%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 0.54s 0.60s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 15 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 28 ~; 34 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 4 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X4,X5] :
( ( incident_point_and_line(X2,line_connecting(X4,X5))
& incident_point_and_line(X1,line_connecting(X4,X5))
& distinct_points(X4,X5)
& distinct_points(X1,X2) )
=> ( incident_point_and_line(X5,line_connecting(X1,X2))
& incident_point_and_line(X4,line_connecting(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(a4,axiom,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a4) ).
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(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| distinct_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(cp2,axiom,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( incident_point_and_line(X2,line_connecting(X4,X5))
& incident_point_and_line(X1,line_connecting(X4,X5))
& distinct_points(X4,X5)
& distinct_points(X1,X2) )
=> ( incident_point_and_line(X5,line_connecting(X1,X2))
& incident_point_and_line(X4,line_connecting(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_9,plain,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4]) ).
fof(c_0_10,negated_conjecture,
( ( ~ incident_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0))
| ~ incident_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) )
& incident_point_and_line(esk2_0,line_connecting(esk3_0,esk4_0))
& incident_point_and_line(esk1_0,line_connecting(esk3_0,esk4_0))
& distinct_points(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_8])])])]) ).
fof(c_0_11,plain,
! [X88,X89] :
( ( incident_point_and_line(X88,X89)
| apart_point_and_line(X88,X89) )
& ( ~ apart_point_and_line(X88,X89)
| ~ incident_point_and_line(X88,X89) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_12,negated_conjecture,
( ~ incident_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0))
| ~ incident_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( incident_point_and_line(X1,X2)
| apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X38,X39,X40] :
( apart_point_and_line(X38,X40)
| distinct_lines(X39,X40)
| ~ apart_point_and_line(X38,X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])])]) ).
cnf(c_0_15,negated_conjecture,
( ~ incident_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_17,plain,
! [X17,X18,X19] :
( distinct_lines(X18,X19)
| distinct_lines(X17,X19)
| ~ distinct_lines(X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])])]) ).
cnf(c_0_18,plain,
( ~ apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| distinct_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( apart_point_and_line(esk4_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
fof(c_0_20,plain,
! [X12] : ~ distinct_lines(X12,X12),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_16])]) ).
cnf(c_0_21,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X2,X3)
| distinct_lines(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_23,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(c_0_24,plain,
! [X44,X45] :
( convergent_lines(X44,X45)
| ~ distinct_lines(X44,X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_25,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( distinct_lines(X1,X2)
| distinct_lines(line_connecting(esk1_0,esk2_0),X2)
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_27,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(c_0_28,plain,
! [X46,X47] : ~ convergent_lines(parallel_through_point(X47,X46),X47),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
cnf(c_0_29,plain,
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( distinct_lines(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_31,plain,
! [X48,X49] : ~ apart_point_and_line(X48,parallel_through_point(X49,X48)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
cnf(c_0_32,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( convergent_lines(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,X1)
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk4_0,parallel_through_point(line_connecting(esk1_0,esk2_0),X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
| apart_point_and_line(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( distinct_lines(X1,X2)
| distinct_lines(line_connecting(esk1_0,esk2_0),X2)
| apart_point_and_line(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( distinct_lines(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( convergent_lines(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
apart_point_and_line(esk3_0,parallel_through_point(line_connecting(esk1_0,esk2_0),X1)),
inference(spm,[status(thm)],[c_0_32,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_34,c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n012.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 13:09:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.02/0.40 Running first-order theorem proving
% 0.02/0.40 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
% 0.54/0.60 % Version: 3.5.1
% 0.54/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.54/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.54/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.54/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.54/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.54/0.60 % Starting sh5l with 300s (1) cores
% 0.54/0.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 273856 completed with status 0
% 0.54/0.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.54/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.54/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.54/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.54/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.54/0.60 % No SInE strategy applied
% 0.54/0.60 % Search class: FGHNF-FFMS22-SFFFFFNN
% 0.54/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.54/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.54/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.54/0.60 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.54/0.60 % Starting new_bool_3 with 136s (1) cores
% 0.54/0.60 % Starting new_bool_1 with 136s (1) cores
% 0.54/0.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 273861 completed with status 0
% 0.54/0.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.54/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.54/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.54/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.54/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.54/0.60 % No SInE strategy applied
% 0.54/0.60 % Search class: FGHNF-FFMS22-SFFFFFNN
% 0.54/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.54/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.54/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.54/0.60 % Preprocessing time : 0.001 s
% 0.54/0.60 % Presaturation interreduction done
% 0.54/0.60
% 0.54/0.60 % Proof found!
% 0.54/0.60 % SZS status Theorem
% 0.54/0.60 % SZS output start CNFRefutation
% See solution above
% 0.54/0.60 % Parsed axioms : 36
% 0.54/0.60 % Removed by relevancy pruning/SinE : 0
% 0.54/0.60 % Initial clauses : 51
% 0.54/0.60 % Removed in clause preprocessing : 0
% 0.54/0.60 % Initial clauses in saturation : 51
% 0.54/0.60 % Processed clauses : 960
% 0.54/0.60 % ...of these trivial : 1
% 0.54/0.60 % ...subsumed : 551
% 0.54/0.60 % ...remaining for further processing : 408
% 0.54/0.60 % Other redundant clauses eliminated : 0
% 0.54/0.60 % Clauses deleted for lack of memory : 0
% 0.54/0.60 % Backward-subsumed : 44
% 0.54/0.60 % Backward-rewritten : 87
% 0.54/0.60 % Generated clauses : 4626
% 0.54/0.60 % ...of the previous two non-redundant : 4298
% 0.54/0.60 % ...aggressively subsumed : 0
% 0.54/0.60 % Contextual simplify-reflections : 0
% 0.54/0.60 % Paramodulations : 4146
% 0.54/0.60 % Factorizations : 480
% 0.54/0.60 % NegExts : 0
% 0.54/0.60 % Equation resolutions : 0
% 0.54/0.60 % Disequality decompositions : 0
% 0.54/0.60 % Total rewrite steps : 441
% 0.54/0.60 % ...of those cached : 394
% 0.54/0.60 % Propositional unsat checks : 0
% 0.54/0.60 % Propositional check models : 0
% 0.54/0.60 % Propositional check unsatisfiable : 0
% 0.54/0.60 % Propositional clauses : 0
% 0.54/0.60 % Propositional clauses after purity: 0
% 0.54/0.60 % Propositional unsat core size : 0
% 0.54/0.60 % Propositional preprocessing time : 0.000
% 0.54/0.60 % Propositional encoding time : 0.000
% 0.54/0.60 % Propositional solver time : 0.000
% 0.54/0.60 % Success case prop preproc time : 0.000
% 0.54/0.60 % Success case prop encoding time : 0.000
% 0.54/0.60 % Success case prop solver time : 0.000
% 0.54/0.60 % Current number of processed clauses : 230
% 0.54/0.60 % Positive orientable unit clauses : 31
% 0.54/0.60 % Positive unorientable unit clauses: 0
% 0.54/0.60 % Negative unit clauses : 9
% 0.54/0.60 % Non-unit-clauses : 190
% 0.54/0.60 % Current number of unprocessed clauses: 3290
% 0.54/0.60 % ...number of literals in the above : 19086
% 0.54/0.60 % Current number of archived formulas : 0
% 0.54/0.60 % Current number of archived clauses : 178
% 0.54/0.60 % Clause-clause subsumption calls (NU) : 32341
% 0.54/0.60 % Rec. Clause-clause subsumption calls : 9810
% 0.54/0.60 % Non-unit clause-clause subsumptions : 572
% 0.54/0.60 % Unit Clause-clause subsumption calls : 1440
% 0.54/0.60 % Rewrite failures with RHS unbound : 0
% 0.54/0.60 % BW rewrite match attempts : 31
% 0.54/0.60 % BW rewrite match successes : 9
% 0.54/0.60 % Condensation attempts : 0
% 0.54/0.60 % Condensation successes : 0
% 0.54/0.60 % Termbank termtop insertions : 74827
% 0.54/0.60 % Search garbage collected termcells : 533
% 0.54/0.60
% 0.54/0.60 % -------------------------------------------------
% 0.54/0.60 % User time : 0.118 s
% 0.54/0.60 % System time : 0.005 s
% 0.54/0.60 % Total time : 0.123 s
% 0.54/0.60 % Maximum resident set size: 3680 pages
% 0.54/0.60
% 0.54/0.60 % -------------------------------------------------
% 0.54/0.60 % User time : 0.612 s
% 0.54/0.60 % System time : 0.033 s
% 0.54/0.60 % Total time : 0.645 s
% 0.54/0.60 % Maximum resident set size: 4608 pages
% 0.54/0.60 % E exiting
%------------------------------------------------------------------------------