%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:27:38 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 35 ~; 50 |; 14 &)
% ( 0 <=>; 10 =>; 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 : 72 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( ~ apart_point_and_line(X3,line_connecting(X1,X2))
& distinct_points(X2,X3)
& distinct_points(X1,X3)
& distinct_points(X1,X2) )
=> ~ apart_point_and_line(X1,line_connecting(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X2,X3)
| distinct_points(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
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/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ apart_point_and_line(X3,line_connecting(X1,X2))
& distinct_points(X2,X3)
& distinct_points(X1,X3)
& distinct_points(X1,X2) )
=> ~ apart_point_and_line(X1,line_connecting(X3,X2)) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ apart_point_and_line(X3,line_connecting(X1,X2))
& distinct_points(X2,X3)
& distinct_points(X1,X3)
& distinct_points(X1,X2) )
=> ~ apart_point_and_line(X1,line_connecting(X3,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_9,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_10,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk3_0,esk2_0))
& ~ apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
& distinct_points(esk2_0,esk3_0)
& distinct_points(esk1_0,esk3_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]) ).
cnf(c_0_12,plain,
( ~ distinct_points(X1,X2)
| distinct_points(X2,X3)
| distinct_points(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
distinct_points(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X6] : ~ distinct_points(X6,X6),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_11])]) ).
cnf(c_0_15,negated_conjecture,
( distinct_points(esk3_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( distinct_points(X1,X2)
| distinct_points(esk3_0,X2)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
fof(c_0_18,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])])]) ).
cnf(c_0_19,negated_conjecture,
( distinct_points(esk2_0,X1)
| distinct_points(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_20,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_21,plain,
( ~ apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
apart_point_and_line(esk1_0,line_connecting(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( distinct_points(X1,X2)
| distinct_points(esk2_0,X2)
| distinct_points(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
fof(c_0_24,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_25,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_20]) ).
cnf(c_0_26,negated_conjecture,
( distinct_lines(line_connecting(esk3_0,esk2_0),X1)
| apart_point_and_line(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( distinct_points(X1,esk3_0)
| distinct_points(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
fof(c_0_28,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_24])])]) ).
cnf(c_0_29,negated_conjecture,
( ~ distinct_points(X1,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X1,X3)
| apart_point_and_line(esk1_0,X3)
| apart_point_and_line(X2,line_connecting(esk3_0,esk2_0))
| apart_point_and_line(X1,line_connecting(esk3_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
distinct_points(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
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_28]) ).
cnf(c_0_32,negated_conjecture,
( apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk3_0,line_connecting(esk3_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_33,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
cnf(c_0_34,negated_conjecture,
~ apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,negated_conjecture,
( apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30])]) ).
fof(c_0_36,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_33])])]) ).
cnf(c_0_37,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_39,plain,
( ~ apart_point_and_line(X2,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk3_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_37]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
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_39,c_0_40]),c_0_30])]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_41]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 13:17:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 739444 completed with status 0
% 0.11/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHNF-FFSS22-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.11/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.46 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 739451 completed with status 0
% 0.11/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHNF-FFSS22-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.11/0.46 % Preprocessing time : 0.001 s
% 0.11/0.46 % Presaturation interreduction done
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Theorem
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 15
% 0.11/0.46 % Removed by relevancy pruning/SinE : 0
% 0.11/0.46 % Initial clauses : 19
% 0.11/0.46 % Removed in clause preprocessing : 0
% 0.11/0.46 % Initial clauses in saturation : 19
% 0.11/0.46 % Processed clauses : 169
% 0.11/0.46 % ...of these trivial : 0
% 0.11/0.46 % ...subsumed : 69
% 0.11/0.46 % ...remaining for further processing : 100
% 0.11/0.46 % Other redundant clauses eliminated : 0
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 2
% 0.11/0.46 % Backward-rewritten : 1
% 0.11/0.46 % Generated clauses : 498
% 0.11/0.46 % ...of the previous two non-redundant : 359
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 0
% 0.11/0.46 % Paramodulations : 408
% 0.11/0.46 % Factorizations : 90
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 0
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 148
% 0.11/0.46 % ...of those cached : 140
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 78
% 0.11/0.46 % Positive orientable unit clauses : 10
% 0.11/0.46 % Positive unorientable unit clauses: 0
% 0.11/0.46 % Negative unit clauses : 4
% 0.11/0.46 % Non-unit-clauses : 64
% 0.11/0.46 % Current number of unprocessed clauses: 226
% 0.11/0.46 % ...number of literals in the above : 1178
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 22
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 784
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 441
% 0.11/0.46 % Non-unit clause-clause subsumptions : 71
% 0.11/0.46 % Unit Clause-clause subsumption calls : 22
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 1
% 0.11/0.46 % BW rewrite match successes : 1
% 0.11/0.46 % Condensation attempts : 0
% 0.11/0.46 % Condensation successes : 0
% 0.11/0.46 % Termbank termtop insertions : 7930
% 0.11/0.46 % Search garbage collected termcells : 219
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.016 s
% 0.11/0.46 % System time : 0.004 s
% 0.11/0.46 % Total time : 0.020 s
% 0.11/0.46 % Maximum resident set size: 3648 pages
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.067 s
% 0.11/0.46 % System time : 0.016 s
% 0.11/0.46 % Total time : 0.083 s
% 0.11/0.46 % Maximum resident set size: 4608 pages
% 0.11/0.46 % E exiting
%------------------------------------------------------------------------------