%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO178+1 : TPTP v9.3.1. Released v3.3.0.
% 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 12:27:34 PM UTC 2026
% Result : Theorem 0.23s 5.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 44 ( 19 ~; 12 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( apart_point_and_line(X3,line_connecting(X1,X2))
& distinct_points(X1,X2) )
=> ( distinct_points(X3,X2)
& distinct_points(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(ci1,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(ceq1,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( apart_point_and_line(X3,X2)
| distinct_points(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( apart_point_and_line(X3,line_connecting(X1,X2))
& distinct_points(X1,X2) )
=> ( distinct_points(X3,X2)
& distinct_points(X3,X1) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_5,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci1]) ).
fof(c_0_6,plain,
! [X17,X18,X19] :
( apart_point_and_line(X19,X18)
| distinct_points(X17,X19)
| ~ apart_point_and_line(X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])])]) ).
fof(c_0_7,negated_conjecture,
( ( ~ distinct_points(esk3_0,esk2_0)
| ~ distinct_points(esk3_0,esk1_0) )
& apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
& distinct_points(esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_8,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
fof(c_0_9,plain,
! [X20,X21] :
( ~ apart_point_and_line(X20,line_connecting(X20,X21))
| ~ distinct_points(X20,X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
( ~ apart_point_and_line(X1,X2)
| apart_point_and_line(X3,X2)
| distinct_points(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X22,X23] :
( ~ apart_point_and_line(X23,line_connecting(X22,X23))
| ~ distinct_points(X22,X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,plain,
( ~ apart_point_and_line(X1,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( distinct_points(esk3_0,X1)
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( ~ apart_point_and_line(X2,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ distinct_points(esk3_0,esk2_0)
| ~ distinct_points(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
distinct_points(esk3_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
distinct_points(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_15])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO178+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.50 % Computer : n018.cluster.edu
% 0.19/5.50 % Model : x86_64 x86_64
% 0.19/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.50 % Memory : 8046.5625MB
% 0.19/5.50 % OS : Linux 6.8.0-71-generic
% 0.19/5.50 % CPULimit : 300
% 0.19/5.50 % WCLimit : 300
% 0.19/5.50 % DateTime : Sun Sep 20 13:04:02 UTC 2026
% 0.19/5.50 % CPUTime :
% 0.19/5.50 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.55 Running first-order theorem proving
% 0.19/5.55 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
% 0.23/5.61 % Version: 3.5.1
% 0.23/5.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/5.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.61 % Starting new_bool_1 with 300s (1) cores
% 0.23/5.61 % Starting sh5l with 300s (1) cores
% 0.23/5.61 % new_bool_3 with pid 3691869 completed with status 0
% 0.23/5.61 % Result found by new_bool_3
% 0.23/5.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/5.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/5.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/5.61 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.23/5.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/5.61 % Starting SubtermCWHack with 31s (1) cores
% 0.23/5.61 % SubtermCWHack with pid 3691873 completed with status 0
% 0.23/5.61 % Result found by SubtermCWHack
% 0.23/5.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/5.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/5.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/5.61 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.23/5.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/5.61 % Starting SubtermCWHack with 31s (1) cores
% 0.23/5.61 % Preprocessing time : 0.002 s
% 0.23/5.61
% 0.23/5.61 % Proof found!
% 0.23/5.61 % SZS status Theorem
% 0.23/5.61 % SZS output start CNFRefutation
% See solution above
% 0.23/5.61 % Parsed axioms : 15
% 0.23/5.61 % Removed by relevancy pruning/SinE : 2
% 0.23/5.61 % Initial clauses : 15
% 0.23/5.61 % Removed in clause preprocessing : 0
% 0.23/5.61 % Initial clauses in saturation : 15
% 0.23/5.61 % Processed clauses : 17
% 0.23/5.61 % ...of these trivial : 0
% 0.23/5.61 % ...subsumed : 1
% 0.23/5.61 % ...remaining for further processing : 15
% 0.23/5.61 % Other redundant clauses eliminated : 0
% 0.23/5.61 % Clauses deleted for lack of memory : 0
% 0.23/5.61 % Backward-subsumed : 0
% 0.23/5.61 % Backward-rewritten : 1
% 0.23/5.61 % Generated clauses : 10
% 0.23/5.61 % ...of the previous two non-redundant : 11
% 0.23/5.61 % ...aggressively subsumed : 0
% 0.23/5.61 % Contextual simplify-reflections : 0
% 0.23/5.61 % Paramodulations : 10
% 0.23/5.61 % Factorizations : 0
% 0.23/5.61 % NegExts : 0
% 0.23/5.61 % Equation resolutions : 0
% 0.23/5.61 % Disequality decompositions : 0
% 0.23/5.61 % Total rewrite steps : 4
% 0.23/5.61 % ...of those cached : 1
% 0.23/5.61 % Propositional unsat checks : 0
% 0.23/5.61 % Propositional check models : 0
% 0.23/5.61 % Propositional check unsatisfiable : 0
% 0.23/5.61 % Propositional clauses : 0
% 0.23/5.61 % Propositional clauses after purity: 0
% 0.23/5.61 % Propositional unsat core size : 0
% 0.23/5.61 % Propositional preprocessing time : 0.000
% 0.23/5.61 % Propositional encoding time : 0.000
% 0.23/5.61 % Propositional solver time : 0.000
% 0.23/5.61 % Success case prop preproc time : 0.000
% 0.23/5.61 % Success case prop encoding time : 0.000
% 0.23/5.61 % Success case prop solver time : 0.000
% 0.23/5.61 % Current number of processed clauses : 14
% 0.23/5.61 % Positive orientable unit clauses : 5
% 0.23/5.61 % Positive unorientable unit clauses: 0
% 0.23/5.61 % Negative unit clauses : 3
% 0.23/5.61 % Non-unit-clauses : 6
% 0.23/5.61 % Current number of unprocessed clauses: 9
% 0.23/5.61 % ...number of literals in the above : 28
% 0.23/5.61 % Current number of archived formulas : 0
% 0.23/5.61 % Current number of archived clauses : 1
% 0.23/5.61 % Clause-clause subsumption calls (NU) : 3
% 0.23/5.61 % Rec. Clause-clause subsumption calls : 3
% 0.23/5.61 % Non-unit clause-clause subsumptions : 1
% 0.23/5.61 % Unit Clause-clause subsumption calls : 5
% 0.23/5.61 % Rewrite failures with RHS unbound : 0
% 0.23/5.61 % BW rewrite match attempts : 1
% 0.23/5.61 % BW rewrite match successes : 1
% 0.23/5.61 % Condensation attempts : 0
% 0.23/5.61 % Condensation successes : 0
% 0.23/5.61 % Termbank termtop insertions : 1197
% 0.23/5.61 % Search garbage collected termcells : 196
% 0.23/5.61
% 0.23/5.61 % -------------------------------------------------
% 0.23/5.61 % User time : 0.005 s
% 0.23/5.61 % System time : 0.005 s
% 0.23/5.61 % Total time : 0.010 s
% 0.23/5.61 % Maximum resident set size: 3648 pages
% 0.23/5.61
% 0.23/5.61 % -------------------------------------------------
% 0.23/5.61 % User time : 0.008 s
% 0.23/5.61 % System time : 0.011 s
% 0.23/5.61 % Total time : 0.019 s
% 0.23/5.61 % Maximum resident set size: 4864 pages
% 0.23/5.61 % E exiting
%------------------------------------------------------------------------------