%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO558+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 : n011.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 04:21:31 PM UTC 2026
% Result : Theorem 3.10s 2.95s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 27
% Syntax : Number of formulae : 129 ( 29 unt; 0 def)
% Number of atoms : 295 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 273 ( 107 ~; 104 |; 34 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 475 ( 30 sgn 248 !; 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/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(exemplo6GDDFULL012018,conjecture,
! [X1,X3,X19,X8,X17,X2,X13,X20,X7,X21,X22,X23] :
( ( circle(X8,X1,X3,X19)
& circle(X8,X1,X17,X21)
& coll(X2,X1,X19)
& coll(X2,X3,X17)
& circle(X13,X1,X3,X2)
& circle(X20,X19,X17,X2)
& circle(X13,X1,X7,X22)
& circle(X20,X19,X7,X23) )
=> perp(X2,X7,X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012018) ).
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] :
( ( 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(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(ruleD11,axiom,
! [X1,X2,X7] :
( midp(X7,X2,X1)
=> midp(X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD11) ).
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] :
( ( 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(ruleD53,axiom,
! [X1,X2,X3,X8] :
( ( circle(X8,X1,X2,X3)
& coll(X8,X1,X3) )
=> perp(X1,X2,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD53) ).
fof(ruleD12,axiom,
! [X1,X2,X3,X8] :
( ( cong(X8,X1,X8,X2)
& cong(X8,X1,X8,X3) )
=> circle(X8,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD12) ).
fof(c_0_27,plain,
! [X590,X591,X592,X593,X594,X595] :
( ~ perp(X590,X591,X592,X593)
| ~ perp(X592,X593,X594,X595)
| para(X590,X591,X594,X595) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
fof(c_0_28,plain,
! [X1032,X1033,X1034,X1035] :
( ~ circle(X1035,X1032,X1033,X1034)
| perp(esk12_4(X1032,X1033,X1034,X1035),X1032,X1032,X1035) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])]) ).
fof(c_0_29,plain,
! [X586,X587,X588,X589] :
( ~ perp(X586,X587,X588,X589)
| perp(X588,X589,X586,X587) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
cnf(c_0_30,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( perp(esk12_4(X2,X3,X4,X1),X2,X2,X1)
| ~ circle(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_33,negated_conjecture,
~ ! [X1,X3,X19,X8,X17,X2,X13,X20,X7,X21,X22,X23] :
( ( circle(X8,X1,X3,X19)
& circle(X8,X1,X17,X21)
& coll(X2,X1,X19)
& coll(X2,X3,X17)
& circle(X13,X1,X3,X2)
& circle(X20,X19,X17,X2)
& circle(X13,X1,X7,X22)
& circle(X20,X19,X7,X23) )
=> perp(X2,X7,X7,X8) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012018]) ).
cnf(c_0_34,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_30,c_0_31]) ).
cnf(c_0_35,plain,
( perp(X1,X2,esk12_4(X1,X3,X4,X2),X1)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
fof(c_0_36,negated_conjecture,
( circle(esk24_0,esk21_0,esk22_0,esk23_0)
& circle(esk24_0,esk21_0,esk25_0,esk30_0)
& coll(esk26_0,esk21_0,esk23_0)
& coll(esk26_0,esk22_0,esk25_0)
& circle(esk27_0,esk21_0,esk22_0,esk26_0)
& circle(esk28_0,esk23_0,esk25_0,esk26_0)
& circle(esk27_0,esk21_0,esk29_0,esk31_0)
& circle(esk28_0,esk23_0,esk29_0,esk32_0)
& ~ perp(esk26_0,esk29_0,esk29_0,esk24_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
fof(c_0_37,plain,
! [X568,X569,X570,X571] :
( ~ para(X568,X569,X570,X571)
| para(X568,X569,X571,X570) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_38,plain,
( para(X1,X2,X1,X2)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
circle(esk28_0,esk23_0,esk25_0,esk26_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_40,plain,
! [X639,X640,X641,X642,X643,X644,X645,X646] :
( ~ eqangle(X639,X640,X641,X642,X643,X644,X645,X646)
| eqangle(X641,X642,X639,X640,X645,X646,X643,X644) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_41,plain,
! [X793,X794,X795,X796,X797,X798] :
( ~ para(X793,X794,X795,X796)
| eqangle(X793,X794,X797,X798,X795,X796,X797,X798) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_42,plain,
! [X572,X573,X574,X575] :
( ~ para(X572,X573,X574,X575)
| para(X574,X575,X572,X573) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_43,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,negated_conjecture,
para(esk23_0,esk28_0,esk23_0,esk28_0),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_45,plain,
! [X787,X788,X789,X790,X791,X792] :
( ~ eqangle(X787,X788,X791,X792,X789,X790,X791,X792)
| para(X787,X788,X789,X790) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
cnf(c_0_46,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_40]) ).
cnf(c_0_47,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
para(esk23_0,esk28_0,esk28_0,esk23_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
para(esk28_0,esk23_0,esk23_0,esk28_0),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_53,plain,
! [X922,X923,X924] :
( ~ para(X922,X923,X922,X924)
| coll(X922,X923,X924) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_54,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
para(esk28_0,esk23_0,esk28_0,esk23_0),
inference(spm,[status(thm)],[c_0_43,c_0_52]) ).
fof(c_0_56,plain,
! [X561,X562,X563] :
( ~ coll(X561,X562,X563)
| coll(X562,X561,X563) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_57,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_59,plain,
! [X558,X559,X560] :
( ~ coll(X558,X559,X560)
| coll(X558,X560,X559) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
cnf(c_0_60,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
fof(c_0_62,plain,
! [X807,X808,X809,X810] :
( ~ eqangle(X809,X807,X809,X808,X810,X807,X810,X808)
| ~ coll(X809,X810,X808)
| cyclic(X807,X808,X809,X810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_63,plain,
! [X564,X565,X566,X567] :
( ~ coll(X564,X565,X566)
| ~ coll(X564,X565,X567)
| coll(X566,X567,X564) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_64,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,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_62]) ).
cnf(c_0_67,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
fof(c_0_69,plain,
! [X618,X619,X620,X621] :
( ~ cyclic(X618,X619,X620,X621)
| cyclic(X618,X620,X619,X621) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_70,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_47]) ).
cnf(c_0_71,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_68])]) ).
fof(c_0_72,plain,
! [X614,X615,X616,X617] :
( ~ cyclic(X614,X615,X616,X617)
| cyclic(X614,X615,X617,X616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_73,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_74,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_58])]),c_0_71])]) ).
fof(c_0_75,plain,
! [X848,X849,X850,X851,X852] :
( ~ circle(X851,X848,X849,X850)
| ~ coll(X852,X849,X850)
| ~ eqangle(X848,X849,X848,X850,X851,X849,X851,X852)
| midp(X852,X849,X850) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD51])]) ).
fof(c_0_76,plain,
! [X799,X800,X801,X802] :
( ~ cyclic(X799,X800,X801,X802)
| eqangle(X801,X799,X801,X800,X802,X799,X802,X800) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_77,plain,
! [X622,X623,X624,X625] :
( ~ cyclic(X622,X623,X624,X625)
| cyclic(X623,X622,X624,X625) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_78,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,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_75]) ).
cnf(c_0_81,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_82,plain,
! [X626,X627,X628,X629,X630] :
( ~ cyclic(X626,X627,X628,X629)
| ~ cyclic(X626,X627,X628,X630)
| cyclic(X627,X628,X629,X630) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_83,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_84,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
fof(c_0_85,plain,
! [X822,X823,X824,X825,X826] :
( ~ midp(X825,X822,X823)
| ~ para(X825,X826,X823,X824)
| ~ coll(X826,X822,X824)
| midp(X826,X822,X824) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
cnf(c_0_86,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_80,c_0_81]) ).
cnf(c_0_87,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_88,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
fof(c_0_89,plain,
! [X827,X828,X829] :
( ~ cong(X829,X827,X829,X828)
| eqangle(X829,X827,X827,X828,X827,X828,X829,X828) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
cnf(c_0_90,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_85]) ).
cnf(c_0_91,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_86,c_0_65])]) ).
cnf(c_0_92,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),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,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_71])]) ).
cnf(c_0_95,plain,
( midp(X1,X2,X1)
| ~ circle(X3,X4,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_96,negated_conjecture,
circle(esk28_0,esk23_0,esk29_0,esk32_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_97,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_93]) ).
fof(c_0_98,plain,
! [X602,X603,X604] :
( ~ midp(X604,X603,X602)
| midp(X604,X602,X603) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD11])]) ).
cnf(c_0_99,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_94,c_0_58]) ).
cnf(c_0_100,negated_conjecture,
midp(esk32_0,esk29_0,esk32_0),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,plain,
( para(X1,X1,X2,X1)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_97]) ).
fof(c_0_102,plain,
! [X928,X929,X930] :
( ~ midp(X928,X929,X930)
| cong(X928,X929,X928,X930) ),
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(X1,esk29_0,X1),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
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_90,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(X1,X1,esk29_0),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
fof(c_0_108,plain,
! [X912,X913,X914,X915,X916] :
( ~ midp(X916,X912,X913)
| ~ para(X912,X914,X913,X915)
| ~ para(X912,X915,X913,X914)
| midp(X916,X914,X915) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_109,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_65])]) ).
cnf(c_0_110,negated_conjecture,
cong(X1,X1,X1,esk29_0),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,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_108]) ).
cnf(c_0_112,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X1,X2,esk29_0) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,negated_conjecture,
para(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_43,c_0_58]) ).
cnf(c_0_114,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_58]),c_0_58])]) ).
cnf(c_0_115,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_112,c_0_107]) ).
cnf(c_0_116,negated_conjecture,
( midp(X1,X2,X3)
| ~ midp(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_113]) ).
cnf(c_0_117,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
fof(c_0_118,plain,
! [X857,X858,X859,X860] :
( ~ circle(X860,X857,X858,X859)
| ~ coll(X860,X857,X859)
| perp(X857,X858,X858,X859) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD53])]) ).
fof(c_0_119,plain,
! [X605,X606,X607,X608] :
( ~ cong(X608,X605,X608,X606)
| ~ cong(X608,X605,X608,X607)
| circle(X608,X605,X606,X607) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD12])]) ).
cnf(c_0_120,negated_conjecture,
midp(X1,X1,X2),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,plain,
( perp(X2,X3,X3,X4)
| ~ circle(X1,X2,X3,X4)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_122,plain,
( circle(X1,X2,X3,X4)
| ~ cong(X1,X2,X1,X3)
| ~ cong(X1,X2,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_123,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_106,c_0_120]) ).
cnf(c_0_124,plain,
( perp(X1,X2,X2,X3)
| ~ circle(X4,X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_71])]) ).
cnf(c_0_125,negated_conjecture,
circle(X1,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_126,negated_conjecture,
~ perp(esk26_0,esk29_0,esk29_0,esk24_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_127,negated_conjecture,
perp(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_128,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO558+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
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:02:47 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.10/2.95 % Version : CSE_E---1.7
% 3.10/2.95 % Problem : theBenchmark.p
% 3.10/2.95 % SZS status Theorem for theBenchmark.p
% 3.10/2.95 % SZS output start CNFRefutation
% See solution above
% 3.10/2.95 % Total time : 2.371s
%------------------------------------------------------------------------------