%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO586+1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:21:36 PM UTC 2026
% Result : Theorem 1.76s 1.89s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 31
% Syntax : Number of formulae : 152 ( 37 unt; 0 def)
% Number of atoms : 332 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 304 ( 124 ~; 121 |; 27 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 551 ( 39 sgn 282 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD9,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( perp(X1,X2,X3,X4)
& perp(X3,X4,X5,X6) )
=> para(X1,X2,X5,X6) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD8) ).
fof(exemplo6GDDFULL416048,conjecture,
! [X1,X2,X3,X8,X4,X5,X19,X20] :
( ( circle(X8,X1,X2,X3)
& circle(X8,X1,X4,X20)
& coll(X5,X1,X3)
& coll(X5,X2,X4)
& circle(X19,X1,X2,X5) )
=> perp(X19,X5,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL416048) ).
fof(ruleD4,axiom,
! [X1,X2,X3,X4] :
( para(X1,X2,X3,X4)
=> para(X1,X2,X4,X3) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD39) ).
fof(ruleD66,axiom,
! [X1,X2,X3] :
( para(X1,X2,X1,X3)
=> coll(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD66) ).
fof(ruleD2,axiom,
! [X1,X2,X3] :
( coll(X1,X2,X3)
=> coll(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD2) ).
fof(ruleD1,axiom,
! [X1,X2,X3] :
( coll(X1,X2,X3)
=> coll(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
fof(ruleD42b,axiom,
! [X1,X2,X9,X10] :
( ( eqangle(X9,X1,X9,X2,X10,X1,X10,X2)
& coll(X9,X10,X2) )
=> cyclic(X1,X2,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD42b) ).
fof(ruleD3,axiom,
! [X1,X2,X3,X4] :
( ( coll(X1,X2,X3)
& coll(X1,X2,X4) )
=> coll(X3,X4,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD15) ).
fof(ruleD14,axiom,
! [X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
=> cyclic(X1,X2,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD14) ).
fof(ruleD51,axiom,
! [X1,X2,X3,X8,X7] :
( ( circle(X8,X1,X2,X3)
& coll(X7,X2,X3)
& eqangle(X1,X2,X1,X3,X8,X2,X8,X7) )
=> midp(X7,X2,X3) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD41) ).
fof(ruleD16,axiom,
! [X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
=> cyclic(X2,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD16) ).
fof(ruleD17,axiom,
! [X1,X2,X3,X4,X5] :
( ( cyclic(X1,X2,X3,X4)
& cyclic(X1,X2,X3,X5) )
=> cyclic(X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
fof(ruleD46,axiom,
! [X1,X2,X8] :
( cong(X8,X1,X8,X2)
=> eqangle(X8,X1,X1,X2,X1,X2,X8,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD46) ).
fof(ruleD45,axiom,
! [X1,X2,X3,X5,X6] :
( ( midp(X5,X1,X2)
& para(X5,X6,X2,X3)
& coll(X6,X1,X3) )
=> midp(X6,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD45) ).
fof(ruleD11,axiom,
! [X1,X2,X7] :
( midp(X7,X2,X1)
=> midp(X7,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD11) ).
fof(ruleD68,axiom,
! [X1,X2,X3] :
( midp(X1,X2,X3)
=> cong(X1,X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD68) ).
fof(ruleD75,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12] :
( ( eqratio(X1,X2,X3,X4,X9,X10,X11,X12)
& cong(X9,X10,X11,X12) )
=> cong(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD75) ).
fof(ruleD70,axiom,
! [X1,X2,X3,X4,X7,X17] :
( ( midp(X7,X1,X2)
& midp(X17,X3,X4) )
=> eqratio(X7,X1,X1,X2,X17,X3,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD70) ).
fof(ruleD64,axiom,
! [X1,X2,X3,X4,X7] :
( ( midp(X7,X1,X2)
& para(X1,X3,X2,X4)
& para(X1,X4,X2,X3) )
=> midp(X7,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
fof(ruleD24,axiom,
! [X1,X2,X3,X4] :
( cong(X1,X2,X3,X4)
=> cong(X3,X4,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD24) ).
fof(ruleD23,axiom,
! [X1,X2,X3,X4] :
( cong(X1,X2,X3,X4)
=> cong(X1,X2,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD23) ).
fof(ruleD67,axiom,
! [X1,X2,X3] :
( ( cong(X1,X2,X1,X3)
& coll(X1,X2,X3) )
=> midp(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD67) ).
fof(ruleD56,axiom,
! [X1,X2,X9,X10] :
( ( cong(X1,X9,X2,X9)
& cong(X1,X10,X2,X10) )
=> perp(X1,X2,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
fof(c_0_31,plain,
! [X583,X584,X585,X586,X587,X588] :
( ~ perp(X583,X584,X585,X586)
| ~ perp(X585,X586,X587,X588)
| para(X583,X584,X587,X588) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
fof(c_0_32,plain,
! [X1025,X1026,X1027,X1028] :
( ~ circle(X1028,X1025,X1026,X1027)
| perp(esk12_4(X1025,X1026,X1027,X1028),X1025,X1025,X1028) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])]) ).
fof(c_0_33,plain,
! [X579,X580,X581,X582] :
( ~ perp(X579,X580,X581,X582)
| perp(X581,X582,X579,X580) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
cnf(c_0_34,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
( perp(esk12_4(X2,X3,X4,X1),X2,X2,X1)
| ~ circle(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,negated_conjecture,
~ ! [X1,X2,X3,X8,X4,X5,X19,X20] :
( ( circle(X8,X1,X2,X3)
& circle(X8,X1,X4,X20)
& coll(X5,X1,X3)
& coll(X5,X2,X4)
& circle(X19,X1,X2,X5) )
=> perp(X19,X5,X3,X4) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416048]) ).
cnf(c_0_38,plain,
( para(X1,X2,X3,X4)
| ~ circle(X4,X3,X5,X6)
| ~ perp(X1,X2,esk12_4(X3,X5,X6,X4),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( perp(X1,X2,esk12_4(X1,X3,X4,X2),X1)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
fof(c_0_40,negated_conjecture,
( circle(esk24_0,esk21_0,esk22_0,esk23_0)
& circle(esk24_0,esk21_0,esk25_0,esk28_0)
& coll(esk26_0,esk21_0,esk23_0)
& coll(esk26_0,esk22_0,esk25_0)
& circle(esk27_0,esk21_0,esk22_0,esk26_0)
& ~ perp(esk27_0,esk26_0,esk23_0,esk25_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
fof(c_0_41,plain,
! [X561,X562,X563,X564] :
( ~ para(X561,X562,X563,X564)
| para(X561,X562,X564,X563) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_42,plain,
( para(X1,X2,X1,X2)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
circle(esk27_0,esk21_0,esk22_0,esk26_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_44,plain,
! [X632,X633,X634,X635,X636,X637,X638,X639] :
( ~ eqangle(X632,X633,X634,X635,X636,X637,X638,X639)
| eqangle(X634,X635,X632,X633,X638,X639,X636,X637) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_45,plain,
! [X786,X787,X788,X789,X790,X791] :
( ~ para(X786,X787,X788,X789)
| eqangle(X786,X787,X790,X791,X788,X789,X790,X791) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_46,plain,
! [X565,X566,X567,X568] :
( ~ para(X565,X566,X567,X568)
| para(X567,X568,X565,X566) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_47,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
para(esk21_0,esk27_0,esk21_0,esk27_0),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_49,plain,
! [X780,X781,X782,X783,X784,X785] :
( ~ eqangle(X780,X781,X784,X785,X782,X783,X784,X785)
| para(X780,X781,X782,X783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
cnf(c_0_50,plain,
( eqangle(X3,X4,X1,X2,X7,X8,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,negated_conjecture,
para(esk21_0,esk27_0,esk27_0,esk21_0),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
para(esk27_0,esk21_0,esk21_0,esk27_0),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_57,plain,
! [X915,X916,X917] :
( ~ para(X915,X916,X915,X917)
| coll(X915,X916,X917) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_58,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
para(esk27_0,esk21_0,esk27_0,esk21_0),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
fof(c_0_60,plain,
! [X554,X555,X556] :
( ~ coll(X554,X555,X556)
| coll(X555,X554,X556) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_61,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_63,plain,
! [X551,X552,X553] :
( ~ coll(X551,X552,X553)
| coll(X551,X553,X552) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
cnf(c_0_64,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_66,plain,
! [X800,X801,X802,X803] :
( ~ eqangle(X802,X800,X802,X801,X803,X800,X803,X801)
| ~ coll(X802,X803,X801)
| cyclic(X800,X801,X802,X803) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_67,plain,
! [X557,X558,X559,X560] :
( ~ coll(X557,X558,X559)
| ~ coll(X557,X558,X560)
| coll(X559,X560,X557) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_68,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,plain,
( cyclic(X2,X3,X1,X4)
| ~ eqangle(X1,X2,X1,X3,X4,X2,X4,X3)
| ~ coll(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_71,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_72,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
fof(c_0_73,plain,
! [X611,X612,X613,X614] :
( ~ cyclic(X611,X612,X613,X614)
| cyclic(X611,X613,X612,X614) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_74,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_51]) ).
cnf(c_0_75,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_72])]) ).
fof(c_0_76,plain,
! [X607,X608,X609,X610] :
( ~ cyclic(X607,X608,X609,X610)
| cyclic(X607,X608,X610,X609) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_77,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_78,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_62])]),c_0_75])]) ).
fof(c_0_79,plain,
! [X841,X842,X843,X844,X845] :
( ~ circle(X844,X841,X842,X843)
| ~ coll(X845,X842,X843)
| ~ eqangle(X841,X842,X841,X843,X844,X842,X844,X845)
| midp(X845,X842,X843) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD51])]) ).
fof(c_0_80,plain,
! [X792,X793,X794,X795] :
( ~ cyclic(X792,X793,X794,X795)
| eqangle(X794,X792,X794,X793,X795,X792,X795,X793) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_81,plain,
! [X615,X616,X617,X618] :
( ~ cyclic(X615,X616,X617,X618)
| cyclic(X616,X615,X617,X618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_82,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,plain,
( midp(X5,X3,X4)
| ~ circle(X1,X2,X3,X4)
| ~ coll(X5,X3,X4)
| ~ eqangle(X2,X3,X2,X4,X1,X3,X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_85,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
fof(c_0_86,plain,
! [X619,X620,X621,X622,X623] :
( ~ cyclic(X619,X620,X621,X622)
| ~ cyclic(X619,X620,X621,X623)
| cyclic(X620,X621,X622,X623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_87,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_88,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
fof(c_0_89,plain,
! [X820,X821,X822] :
( ~ cong(X822,X820,X822,X821)
| eqangle(X822,X820,X820,X821,X820,X821,X822,X821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
cnf(c_0_90,plain,
( midp(X1,X2,X1)
| ~ cyclic(X2,X1,X3,X4)
| ~ circle(X4,X3,X2,X1)
| ~ coll(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,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,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_94,plain,
( midp(X1,X2,X1)
| ~ cyclic(X2,X1,X3,X4)
| ~ circle(X4,X3,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_69])]) ).
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,
! [X815,X816,X817,X818,X819] :
( ~ midp(X818,X815,X816)
| ~ para(X818,X819,X816,X817)
| ~ coll(X819,X815,X817)
| midp(X819,X815,X817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
cnf(c_0_97,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_93]) ).
fof(c_0_98,plain,
! [X595,X596,X597] :
( ~ midp(X597,X596,X595)
| midp(X597,X595,X596) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD11])]) ).
cnf(c_0_99,plain,
( midp(X1,X2,X1)
| ~ circle(X3,X4,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
cnf(c_0_100,plain,
( midp(X4,X2,X5)
| ~ midp(X1,X2,X3)
| ~ para(X1,X4,X3,X5)
| ~ coll(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_101,plain,
( para(X1,X1,X2,X1)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_97]) ).
fof(c_0_102,plain,
! [X921,X922,X923] :
( ~ midp(X921,X922,X923)
| cong(X921,X922,X921,X923) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_103,plain,
( midp(X1,X3,X2)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_104,negated_conjecture,
midp(esk26_0,esk22_0,esk26_0),
inference(spm,[status(thm)],[c_0_99,c_0_43]) ).
cnf(c_0_105,plain,
( midp(X1,X2,X1)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X1,X2,X3)
| ~ coll(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_106,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_107,negated_conjecture,
midp(esk26_0,esk26_0,esk22_0),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
fof(c_0_108,plain,
! [X957,X958,X959,X960,X961,X962,X963,X964] :
( ~ eqratio(X957,X958,X959,X960,X961,X962,X963,X964)
| ~ cong(X961,X962,X963,X964)
| cong(X957,X958,X959,X960) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD75])]) ).
fof(c_0_109,plain,
! [X927,X928,X929,X930,X931,X932] :
( ~ midp(X931,X927,X928)
| ~ midp(X932,X929,X930)
| eqratio(X931,X927,X927,X928,X932,X929,X929,X930) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD70])]) ).
fof(c_0_110,plain,
! [X905,X906,X907,X908,X909] :
( ~ midp(X909,X905,X906)
| ~ para(X905,X907,X906,X908)
| ~ para(X905,X908,X906,X907)
| midp(X909,X907,X908) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_111,plain,
( midp(X1,X2,X1)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_69])]) ).
cnf(c_0_112,negated_conjecture,
cong(esk26_0,esk26_0,esk26_0,esk22_0),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,plain,
( cong(X1,X2,X3,X4)
| ~ eqratio(X1,X2,X3,X4,X5,X6,X7,X8)
| ~ cong(X5,X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_114,plain,
( eqratio(X1,X2,X2,X3,X4,X5,X5,X6)
| ~ midp(X1,X2,X3)
| ~ midp(X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_115,plain,
( midp(X1,X4,X5)
| ~ midp(X1,X2,X3)
| ~ para(X2,X4,X3,X5)
| ~ para(X2,X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_116,negated_conjecture,
( midp(esk26_0,X1,esk26_0)
| ~ midp(esk26_0,X1,esk22_0) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,plain,
( cong(X1,X2,X2,X3)
| ~ cong(X4,X5,X5,X6)
| ~ midp(X4,X5,X6)
| ~ midp(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_62]),c_0_62])]) ).
cnf(c_0_119,negated_conjecture,
midp(esk26_0,esk26_0,esk26_0),
inference(spm,[status(thm)],[c_0_116,c_0_107]) ).
fof(c_0_120,plain,
! [X672,X673,X674,X675] :
( ~ cong(X672,X673,X674,X675)
| cong(X674,X675,X672,X673) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD24])]) ).
cnf(c_0_121,negated_conjecture,
( cong(X1,X2,X2,X3)
| ~ midp(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_112]),c_0_107])]) ).
cnf(c_0_122,negated_conjecture,
midp(esk26_0,X1,X1),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
fof(c_0_123,plain,
! [X668,X669,X670,X671] :
( ~ cong(X668,X669,X670,X671)
| cong(X668,X669,X671,X670) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD23])]) ).
cnf(c_0_124,plain,
( cong(X3,X4,X1,X2)
| ~ cong(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_125,negated_conjecture,
cong(esk26_0,X1,X1,X1),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
fof(c_0_126,plain,
! [X918,X919,X920] :
( ~ cong(X918,X919,X918,X920)
| ~ coll(X918,X919,X920)
| midp(X918,X919,X920) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD67])]) ).
cnf(c_0_127,plain,
( cong(X1,X2,X4,X3)
| ~ cong(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_128,negated_conjecture,
cong(X1,X1,esk26_0,X1),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_129,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_130,negated_conjecture,
cong(X1,X1,X1,esk26_0),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_131,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_75])]) ).
cnf(c_0_132,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X1,X2,esk26_0) ),
inference(spm,[status(thm)],[c_0_111,c_0_130]) ).
cnf(c_0_133,negated_conjecture,
midp(X1,X1,esk26_0),
inference(spm,[status(thm)],[c_0_131,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_135,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_118,c_0_134]) ).
cnf(c_0_136,negated_conjecture,
cong(X1,X2,X2,X2),
inference(spm,[status(thm)],[c_0_121,c_0_135]) ).
cnf(c_0_137,negated_conjecture,
cong(X1,X1,X2,X1),
inference(spm,[status(thm)],[c_0_124,c_0_136]) ).
cnf(c_0_138,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_75])]) ).
cnf(c_0_139,plain,
( para(X1,X2,X1,X1)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_97]) ).
cnf(c_0_140,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_127,c_0_137]) ).
cnf(c_0_141,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_138,c_0_62]) ).
cnf(c_0_142,plain,
para(X1,X2,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140])]) ).
cnf(c_0_143,negated_conjecture,
midp(X1,X2,X1),
inference(spm,[status(thm)],[c_0_141,c_0_135]) ).
cnf(c_0_144,plain,
midp(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_142]),c_0_143])]) ).
fof(c_0_145,plain,
! [X862,X863,X864,X865] :
( ~ cong(X862,X864,X863,X864)
| ~ cong(X862,X865,X863,X865)
| perp(X862,X863,X864,X865) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD56])]) ).
cnf(c_0_146,negated_conjecture,
cong(X1,X2,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_144])]) ).
cnf(c_0_147,plain,
( perp(X1,X3,X2,X4)
| ~ cong(X1,X2,X3,X2)
| ~ cong(X1,X4,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_148,negated_conjecture,
cong(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_127,c_0_146]) ).
cnf(c_0_149,negated_conjecture,
~ perp(esk27_0,esk26_0,esk23_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_150,plain,
perp(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148]),c_0_148])]) ).
cnf(c_0_151,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO586+1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n002.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 18:03:46 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.76/1.89 % Version : CSE_E---1.7
% 1.76/1.89 % Problem : theBenchmark.p
% 1.76/1.89 % SZS status Theorem for theBenchmark.p
% 1.76/1.89 % SZS output start CNFRefutation
% See solution above
% 1.86/1.90 % Total time : 1.372s
%------------------------------------------------------------------------------