( ~ between(a,b,c)
| ~ between(c,b,a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_18]),c_0_19]) ).
cnf(c_0_56,hypothesis,
( ~ between(b,X1,c)
| between(X1,b,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
~ between(c,b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_54])]) ).
cnf(c_0_58,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_44]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/10.38 % Computer : n004.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sun Sep 20 08:16:46 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 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
% 0.14/10.45 % Version: 3.5.1
% 0.14/10.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/10.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/10.45 % Starting sh5l with 300s (1) cores
% 0.14/10.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 568774 completed with status 0
% 0.14/10.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/10.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/10.45 % No SInE strategy applied
% 0.14/10.45 % Search class: FGHSS-FFMF33-SFFFFFNN
% 0.14/10.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/10.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/10.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 203s (1) cores
% 0.14/10.45 % Starting new_bool_3 with 203s (1) cores
% 0.14/10.45 % Starting new_bool_1 with 203s (1) cores
% 0.14/10.45 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 568782 completed with status 0
% 0.14/10.45 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.14/10.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/10.45 % No SInE strategy applied
% 0.14/10.45 % Search class: FGHSS-FFMF33-SFFFFFNN
% 0.14/10.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/10.45 % Starting SubtermCWHack with 136s (1) cores
% 0.14/10.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/10.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 203s (1) cores
% 0.14/10.45 % Preprocessing time : 0.001 s
% 0.14/10.45 % Presaturation interreduction done
% 0.14/10.45
% 0.14/10.45 % Proof found!
% 0.14/10.45 % SZS status Unsatisfiable
% 0.14/10.45 % SZS output start CNFRefutation
% See solution above
% 0.14/10.45 % Parsed axioms : 24
% 0.14/10.45 % Removed by relevancy pruning/SinE : 0
% 0.14/10.45 % Initial clauses : 24
% 0.14/10.45 % Removed in clause preprocessing : 0
% 0.14/10.45 % Initial clauses in saturation : 24
% 0.14/10.45 % Processed clauses : 95
% 0.14/10.45 % ...of these trivial : 2
% 0.14/10.45 % ...subsumed : 2
% 0.14/10.45 % ...remaining for further processing : 91
% 0.14/10.45 % Other redundant clauses eliminated : 0
% 0.14/10.45 % Clauses deleted for lack of memory : 0
% 0.14/10.45 % Backward-subsumed : 15
% 0.14/10.45 % Backward-rewritten : 3
% 0.14/10.45 % Generated clauses : 153
% 0.14/10.45 % ...of the previous two non-redundant : 110
% 0.14/10.45 % ...aggressively subsumed : 0
% 0.14/10.45 % Contextual simplify-reflections : 21
% 0.14/10.45 % Paramodulations : 153
% 0.14/10.45 % Factorizations : 0
% 0.14/10.45 % NegExts : 0
% 0.14/10.45 % Equation resolutions : 0
% 0.14/10.45 % Disequality decompositions : 0
% 0.14/10.45 % Total rewrite steps : 48
% 0.14/10.45 % ...of those cached : 26
% 0.14/10.45 % Propositional unsat checks : 0
% 0.14/10.45 % Propositional check models : 0
% 0.14/10.45 % Propositional check unsatisfiable : 0
% 0.14/10.45 % Propositional clauses : 0
% 0.14/10.45 % Propositional clauses after purity: 0
% 0.14/10.45 % Propositional unsat core size : 0
% 0.14/10.45 % Propositional preprocessing time : 0.000
% 0.14/10.45 % Propositional encoding time : 0.000
% 0.14/10.45 % Propositional solver time : 0.000
% 0.14/10.45 % Success case prop preproc time : 0.000
% 0.14/10.45 % Success case prop encoding time : 0.000
% 0.14/10.45 % Success case prop solver time : 0.000
% 0.14/10.45 % Current number of processed clauses : 49
% 0.14/10.45 % Positive orientable unit clauses : 17
% 0.14/10.45 % Positive unorientable unit clauses: 0
% 0.14/10.45 % Negative unit clauses : 6
% 0.14/10.45 % Non-unit-clauses : 26
% 0.14/10.45 % Current number of unprocessed clauses: 57
% 0.14/10.45 % ...number of literals in the above : 259
% 0.14/10.45 % Current number of archived formulas : 0
% 0.14/10.45 % Current number of archived clauses : 42
% 0.14/10.45 % Clause-clause subsumption calls (NU) : 654
% 0.14/10.45 % Rec. Clause-clause subsumption calls : 375
% 0.14/10.45 % Non-unit clause-clause subsumptions : 27
% 0.14/10.45 % Unit Clause-clause subsumption calls : 53
% 0.14/10.45 % Rewrite failures with RHS unbound : 0
% 0.14/10.45 % BW rewrite match attempts : 217
% 0.14/10.45 % BW rewrite match successes : 1
% 0.14/10.45 % Condensation attempts : 0
% 0.14/10.45 % Condensation successes : 0
% 0.14/10.45 % Termbank termtop insertions : 2776
% 0.14/10.45 % Search garbage collected termcells : 91
% 0.14/10.45
% 0.14/10.45 % -------------------------------------------------
% 0.14/10.45 % User time : 0.007 s
% 0.14/10.45 % System time : 0.006 s
% 0.14/10.45 % Total time : 0.013 s
% 0.14/10.45 % Maximum resident set size: 3660 pages
% 0.14/10.45
% 0.14/10.45 % -------------------------------------------------
% 0.14/10.45 % User time : 0.044 s
% 0.14/10.45 % System time : 0.016 s
% 0.14/10.45 % Total time : 0.060 s
% 0.14/10.45 % Maximum resident set size: 4864 pages
% 0.14/10.45 % E exiting
%------------------------------------------------------------------------------