%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO659+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 12:28:42 PM UTC 2026
% Result : Theorem 4.49s 1.29s
% Output : CNFRefutation 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 28
% Syntax : Number of formulae : 133 ( 31 unt; 0 def)
% Number of atoms : 333 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 317 ( 117 ~; 114 |; 57 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-6 aty)
% Number of variables : 515 ( 38 sgn 272 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD9,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( perp(X3,X4,X5,X6)
& perp(X1,X2,X3,X4) )
=> para(X1,X2,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD9) ).
fof(ruleX11,axiom,
! [X1,X2,X3,X8] :
? [X9] :
( circle(X8,X1,X2,X3)
=> perp(X9,X1,X1,X8) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleX11) ).
fof(ruleD8,axiom,
! [X1,X2,X3,X4] :
( perp(X1,X2,X3,X4)
=> perp(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD8) ).
fof(exemplo6GDDFULLmoreE02317,conjecture,
! [X1,X2,X3,X4,X5,X6,X13,X14,X19,X20,X21,X22,X23] :
( ( circle(X6,X1,X14,X23)
& coll(X1,X4,X14)
& circle(X6,X2,X13,X22)
& coll(X2,X5,X13)
& perp(X3,X2,X21,X6)
& midp(X21,X3,X2)
& perp(X1,X2,X20,X6)
& midp(X20,X1,X2)
& perp(X1,X3,X19,X6)
& midp(X19,X1,X3)
& coll(X5,X1,X3)
& perp(X5,X2,X1,X3)
& coll(X4,X2,X3)
& perp(X4,X1,X2,X3) )
=> para(X4,X5,X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE02317) ).
fof(ruleD4,axiom,
! [X1,X2,X3,X4] :
( para(X1,X2,X3,X4)
=> para(X1,X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD4) ).
fof(ruleD19,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12] :
( eqangle(X1,X2,X3,X4,X9,X10,X11,X12)
=> eqangle(X3,X4,X1,X2,X11,X12,X9,X10) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD19) ).
fof(ruleD40,axiom,
! [X1,X2,X3,X4,X9,X10] :
( para(X1,X2,X3,X4)
=> eqangle(X1,X2,X9,X10,X3,X4,X9,X10) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD40) ).
fof(ruleD5,axiom,
! [X1,X2,X3,X4] :
( para(X1,X2,X3,X4)
=> para(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD5) ).
fof(ruleD39,axiom,
! [X1,X2,X3,X4,X9,X10] :
( eqangle(X1,X2,X9,X10,X3,X4,X9,X10)
=> para(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD39) ).
fof(ruleD66,axiom,
! [X1,X2,X3] :
( para(X1,X2,X1,X3)
=> coll(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD66) ).
fof(ruleD2,axiom,
! [X1,X2,X3] :
( coll(X1,X2,X3)
=> coll(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD2) ).
fof(ruleD1,axiom,
! [X1,X2,X3] :
( coll(X1,X2,X3)
=> coll(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
fof(ruleD42b,axiom,
! [X1,X2,X9,X10] :
( ( coll(X9,X10,X2)
& eqangle(X9,X1,X9,X2,X10,X1,X10,X2) )
=> cyclic(X1,X2,X9,X10) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD42b) ).
fof(ruleD3,axiom,
! [X1,X2,X3,X4] :
( ( coll(X1,X2,X4)
& coll(X1,X2,X3) )
=> coll(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD3) ).
fof(ruleD15,axiom,
! [X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
=> cyclic(X1,X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD15) ).
fof(ruleD51,axiom,
! [X1,X2,X3,X8,X7] :
( ( eqangle(X1,X2,X1,X3,X8,X2,X8,X7)
& coll(X7,X2,X3)
& circle(X8,X1,X2,X3) )
=> midp(X7,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD51) ).
fof(ruleD41,axiom,
! [X1,X2,X9,X10] :
( cyclic(X1,X2,X9,X10)
=> eqangle(X9,X1,X9,X2,X10,X1,X10,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD41) ).
fof(ruleD14,axiom,
! [X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
=> cyclic(X1,X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD14) ).
fof(ruleD16,axiom,
! [X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
=> cyclic(X2,X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD16) ).
fof(ruleD45,axiom,
! [X1,X2,X3,X5,X6] :
( ( coll(X6,X1,X3)
& para(X5,X6,X2,X3)
& midp(X5,X1,X2) )
=> midp(X6,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD45) ).
fof(ruleD17,axiom,
! [X1,X2,X3,X4,X5] :
( ( cyclic(X1,X2,X3,X5)
& cyclic(X1,X2,X3,X4) )
=> cyclic(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
fof(ruleD11,axiom,
! [X1,X2,X7] :
( midp(X7,X2,X1)
=> midp(X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD11) ).
fof(ruleD73,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12] :
( ( para(X9,X10,X11,X12)
& eqangle(X1,X2,X3,X4,X9,X10,X11,X12) )
=> para(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD73) ).
fof(ruleD46,axiom,
! [X1,X2,X8] :
( cong(X8,X1,X8,X2)
=> eqangle(X8,X1,X1,X2,X1,X2,X8,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD46) ).
fof(ruleD68,axiom,
! [X1,X2,X3] :
( midp(X1,X2,X3)
=> cong(X1,X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD68) ).
fof(ruleD64,axiom,
! [X1,X2,X3,X4,X7] :
( ( para(X1,X4,X2,X3)
& para(X1,X3,X2,X4)
& midp(X7,X1,X2) )
=> midp(X7,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
fof(ruleX6,axiom,
! [X1,X2,X3,X4,X7,X17] :
? [X9] :
( ( midp(X17,X3,X4)
& midp(X7,X1,X2) )
=> ( para(X9,X17,X1,X3)
& para(X9,X7,X2,X4)
& midp(X9,X1,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleX6) ).
fof(ruleD44,axiom,
! [X1,X2,X3,X5,X6] :
( ( midp(X6,X1,X3)
& midp(X5,X1,X2) )
=> para(X5,X6,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD44) ).
fof(c_0_28,plain,
! [X56,X57,X58,X59,X60,X61] :
( para(X56,X57,X60,X61)
| ~ perp(X58,X59,X60,X61)
| ~ perp(X56,X57,X58,X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])])]) ).
fof(c_0_29,plain,
! [X498,X499,X500,X501] :
( perp(esk12_4(X498,X499,X500,X501),X498,X498,X501)
| ~ circle(X501,X498,X499,X500) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])])]) ).
fof(c_0_30,plain,
! [X52,X53,X54,X55] :
( perp(X54,X55,X52,X53)
| ~ perp(X52,X53,X54,X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])])]) ).
cnf(c_0_31,plain,
( ~ perp(X3,X4,X5,X6)
| ~ perp(X1,X2,X3,X4)
| para(X1,X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
( ~ circle(X1,X2,X3,X4)
| perp(esk12_4(X2,X3,X4,X1),X2,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( ~ perp(X1,X2,X3,X4)
| perp(X3,X4,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,negated_conjecture,
~ ! [X1,X2,X3,X4,X5,X6,X13,X14,X19,X20,X21,X22,X23] :
( ( circle(X6,X1,X14,X23)
& coll(X1,X4,X14)
& circle(X6,X2,X13,X22)
& coll(X2,X5,X13)
& perp(X3,X2,X21,X6)
& midp(X21,X3,X2)
& perp(X1,X2,X20,X6)
& midp(X20,X1,X2)
& perp(X1,X3,X19,X6)
& midp(X19,X1,X3)
& coll(X5,X1,X3)
& perp(X5,X2,X1,X3)
& coll(X4,X2,X3)
& perp(X4,X1,X2,X3) )
=> para(X4,X5,X13,X14) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE02317]) ).
cnf(c_0_35,plain,
( ~ perp(X1,X2,esk12_4(X3,X5,X6,X4),X3)
| ~ circle(X4,X3,X5,X6)
| para(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( ~ circle(X2,X1,X3,X4)
| perp(X1,X2,esk12_4(X1,X3,X4,X2),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
fof(c_0_37,negated_conjecture,
( ~ para(esk24_0,esk25_0,esk27_0,esk28_0)
& circle(esk26_0,esk21_0,esk28_0,esk33_0)
& coll(esk21_0,esk24_0,esk28_0)
& circle(esk26_0,esk22_0,esk27_0,esk32_0)
& coll(esk22_0,esk25_0,esk27_0)
& perp(esk23_0,esk22_0,esk31_0,esk26_0)
& midp(esk31_0,esk23_0,esk22_0)
& perp(esk21_0,esk22_0,esk30_0,esk26_0)
& midp(esk30_0,esk21_0,esk22_0)
& perp(esk21_0,esk23_0,esk29_0,esk26_0)
& midp(esk29_0,esk21_0,esk23_0)
& coll(esk25_0,esk21_0,esk23_0)
& perp(esk25_0,esk22_0,esk21_0,esk23_0)
& coll(esk24_0,esk22_0,esk23_0)
& perp(esk24_0,esk21_0,esk22_0,esk23_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
fof(c_0_38,plain,
! [X34,X35,X36,X37] :
( para(X34,X35,X37,X36)
| ~ para(X34,X35,X36,X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])])]) ).
cnf(c_0_39,plain,
( ~ circle(X2,X1,X3,X4)
| para(X1,X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
circle(esk26_0,esk22_0,esk27_0,esk32_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_41,plain,
! [X105,X106,X107,X108,X109,X110,X111,X112] :
( eqangle(X107,X108,X105,X106,X111,X112,X109,X110)
| ~ eqangle(X105,X106,X107,X108,X109,X110,X111,X112) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])])]) ).
fof(c_0_42,plain,
! [X259,X260,X261,X262,X263,X264] :
( eqangle(X259,X260,X263,X264,X261,X262,X263,X264)
| ~ para(X259,X260,X261,X262) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])])]) ).
fof(c_0_43,plain,
! [X38,X39,X40,X41] :
( para(X40,X41,X38,X39)
| ~ para(X38,X39,X40,X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])])]) ).
cnf(c_0_44,plain,
( ~ para(X1,X2,X3,X4)
| para(X1,X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
para(esk22_0,esk26_0,esk22_0,esk26_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_46,plain,
! [X253,X254,X255,X256,X257,X258] :
( para(X253,X254,X255,X256)
| ~ eqangle(X253,X254,X257,X258,X255,X256,X257,X258) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])])]) ).
cnf(c_0_47,plain,
( ~ eqangle(X1,X2,X3,X4,X5,X6,X7,X8)
| eqangle(X3,X4,X1,X2,X7,X8,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
( ~ para(X1,X2,X3,X4)
| eqangle(X1,X2,X5,X6,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
( ~ para(X1,X2,X3,X4)
| para(X3,X4,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,negated_conjecture,
para(esk22_0,esk26_0,esk26_0,esk22_0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
( ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4)
| para(X1,X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( ~ para(X3,X4,X5,X6)
| eqangle(X1,X2,X3,X4,X1,X2,X5,X6) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
para(esk26_0,esk22_0,esk22_0,esk26_0),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_54,plain,
! [X388,X389,X390] :
( coll(X388,X389,X390)
| ~ para(X388,X389,X388,X390) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])])]) ).
cnf(c_0_55,plain,
( ~ para(X3,X4,X3,X4)
| para(X1,X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
para(esk26_0,esk22_0,esk26_0,esk22_0),
inference(spm,[status(thm)],[c_0_44,c_0_53]) ).
fof(c_0_57,plain,
! [X27,X28,X29] :
( coll(X28,X27,X29)
| ~ coll(X27,X28,X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])])]) ).
cnf(c_0_58,plain,
( ~ para(X1,X2,X1,X3)
| coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_60,plain,
! [X24,X25,X26] :
( coll(X24,X26,X25)
| ~ coll(X24,X25,X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])])]) ).
cnf(c_0_61,plain,
( ~ coll(X1,X2,X3)
| coll(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_63,plain,
! [X273,X274,X275,X276] :
( cyclic(X273,X274,X275,X276)
| ~ coll(X275,X276,X274)
| ~ eqangle(X275,X273,X275,X274,X276,X273,X276,X274) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])])]) ).
fof(c_0_64,plain,
! [X30,X31,X32,X33] :
( coll(X32,X33,X30)
| ~ coll(X30,X31,X33)
| ~ coll(X30,X31,X32) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])])]) ).
cnf(c_0_65,plain,
( ~ coll(X1,X2,X3)
| coll(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
( ~ coll(X1,X4,X3)
| ~ eqangle(X1,X2,X1,X3,X4,X2,X4,X3)
| cyclic(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,plain,
( ~ coll(X1,X2,X4)
| ~ coll(X1,X2,X3)
| coll(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
fof(c_0_70,plain,
! [X84,X85,X86,X87] :
( cyclic(X84,X86,X85,X87)
| ~ cyclic(X84,X85,X86,X87) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])])]) ).
cnf(c_0_71,plain,
( ~ coll(X3,X3,X2)
| ~ para(X3,X1,X3,X1)
| cyclic(X1,X2,X3,X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_48]) ).
cnf(c_0_72,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_69])]) ).
fof(c_0_73,plain,
! [X314,X315,X316,X317,X318] :
( midp(X318,X315,X316)
| ~ eqangle(X314,X315,X314,X316,X317,X315,X317,X318)
| ~ coll(X318,X315,X316)
| ~ circle(X317,X314,X315,X316) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD51])])]) ).
fof(c_0_74,plain,
! [X265,X266,X267,X268] :
( eqangle(X267,X265,X267,X266,X268,X265,X268,X266)
| ~ cyclic(X265,X266,X267,X268) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])])]) ).
fof(c_0_75,plain,
! [X80,X81,X82,X83] :
( cyclic(X80,X81,X83,X82)
| ~ cyclic(X80,X81,X82,X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])])]) ).
cnf(c_0_76,plain,
( ~ cyclic(X1,X2,X3,X4)
| cyclic(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_59])]),c_0_72])]) ).
cnf(c_0_78,plain,
( ~ eqangle(X2,X3,X2,X4,X1,X3,X1,X5)
| ~ coll(X5,X3,X4)
| ~ circle(X1,X2,X3,X4)
| midp(X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,plain,
( ~ cyclic(X1,X2,X3,X4)
| eqangle(X3,X1,X3,X2,X4,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_80,plain,
! [X88,X89,X90,X91] :
( cyclic(X89,X88,X90,X91)
| ~ cyclic(X88,X89,X90,X91) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])])]) ).
cnf(c_0_81,plain,
( ~ cyclic(X1,X2,X3,X4)
| cyclic(X1,X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
fof(c_0_83,plain,
! [X288,X289,X290,X291,X292] :
( midp(X292,X288,X290)
| ~ coll(X292,X288,X290)
| ~ para(X291,X292,X289,X290)
| ~ midp(X291,X288,X289) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])])]) ).
cnf(c_0_84,plain,
( ~ coll(X1,X2,X1)
| ~ circle(X4,X3,X2,X1)
| ~ cyclic(X2,X1,X3,X4)
| midp(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,negated_conjecture,
circle(esk26_0,esk21_0,esk28_0,esk33_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_86,plain,
! [X92,X93,X94,X95,X96] :
( cyclic(X93,X94,X95,X96)
| ~ cyclic(X92,X93,X94,X96)
| ~ cyclic(X92,X93,X94,X95) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])])]) ).
cnf(c_0_87,plain,
( ~ cyclic(X1,X2,X3,X4)
| cyclic(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_88,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,plain,
( ~ coll(X4,X2,X5)
| ~ para(X1,X4,X3,X5)
| ~ midp(X1,X2,X3)
| midp(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( ~ coll(esk33_0,esk28_0,esk33_0)
| ~ cyclic(esk28_0,esk33_0,esk21_0,esk26_0)
| midp(esk33_0,esk28_0,esk33_0) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,plain,
( ~ cyclic(X1,X2,X3,X5)
| ~ cyclic(X1,X2,X3,X4)
| cyclic(X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,plain,
( ~ para(X4,X1,X5,X3)
| ~ midp(X4,X2,X5)
| midp(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_72])]) ).
cnf(c_0_94,negated_conjecture,
( ~ cyclic(esk28_0,esk33_0,esk21_0,esk26_0)
| midp(esk33_0,esk28_0,esk33_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_66])]) ).
cnf(c_0_95,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_92])]) ).
fof(c_0_96,plain,
! [X68,X69,X70] :
( midp(X70,X68,X69)
| ~ midp(X70,X69,X68) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD11])])]) ).
cnf(c_0_97,negated_conjecture,
( ~ midp(X3,X2,X3)
| midp(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_59]) ).
cnf(c_0_98,negated_conjecture,
midp(esk33_0,esk28_0,esk33_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
fof(c_0_99,plain,
! [X414,X415,X416,X417,X418,X419,X420,X421] :
( para(X414,X415,X416,X417)
| ~ para(X418,X419,X420,X421)
| ~ eqangle(X414,X415,X416,X417,X418,X419,X420,X421) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD73])])]) ).
fof(c_0_100,plain,
! [X293,X294,X295] :
( eqangle(X295,X293,X293,X294,X293,X294,X295,X294)
| ~ cong(X295,X293,X295,X294) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])])]) ).
fof(c_0_101,plain,
! [X394,X395,X396] :
( cong(X394,X395,X394,X396)
| ~ midp(X394,X395,X396) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])])]) ).
cnf(c_0_102,plain,
( ~ midp(X1,X2,X3)
| midp(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_103,negated_conjecture,
midp(X1,esk28_0,X1),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,plain,
( ~ para(X5,X6,X7,X8)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X7,X8)
| para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_105,plain,
( ~ cong(X1,X2,X1,X3)
| eqangle(X1,X2,X2,X3,X2,X3,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_106,plain,
( ~ midp(X1,X2,X3)
| cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_107,negated_conjecture,
midp(X1,X1,esk28_0),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,plain,
( ~ para(X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3)
| para(X1,X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
cong(X1,X1,X1,esk28_0),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
fof(c_0_110,plain,
! [X378,X379,X380,X381,X382] :
( midp(X382,X380,X381)
| ~ para(X378,X381,X379,X380)
| ~ para(X378,X380,X379,X381)
| ~ midp(X382,X378,X379) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])])]) ).
cnf(c_0_111,negated_conjecture,
para(X1,X1,X1,esk28_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_59])]) ).
cnf(c_0_112,plain,
( ~ para(X2,X5,X3,X4)
| ~ para(X2,X4,X3,X5)
| ~ midp(X1,X2,X3)
| midp(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_113,negated_conjecture,
( ~ midp(X1,X2,X1)
| midp(X1,X2,esk28_0) ),
inference(spm,[status(thm)],[c_0_93,c_0_111]) ).
fof(c_0_114,plain,
! [X464,X465,X466,X467,X468,X469] :
( ( ~ midp(X469,X466,X467)
| ~ midp(X468,X464,X465)
| para(esk6_6(X464,X465,X466,X467,X468,X469),X469,X464,X466) )
& ( ~ midp(X469,X466,X467)
| ~ midp(X468,X464,X465)
| para(esk6_6(X464,X465,X466,X467,X468,X469),X468,X465,X467) )
& ( ~ midp(X469,X466,X467)
| ~ midp(X468,X464,X465)
| midp(esk6_6(X464,X465,X466,X467,X468,X469),X464,X467) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX6])])])])])]) ).
cnf(c_0_115,negated_conjecture,
( ~ midp(X1,X3,X3)
| midp(X1,X2,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_59]),c_0_59])]) ).
cnf(c_0_116,negated_conjecture,
midp(X1,esk28_0,esk28_0),
inference(spm,[status(thm)],[c_0_113,c_0_103]) ).
cnf(c_0_117,plain,
( ~ midp(X6,X3,X4)
| ~ midp(X5,X1,X2)
| para(esk6_6(X1,X2,X3,X4,X5,X6),X5,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_118,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_119,plain,
( ~ coll(X1,X2,X3)
| ~ midp(X1,X4,X5)
| ~ midp(X7,X6,X3)
| ~ midp(esk6_6(X4,X5,X6,X3,X1,X7),X2,X5)
| midp(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_89,c_0_117]) ).
cnf(c_0_120,negated_conjecture,
midp(X1,X2,X1),
inference(spm,[status(thm)],[c_0_97,c_0_118]) ).
cnf(c_0_121,negated_conjecture,
para(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_59]) ).
cnf(c_0_122,plain,
( ~ midp(X1,X4,X5)
| ~ midp(X7,X6,X3)
| ~ midp(esk6_6(X4,X5,X6,X3,X1,X7),X2,X5)
| midp(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_72])]) ).
cnf(c_0_123,negated_conjecture,
midp(X1,X2,esk28_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_120])]) ).
cnf(c_0_124,negated_conjecture,
( ~ midp(X3,X2,X1)
| midp(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_93,c_0_121]) ).
fof(c_0_125,plain,
! [X283,X284,X285,X286,X287] :
( para(X286,X287,X284,X285)
| ~ midp(X287,X283,X285)
| ~ midp(X286,X283,X284) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD44])])]) ).
cnf(c_0_126,negated_conjecture,
( ~ midp(X4,X5,X3)
| midp(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_123])]) ).
cnf(c_0_127,negated_conjecture,
midp(esk28_0,X1,X2),
inference(spm,[status(thm)],[c_0_124,c_0_123]) ).
cnf(c_0_128,plain,
( ~ midp(X4,X2,X5)
| ~ midp(X1,X2,X3)
| para(X1,X4,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_129,negated_conjecture,
midp(X1,X2,X3),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_130,negated_conjecture,
~ para(esk24_0,esk25_0,esk27_0,esk28_0),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_131,plain,
para(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129]),c_0_129])]) ).
cnf(c_0_132,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO659+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.58 % Computer : n001.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Sun Sep 20 18:20:43 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.63 Running first-order theorem proving
% 0.15/0.63 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
% 4.49/1.29 % Version: 3.5.1
% 4.49/1.29 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.49/1.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.49/1.29 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.49/1.29 % Starting new_bool_3 with 300s (1) cores
% 4.49/1.29 % Starting new_bool_1 with 300s (1) cores
% 4.49/1.29 % Starting sh5l with 300s (1) cores
% 4.49/1.29 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1128671 completed with status 0
% 4.49/1.29 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.49/1.29 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.49/1.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.49/1.29 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.49/1.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.49/1.29 % No SInE strategy applied
% 4.49/1.29 % Search class: FGUSF-FFLM33-SFFFFFNN
% 4.49/1.29 % partial match(1): FGUSF-FFMM33-SFFFFFNN
% 4.49/1.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.49/1.29 % Starting SubtermCWHack with 136s (1) cores
% 4.49/1.29 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.49/1.29 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 4.49/1.29 % Starting new_bool_3 with 136s (1) cores
% 4.49/1.29 % Starting new_bool_1 with 136s (1) cores
% 4.49/1.29 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1128679 completed with status 0
% 4.49/1.29 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 4.49/1.29 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.49/1.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.49/1.29 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.49/1.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.49/1.29 % No SInE strategy applied
% 4.49/1.29 % Search class: FGUSF-FFLM33-SFFFFFNN
% 4.49/1.29 % partial match(1): FGUSF-FFMM33-SFFFFFNN
% 4.49/1.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.49/1.29 % Starting SubtermCWHack with 136s (1) cores
% 4.49/1.29 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.49/1.29 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 4.49/1.29 % Preprocessing time : 0.003 s
% 4.49/1.29 % Presaturation interreduction done
% 4.49/1.29
% 4.49/1.29 % Proof found!
% 4.49/1.29 % SZS status Theorem
% 4.49/1.29 % SZS output start CNFRefutation
% See solution above
% 4.49/1.29 % Parsed axioms : 95
% 4.49/1.29 % Removed by relevancy pruning/SinE : 0
% 4.49/1.29 % Initial clauses : 128
% 4.49/1.29 % Removed in clause preprocessing : 0
% 4.49/1.29 % Initial clauses in saturation : 128
% 4.49/1.29 % Processed clauses : 4595
% 4.49/1.29 % ...of these trivial : 473
% 4.49/1.29 % ...subsumed : 401
% 4.49/1.29 % ...remaining for further processing : 3721
% 4.49/1.29 % Other redundant clauses eliminated : 0
% 4.49/1.29 % Clauses deleted for lack of memory : 0
% 4.49/1.29 % Backward-subsumed : 52
% 4.49/1.29 % Backward-rewritten : 3108
% 4.49/1.29 % Generated clauses : 30226
% 4.49/1.29 % ...of the previous two non-redundant : 15735
% 4.49/1.29 % ...aggressively subsumed : 0
% 4.49/1.29 % Contextual simplify-reflections : 3
% 4.49/1.29 % Paramodulations : 30226
% 4.49/1.29 % Factorizations : 0
% 4.49/1.29 % NegExts : 0
% 4.49/1.29 % Equation resolutions : 0
% 4.49/1.29 % Disequality decompositions : 0
% 4.49/1.29 % Total rewrite steps : 19522
% 4.49/1.29 % ...of those cached : 15722
% 4.49/1.29 % Propositional unsat checks : 0
% 4.49/1.29 % Propositional check models : 0
% 4.49/1.29 % Propositional check unsatisfiable : 0
% 4.49/1.29 % Propositional clauses : 0
% 4.49/1.29 % Propositional clauses after purity: 0
% 4.49/1.29 % Propositional unsat core size : 0
% 4.49/1.29 % Propositional preprocessing time : 0.000
% 4.49/1.29 % Propositional encoding time : 0.000
% 4.49/1.29 % Propositional solver time : 0.000
% 4.49/1.29 % Success case prop preproc time : 0.000
% 4.49/1.29 % Success case prop encoding time : 0.000
% 4.49/1.29 % Success case prop solver time : 0.000
% 4.49/1.29 % Current number of processed clauses : 434
% 4.49/1.29 % Positive orientable unit clauses : 150
% 4.49/1.29 % Positive unorientable unit clauses: 0
% 4.49/1.29 % Negative unit clauses : 0
% 4.49/1.29 % Non-unit-clauses : 284
% 4.49/1.29 % Current number of unprocessed clauses: 10820
% 4.49/1.29 % ...number of literals in the above : 35745
% 4.49/1.29 % Current number of archived formulas : 0
% 4.49/1.29 % Current number of archived clauses : 3287
% 4.49/1.29 % Clause-clause subsumption calls (NU) : 311750
% 4.49/1.29 % Rec. Clause-clause subsumption calls : 276214
% 4.49/1.29 % Non-unit clause-clause subsumptions : 451
% 4.49/1.29 % Unit Clause-clause subsumption calls : 200701
% 4.49/1.29 % Rewrite failures with RHS unbound : 0
% 4.49/1.29 % BW rewrite match attempts : 17302
% 4.49/1.29 % BW rewrite match successes : 2182
% 4.49/1.29 % Condensation attempts : 0
% 4.49/1.29 % Condensation successes : 0
% 4.49/1.29 % Termbank termtop insertions : 307352
% 4.49/1.29 % Search garbage collected termcells : 2913
% 4.49/1.29
% 4.49/1.29 % -------------------------------------------------
% 4.49/1.29 % User time : 0.600 s
% 4.49/1.29 % System time : 0.029 s
% 4.49/1.29 % Total time : 0.629 s
% 4.49/1.29 % Maximum resident set size: 4308 pages
% 4.49/1.29
% 4.49/1.29 % -------------------------------------------------
% 4.49/1.29 % User time : 2.987 s
% 4.49/1.29 % System time : 0.143 s
% 4.49/1.29 % Total time : 3.130 s
% 4.49/1.29 % Maximum resident set size: 5120 pages
% 4.49/1.29 % E exiting
%------------------------------------------------------------------------------