%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO181+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 : n007.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 12:27:35 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 98 ( 31 ~; 52 |; 3 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> apart_point_and_line(X2,line_connecting(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(ceq2,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( apart_point_and_line(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X2,X3)
| distinct_points(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(cu1,axiom,
! [X1,X2,X4,X5] :
( ( distinct_lines(X4,X5)
& distinct_points(X1,X2) )
=> ( apart_point_and_line(X2,X5)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X1,X5)
| apart_point_and_line(X1,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
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_8,negated_conjecture,
~ ! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> apart_point_and_line(X2,line_connecting(X1,X3)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_9,plain,
! [X33,X34,X35] :
( apart_point_and_line(X33,X35)
| distinct_lines(X34,X35)
| ~ apart_point_and_line(X33,X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])])]) ).
fof(c_0_10,negated_conjecture,
( ~ apart_point_and_line(esk2_0,line_connecting(esk1_0,esk3_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_8])])])]) ).
fof(c_0_11,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_12,plain,
! [X9,X10,X11] :
( distinct_points(X10,X11)
| distinct_points(X9,X11)
| ~ distinct_points(X9,X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])])]) ).
fof(c_0_13,plain,
! [X26,X27,X28,X29] :
( apart_point_and_line(X27,X29)
| apart_point_and_line(X27,X28)
| apart_point_and_line(X26,X29)
| apart_point_and_line(X26,X28)
| ~ distinct_lines(X28,X29)
| ~ distinct_points(X26,X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])])]) ).
cnf(c_0_14,plain,
( ~ apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X6] : ~ distinct_points(X6,X6),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_11])]) ).
cnf(c_0_17,plain,
( ~ distinct_points(X1,X2)
| distinct_points(X2,X3)
| distinct_points(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_19,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci1]) ).
cnf(c_0_20,plain,
( ~ distinct_lines(X3,X4)
| ~ distinct_points(X1,X2)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
| apart_point_and_line(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( distinct_points(esk2_0,X1)
| distinct_points(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_24,plain,
! [X30,X31,X32] :
( apart_point_and_line(X32,X31)
| distinct_points(X30,X32)
| ~ apart_point_and_line(X30,X31) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])])]) ).
fof(c_0_25,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_26,plain,
! [X18,X19] :
( ~ apart_point_and_line(X18,line_connecting(X18,X19))
| ~ distinct_points(X18,X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_27,negated_conjecture,
( ~ distinct_points(X1,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X1,X3)
| apart_point_and_line(esk3_0,X3)
| apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
distinct_points(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( ~ apart_point_and_line(X1,X2)
| apart_point_and_line(X3,X2)
| distinct_points(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X20,X21] :
( ~ apart_point_and_line(X21,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_25])])]) ).
cnf(c_0_31,plain,
( ~ apart_point_and_line(X1,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( distinct_points(esk3_0,X1)
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_34,plain,
( ~ apart_point_and_line(X2,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_18])]) ).
cnf(c_0_36,negated_conjecture,
distinct_points(esk3_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_18])]) ).
cnf(c_0_37,negated_conjecture,
( apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_18])]) ).
cnf(c_0_38,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( ~ distinct_points(X1,esk3_0)
| apart_point_and_line(esk1_0,line_connecting(X1,esk3_0))
| apart_point_and_line(esk2_0,line_connecting(X1,esk3_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
distinct_points(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
~ apart_point_and_line(esk2_0,line_connecting(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_42,negated_conjecture,
apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_42]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO181+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 20 13:03:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2932655 completed with status 0
% 0.13/0.42 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.42 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2932662 completed with status 0
% 0.13/0.42 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.42 % No SInE strategy applied
% 0.13/0.42 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.42 % Preprocessing time : 0.001 s
% 0.13/0.42 % Presaturation interreduction done
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 15
% 0.13/0.42 % Removed by relevancy pruning/SinE : 0
% 0.13/0.42 % Initial clauses : 17
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 17
% 0.13/0.42 % Processed clauses : 108
% 0.13/0.42 % ...of these trivial : 0
% 0.13/0.42 % ...subsumed : 17
% 0.13/0.42 % ...remaining for further processing : 91
% 0.13/0.42 % Other redundant clauses eliminated : 0
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 2
% 0.13/0.42 % Backward-rewritten : 0
% 0.13/0.42 % Generated clauses : 369
% 0.13/0.42 % ...of the previous two non-redundant : 271
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 0
% 0.13/0.42 % Paramodulations : 343
% 0.13/0.42 % Factorizations : 26
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 0
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 106
% 0.13/0.42 % ...of those cached : 97
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 72
% 0.13/0.42 % Positive orientable unit clauses : 12
% 0.13/0.42 % Positive unorientable unit clauses: 0
% 0.13/0.42 % Negative unit clauses : 4
% 0.13/0.42 % Non-unit-clauses : 56
% 0.13/0.42 % Current number of unprocessed clauses: 195
% 0.13/0.42 % ...number of literals in the above : 807
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 19
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 357
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 240
% 0.13/0.42 % Non-unit clause-clause subsumptions : 19
% 0.13/0.42 % Unit Clause-clause subsumption calls : 17
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 0
% 0.13/0.42 % BW rewrite match successes : 0
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 6604
% 0.13/0.42 % Search garbage collected termcells : 202
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.011 s
% 0.13/0.42 % System time : 0.005 s
% 0.13/0.42 % Total time : 0.016 s
% 0.13/0.42 % Maximum resident set size: 3648 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.052 s
% 0.13/0.42 % System time : 0.018 s
% 0.13/0.42 % Total time : 0.070 s
% 0.13/0.42 % Maximum resident set size: 4864 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------