%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO576+1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 04:21:34 PM UTC 2026
% Result : Theorem 2.01s 1.91s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 29
% Syntax : Number of formulae : 143 ( 35 unt; 0 def)
% Number of atoms : 315 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 285 ( 113 ~; 110 |; 32 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 600 ( 57 sgn 300 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(exemplo6GDDFULL214038,conjecture,
! [X1,X2,X3,X4,X8,X19,X9,X20] :
( ( perp(X4,X1,X2,X3)
& coll(X4,X2,X3)
& circle(X8,X1,X2,X3)
& circle(X8,X1,X19,X20)
& coll(X19,X1,X4)
& perp(X1,X3,X19,X9)
& coll(X9,X2,X3) )
=> eqangle(X8,X1,X1,X4,X3,X1,X1,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL214038) ).
fof(ruleD7,axiom,
! [X1,X2,X3,X4] :
( perp(X1,X2,X3,X4)
=> perp(X1,X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD7) ).
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(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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD9) ).
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(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(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(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] :
( ( eqangle(X9,X1,X9,X2,X10,X1,X10,X2)
& coll(X9,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,X3)
& coll(X1,X2,X4) )
=> 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(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(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/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(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(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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD45) ).
fof(ruleD20,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12] :
( eqangle(X1,X2,X3,X4,X9,X10,X11,X12)
=> eqangle(X9,X10,X11,X12,X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD20) ).
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(ruleD73,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12] :
( ( eqangle(X1,X2,X3,X4,X9,X10,X11,X12)
& para(X9,X10,X11,X12) )
=> para(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD73) ).
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(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(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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
fof(ruleD44,axiom,
! [X1,X2,X3,X5,X6] :
( ( midp(X5,X1,X2)
& midp(X6,X1,X3) )
=> para(X5,X6,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD44) ).
fof(ruleD21,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12] :
( eqangle(X1,X2,X3,X4,X9,X10,X11,X12)
=> eqangle(X1,X2,X9,X10,X3,X4,X11,X12) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD21) ).
fof(ruleD22,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12,X5,X6,X13,X14] :
( ( eqangle(X1,X2,X3,X4,X9,X10,X11,X12)
& eqangle(X9,X10,X11,X12,X5,X6,X13,X14) )
=> eqangle(X1,X2,X3,X4,X5,X6,X13,X14) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD22) ).
fof(c_0_29,negated_conjecture,
~ ! [X1,X2,X3,X4,X8,X19,X9,X20] :
( ( perp(X4,X1,X2,X3)
& coll(X4,X2,X3)
& circle(X8,X1,X2,X3)
& circle(X8,X1,X19,X20)
& coll(X19,X1,X4)
& perp(X1,X3,X19,X9)
& coll(X9,X2,X3) )
=> eqangle(X8,X1,X1,X4,X3,X1,X1,X9) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214038]) ).
fof(c_0_30,plain,
! [X575,X576,X577,X578] :
( ~ perp(X575,X576,X577,X578)
| perp(X575,X576,X578,X577) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD7])]) ).
fof(c_0_31,negated_conjecture,
( perp(esk24_0,esk21_0,esk22_0,esk23_0)
& coll(esk24_0,esk22_0,esk23_0)
& circle(esk25_0,esk21_0,esk22_0,esk23_0)
& circle(esk25_0,esk21_0,esk26_0,esk28_0)
& coll(esk26_0,esk21_0,esk24_0)
& perp(esk21_0,esk23_0,esk26_0,esk27_0)
& coll(esk27_0,esk22_0,esk23_0)
& ~ eqangle(esk25_0,esk21_0,esk21_0,esk24_0,esk23_0,esk21_0,esk21_0,esk27_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
fof(c_0_32,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_33,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_34,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])]) ).
cnf(c_0_35,plain,
( perp(X1,X2,X4,X3)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
perp(esk21_0,esk23_0,esk26_0,esk27_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_37,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_38,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_32]) ).
cnf(c_0_39,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_40,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_41,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
perp(esk21_0,esk23_0,esk27_0,esk26_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_43,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_44,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( para(X1,X2,esk27_0,esk26_0)
| ~ perp(X1,X2,esk21_0,esk23_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_49,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_50,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( para(esk27_0,esk26_0,X1,X2)
| ~ perp(X1,X2,esk21_0,esk23_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
perp(esk27_0,esk26_0,esk21_0,esk23_0),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
fof(c_0_53,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_54,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,negated_conjecture,
para(X1,X2,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
fof(c_0_56,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_57,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_59,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_60,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_61,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,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_59]) ).
cnf(c_0_64,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_66,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_67,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_39]) ).
cnf(c_0_68,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_65])]) ).
fof(c_0_69,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_70,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_71,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_55])]),c_0_68])]) ).
fof(c_0_72,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_73,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_74,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_75,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,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_72]) ).
cnf(c_0_78,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
fof(c_0_79,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_80,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_81,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
fof(c_0_82,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_83,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_77,c_0_78]) ).
cnf(c_0_84,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_85,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,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_82]) ).
cnf(c_0_87,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_83,c_0_62])]) ).
cnf(c_0_88,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_85])]) ).
fof(c_0_89,plain,
! [X640,X641,X642,X643,X644,X645,X646,X647] :
( ~ eqangle(X640,X641,X642,X643,X644,X645,X646,X647)
| eqangle(X644,X645,X646,X647,X640,X641,X642,X643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD20])]) ).
fof(c_0_90,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_91,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_68])]) ).
cnf(c_0_92,plain,
( midp(X1,X2,X1)
| ~ circle(X3,X4,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88])]) ).
cnf(c_0_93,negated_conjecture,
circle(esk25_0,esk21_0,esk26_0,esk28_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_94,plain,
! [X941,X942,X943,X944,X945,X946,X947,X948] :
( ~ eqangle(X941,X942,X943,X944,X945,X946,X947,X948)
| ~ para(X945,X946,X947,X948)
| para(X941,X942,X943,X944) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD73])]) ).
cnf(c_0_95,plain,
( eqangle(X5,X6,X7,X8,X1,X2,X3,X4)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_96,plain,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
fof(c_0_97,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_98,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_91,c_0_55]) ).
cnf(c_0_99,negated_conjecture,
midp(esk28_0,esk26_0,esk28_0),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
fof(c_0_100,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_101,plain,
( para(X1,X2,X3,X4)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X7,X8)
| ~ para(X5,X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_102,plain,
( eqangle(X1,X2,X3,X2,X3,X1,X1,X2)
| ~ cong(X3,X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_104,negated_conjecture,
midp(X1,esk26_0,X1),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_106,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_107,plain,
( para(X1,X2,X3,X2)
| ~ cong(X3,X1,X3,X2)
| ~ para(X3,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
cong(X1,esk26_0,X1,X1),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
para(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_105,c_0_55]) ).
cnf(c_0_110,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_106]) ).
cnf(c_0_111,negated_conjecture,
para(esk26_0,X1,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109])]) ).
cnf(c_0_112,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_55]),c_0_55])]) ).
cnf(c_0_113,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(esk26_0,X2,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_111]) ).
cnf(c_0_114,negated_conjecture,
midp(esk26_0,X1,X1),
inference(spm,[status(thm)],[c_0_112,c_0_104]) ).
cnf(c_0_115,plain,
( eqangle(X1,X2,X1,X3,X4,X2,X4,X3)
| ~ cyclic(X2,X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_78]) ).
cnf(c_0_116,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_117,plain,
( para(X1,X2,X1,X3)
| ~ cyclic(X2,X3,X4,X1)
| ~ para(X4,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_101,c_0_115]) ).
cnf(c_0_118,negated_conjecture,
( midp(X1,X2,X3)
| ~ midp(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_109]) ).
cnf(c_0_119,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_112,c_0_116]) ).
cnf(c_0_120,plain,
( para(X1,X2,X1,X3)
| ~ para(X4,X2,X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_88])]) ).
cnf(c_0_121,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_96]) ).
cnf(c_0_122,negated_conjecture,
midp(X1,X1,X2),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,plain,
( para(X1,X2,X1,X3)
| ~ cong(X2,X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_124,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_103,c_0_122]) ).
fof(c_0_125,plain,
! [X810,X811,X812,X813,X814] :
( ~ midp(X813,X810,X811)
| ~ midp(X814,X810,X812)
| para(X813,X814,X811,X812) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD44])]) ).
cnf(c_0_126,plain,
para(X1,X2,X1,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_127,negated_conjecture,
midp(X1,X2,X1),
inference(spm,[status(thm)],[c_0_98,c_0_119]) ).
cnf(c_0_128,plain,
( para(X1,X4,X3,X5)
| ~ midp(X1,X2,X3)
| ~ midp(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_129,plain,
midp(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_126]),c_0_127])]) ).
fof(c_0_130,plain,
! [X648,X649,X650,X651,X652,X653,X654,X655] :
( ~ eqangle(X648,X649,X650,X651,X652,X653,X654,X655)
| eqangle(X648,X649,X652,X653,X650,X651,X654,X655) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD21])]) ).
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,plain,
( eqangle(X1,X2,X3,X4,X5,X6,X3,X4)
| ~ para(X5,X6,X1,X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_39]) ).
fof(c_0_133,plain,
! [X656,X657,X658,X659,X660,X661,X662,X663,X664,X665,X666,X667] :
( ~ eqangle(X656,X657,X658,X659,X660,X661,X662,X663)
| ~ eqangle(X660,X661,X662,X663,X664,X665,X666,X667)
| eqangle(X656,X657,X658,X659,X664,X665,X666,X667) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD22])]) ).
cnf(c_0_134,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X7,X8)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_135,plain,
eqangle(X1,X2,X3,X4,X1,X2,X5,X6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_131])]) ).
cnf(c_0_136,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_131])]) ).
cnf(c_0_137,plain,
( eqangle(X1,X2,X3,X4,X9,X10,X11,X12)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X7,X8)
| ~ eqangle(X5,X6,X7,X8,X9,X10,X11,X12) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_138,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_139,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(spm,[status(thm)],[c_0_134,c_0_136]) ).
cnf(c_0_140,negated_conjecture,
~ eqangle(esk25_0,esk21_0,esk21_0,esk24_0,esk23_0,esk21_0,esk21_0,esk27_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_141,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139])]) ).
cnf(c_0_142,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO576+1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:03:15 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.01/1.91 % Version : CSE_E---1.7
% 2.01/1.91 % Problem : theBenchmark.p
% 2.01/1.91 % SZS status Theorem for theBenchmark.p
% 2.01/1.91 % SZS output start CNFRefutation
% See solution above
% 2.01/1.91 % Total time : 1.375s
%------------------------------------------------------------------------------