%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO186+2 : 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 : n006.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 12:27:37 PM UTC 2026
% Result : Theorem 0.13s 0.64s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 20 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 126 ( 51 ~; 51 |; 15 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X4,X5] :
( ( ~ apart_point_and_line(X1,X5)
& ~ apart_point_and_line(X1,X4)
& convergent_lines(X4,X5)
& distinct_points(X1,X2) )
=> ~ distinct_points(X1,intersection_point(X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(apart6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| distinct_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).
fof(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
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/GEO008+0.ax',cu1) ).
fof(con2,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( ( apart_point_and_line(X3,X2)
| apart_point_and_line(X3,X1) )
=> distinct_points(X3,intersection_point(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( ~ apart_point_and_line(X1,X5)
& ~ apart_point_and_line(X1,X4)
& convergent_lines(X4,X5)
& distinct_points(X1,X2) )
=> ~ distinct_points(X1,intersection_point(X4,X5)) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( ~ apart_point_and_line(X1,X5)
& ~ apart_point_and_line(X1,X4)
& convergent_lines(X4,X5)
& distinct_points(X1,X2) )
=> ~ distinct_points(X1,intersection_point(X4,X5)) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_11,plain,
! [X15,X16,X17] :
( convergent_lines(X16,X17)
| convergent_lines(X15,X17)
| ~ convergent_lines(X15,X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])])]) ).
fof(c_0_12,negated_conjecture,
( distinct_points(esk1_0,intersection_point(esk3_0,esk4_0))
& ~ apart_point_and_line(esk1_0,esk4_0)
& ~ apart_point_and_line(esk1_0,esk3_0)
& convergent_lines(esk3_0,esk4_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_10])])])]) ).
fof(c_0_13,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_14,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
convergent_lines(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X8] : ~ convergent_lines(X8,X8),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_13])]) ).
cnf(c_0_17,negated_conjecture,
( convergent_lines(esk4_0,X1)
| convergent_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(esk4_0,X2)
| convergent_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( convergent_lines(esk3_0,X1)
| convergent_lines(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_21,plain,
! [X12,X13,X14] :
( distinct_lines(X13,X14)
| distinct_lines(X12,X14)
| ~ distinct_lines(X12,X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])])]) ).
fof(c_0_22,plain,
! [X34,X35] :
( distinct_lines(X34,X35)
| ~ convergent_lines(X34,X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])])]) ).
cnf(c_0_23,negated_conjecture,
( convergent_lines(X1,X2)
| convergent_lines(esk3_0,X2)
| convergent_lines(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
fof(c_0_24,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_25,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X2,X3)
| distinct_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ convergent_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( convergent_lines(X1,esk4_0)
| convergent_lines(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
fof(c_0_28,plain,
! [X7] : ~ distinct_lines(X7,X7),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_24])]) ).
cnf(c_0_29,plain,
( ~ convergent_lines(X1,X3)
| distinct_lines(X3,X2)
| distinct_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
convergent_lines(esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
fof(c_0_31,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_32,plain,
! [X24,X25,X26,X27] :
( apart_point_and_line(X25,X27)
| apart_point_and_line(X25,X26)
| apart_point_and_line(X24,X27)
| apart_point_and_line(X24,X26)
| ~ distinct_lines(X26,X27)
| ~ distinct_points(X24,X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])])]) ).
cnf(c_0_33,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( distinct_lines(esk4_0,X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_35,plain,
! [X6] : ~ distinct_points(X6,X6),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_36,plain,
! [X21,X22,X23] :
( ( ~ convergent_lines(X21,X22)
| distinct_points(X23,intersection_point(X21,X22))
| ~ apart_point_and_line(X23,X22) )
& ( ~ convergent_lines(X21,X22)
| distinct_points(X23,intersection_point(X21,X22))
| ~ apart_point_and_line(X23,X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])])]) ).
cnf(c_0_37,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_32]) ).
cnf(c_0_38,negated_conjecture,
distinct_lines(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
( ~ convergent_lines(X3,X2)
| ~ apart_point_and_line(X1,X2)
| distinct_points(X1,intersection_point(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( ~ distinct_points(X1,X2)
| apart_point_and_line(X2,esk4_0)
| apart_point_and_line(X2,esk3_0)
| apart_point_and_line(X1,esk4_0)
| apart_point_and_line(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
distinct_points(esk1_0,intersection_point(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_43,negated_conjecture,
~ apart_point_and_line(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_44,negated_conjecture,
~ apart_point_and_line(esk1_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_45,plain,
( ~ convergent_lines(X2,X3)
| ~ apart_point_and_line(X1,X2)
| distinct_points(X1,intersection_point(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0)
| apart_point_and_line(intersection_point(esk3_0,esk4_0),esk4_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_15])]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.57 % Computer : n006.cluster.edu
% 0.08/0.57 % Model : x86_64 x86_64
% 0.08/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.57 % Memory : 8046.5625MB
% 0.08/0.57 % OS : Linux 6.8.0-71-generic
% 0.08/0.57 % CPULimit : 300
% 0.08/0.57 % WCLimit : 300
% 0.08/0.57 % DateTime : Sun Sep 20 13:12:13 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.61 Running first-order theorem proving
% 0.13/0.62 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
% 0.13/0.64 % Version: 3.5.1
% 0.13/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.64 % Starting sh5l with 300s (1) cores
% 0.13/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 650318 completed with status 0
% 0.13/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.64 % No SInE strategy applied
% 0.13/0.64 % Search class: FGUNF-FFSS22-SFFFFFNN
% 0.13/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.64 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 650325 completed with status 0
% 0.13/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.13/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.64 % No SInE strategy applied
% 0.13/0.64 % Search class: FGUNF-FFSS22-SFFFFFNN
% 0.13/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.64 % Preprocessing time : 0.001 s
% 0.13/0.64 % Presaturation interreduction done
% 0.13/0.64
% 0.13/0.64 % Proof found!
% 0.13/0.64 % SZS status Theorem
% 0.13/0.64 % SZS output start CNFRefutation
% See solution above
% 0.13/0.64 % Parsed axioms : 13
% 0.13/0.64 % Removed by relevancy pruning/SinE : 0
% 0.13/0.64 % Initial clauses : 19
% 0.13/0.64 % Removed in clause preprocessing : 0
% 0.13/0.64 % Initial clauses in saturation : 19
% 0.13/0.64 % Processed clauses : 112
% 0.13/0.64 % ...of these trivial : 0
% 0.13/0.64 % ...subsumed : 27
% 0.13/0.64 % ...remaining for further processing : 85
% 0.13/0.64 % Other redundant clauses eliminated : 0
% 0.13/0.64 % Clauses deleted for lack of memory : 0
% 0.13/0.64 % Backward-subsumed : 0
% 0.13/0.64 % Backward-rewritten : 1
% 0.13/0.64 % Generated clauses : 277
% 0.13/0.64 % ...of the previous two non-redundant : 208
% 0.13/0.64 % ...aggressively subsumed : 0
% 0.13/0.64 % Contextual simplify-reflections : 0
% 0.13/0.64 % Paramodulations : 223
% 0.13/0.64 % Factorizations : 54
% 0.13/0.64 % NegExts : 0
% 0.13/0.64 % Equation resolutions : 0
% 0.13/0.64 % Disequality decompositions : 0
% 0.13/0.64 % Total rewrite steps : 71
% 0.13/0.64 % ...of those cached : 65
% 0.13/0.64 % Propositional unsat checks : 0
% 0.13/0.64 % Propositional check models : 0
% 0.13/0.64 % Propositional check unsatisfiable : 0
% 0.13/0.64 % Propositional clauses : 0
% 0.13/0.64 % Propositional clauses after purity: 0
% 0.13/0.64 % Propositional unsat core size : 0
% 0.13/0.64 % Propositional preprocessing time : 0.000
% 0.13/0.64 % Propositional encoding time : 0.000
% 0.13/0.64 % Propositional solver time : 0.000
% 0.13/0.64 % Success case prop preproc time : 0.000
% 0.13/0.64 % Success case prop encoding time : 0.000
% 0.13/0.64 % Success case prop solver time : 0.000
% 0.13/0.64 % Current number of processed clauses : 65
% 0.13/0.64 % Positive orientable unit clauses : 7
% 0.13/0.64 % Positive unorientable unit clauses: 0
% 0.13/0.64 % Negative unit clauses : 5
% 0.13/0.64 % Non-unit-clauses : 53
% 0.13/0.64 % Current number of unprocessed clauses: 130
% 0.13/0.64 % ...number of literals in the above : 589
% 0.13/0.64 % Current number of archived formulas : 0
% 0.13/0.64 % Current number of archived clauses : 20
% 0.13/0.64 % Clause-clause subsumption calls (NU) : 478
% 0.13/0.64 % Rec. Clause-clause subsumption calls : 310
% 0.13/0.64 % Non-unit clause-clause subsumptions : 26
% 0.13/0.64 % Unit Clause-clause subsumption calls : 15
% 0.13/0.64 % Rewrite failures with RHS unbound : 0
% 0.13/0.64 % BW rewrite match attempts : 1
% 0.13/0.64 % BW rewrite match successes : 1
% 0.13/0.64 % Condensation attempts : 0
% 0.13/0.64 % Condensation successes : 0
% 0.13/0.64 % Termbank termtop insertions : 4204
% 0.13/0.64 % Search garbage collected termcells : 233
% 0.13/0.64
% 0.13/0.64 % -------------------------------------------------
% 0.13/0.64 % User time : 0.009 s
% 0.13/0.64 % System time : 0.005 s
% 0.13/0.64 % Total time : 0.014 s
% 0.13/0.64 % Maximum resident set size: 3648 pages
% 0.13/0.64
% 0.13/0.64 % -------------------------------------------------
% 0.13/0.64 % User time : 0.052 s
% 0.13/0.64 % System time : 0.010 s
% 0.13/0.64 % Total time : 0.062 s
% 0.13/0.64 % Maximum resident set size: 4864 pages
% 0.13/0.64 % E exiting
%------------------------------------------------------------------------------