%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO559+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 : n012.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 1.62s 1.74s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 32
% Syntax : Number of formulae : 160 ( 38 unt; 0 def)
% Number of atoms : 357 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 333 ( 136 ~; 133 |; 31 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 590 ( 35 sgn 304 !; 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(exemplo6GDDFULL012019,conjecture,
! [X1,X2,X3,X8,X6,X9,X5,X4,X19,X20] :
( ( circle(X8,X1,X2,X3)
& circle(X9,X1,X2,X6)
& circle(X9,X1,X5,X19)
& coll(X5,X1,X3)
& circle(X8,X2,X4,X20)
& coll(X4,X2,X6) )
=> para(X3,X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012019) ).
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(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(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(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(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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD67) ).
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(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(c_0_32,plain,
! [X585,X586,X587,X588,X589,X590] :
( ~ perp(X585,X586,X587,X588)
| ~ perp(X587,X588,X589,X590)
| para(X585,X586,X589,X590) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
fof(c_0_33,plain,
! [X1027,X1028,X1029,X1030] :
( ~ circle(X1030,X1027,X1028,X1029)
| perp(esk12_4(X1027,X1028,X1029,X1030),X1027,X1027,X1030) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])]) ).
fof(c_0_34,plain,
! [X581,X582,X583,X584] :
( ~ perp(X581,X582,X583,X584)
| perp(X583,X584,X581,X582) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
cnf(c_0_35,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( perp(esk12_4(X2,X3,X4,X1),X2,X2,X1)
| ~ circle(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_38,negated_conjecture,
~ ! [X1,X2,X3,X8,X6,X9,X5,X4,X19,X20] :
( ( circle(X8,X1,X2,X3)
& circle(X9,X1,X2,X6)
& circle(X9,X1,X5,X19)
& coll(X5,X1,X3)
& circle(X8,X2,X4,X20)
& coll(X4,X2,X6) )
=> para(X3,X4,X5,X6) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012019]) ).
cnf(c_0_39,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_35,c_0_36]) ).
cnf(c_0_40,plain,
( perp(X1,X2,esk12_4(X1,X3,X4,X2),X1)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
fof(c_0_41,negated_conjecture,
( circle(esk24_0,esk21_0,esk22_0,esk23_0)
& circle(esk26_0,esk21_0,esk22_0,esk25_0)
& circle(esk26_0,esk21_0,esk27_0,esk29_0)
& coll(esk27_0,esk21_0,esk23_0)
& circle(esk24_0,esk22_0,esk28_0,esk30_0)
& coll(esk28_0,esk22_0,esk25_0)
& ~ para(esk23_0,esk28_0,esk27_0,esk25_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
fof(c_0_42,plain,
! [X563,X564,X565,X566] :
( ~ para(X563,X564,X565,X566)
| para(X563,X564,X566,X565) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_43,plain,
( para(X1,X2,X1,X2)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
circle(esk26_0,esk21_0,esk22_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_45,plain,
! [X634,X635,X636,X637,X638,X639,X640,X641] :
( ~ eqangle(X634,X635,X636,X637,X638,X639,X640,X641)
| eqangle(X636,X637,X634,X635,X640,X641,X638,X639) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_46,plain,
! [X788,X789,X790,X791,X792,X793] :
( ~ para(X788,X789,X790,X791)
| eqangle(X788,X789,X792,X793,X790,X791,X792,X793) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_47,plain,
! [X567,X568,X569,X570] :
( ~ para(X567,X568,X569,X570)
| para(X569,X570,X567,X568) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_48,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
para(esk21_0,esk26_0,esk21_0,esk26_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_50,plain,
! [X782,X783,X784,X785,X786,X787] :
( ~ eqangle(X782,X783,X786,X787,X784,X785,X786,X787)
| para(X782,X783,X784,X785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
cnf(c_0_51,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_45]) ).
cnf(c_0_52,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,negated_conjecture,
para(esk21_0,esk26_0,esk26_0,esk21_0),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_56,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
para(esk26_0,esk21_0,esk21_0,esk26_0),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_58,plain,
! [X917,X918,X919] :
( ~ para(X917,X918,X917,X919)
| coll(X917,X918,X919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_59,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
para(esk26_0,esk21_0,esk26_0,esk21_0),
inference(spm,[status(thm)],[c_0_48,c_0_57]) ).
fof(c_0_61,plain,
! [X556,X557,X558] :
( ~ coll(X556,X557,X558)
| coll(X557,X556,X558) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_62,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
fof(c_0_64,plain,
! [X553,X554,X555] :
( ~ coll(X553,X554,X555)
| coll(X553,X555,X554) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
cnf(c_0_65,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_67,plain,
! [X802,X803,X804,X805] :
( ~ eqangle(X804,X802,X804,X803,X805,X802,X805,X803)
| ~ coll(X804,X805,X803)
| cyclic(X802,X803,X804,X805) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_68,plain,
! [X559,X560,X561,X562] :
( ~ coll(X559,X560,X561)
| ~ coll(X559,X560,X562)
| coll(X561,X562,X559) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_69,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,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_67]) ).
cnf(c_0_72,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_73,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
fof(c_0_74,plain,
! [X613,X614,X615,X616] :
( ~ cyclic(X613,X614,X615,X616)
| cyclic(X613,X615,X614,X616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_75,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_52]) ).
cnf(c_0_76,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_73])]) ).
fof(c_0_77,plain,
! [X609,X610,X611,X612] :
( ~ cyclic(X609,X610,X611,X612)
| cyclic(X609,X610,X612,X611) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_78,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_79,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_63])]),c_0_76])]) ).
fof(c_0_80,plain,
! [X843,X844,X845,X846,X847] :
( ~ circle(X846,X843,X844,X845)
| ~ coll(X847,X844,X845)
| ~ eqangle(X843,X844,X843,X845,X846,X844,X846,X847)
| midp(X847,X844,X845) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD51])]) ).
fof(c_0_81,plain,
! [X794,X795,X796,X797] :
( ~ cyclic(X794,X795,X796,X797)
| eqangle(X796,X794,X796,X795,X797,X794,X797,X795) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_82,plain,
! [X617,X618,X619,X620] :
( ~ cyclic(X617,X618,X619,X620)
| cyclic(X618,X617,X619,X620) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_83,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_84,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,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_80]) ).
cnf(c_0_86,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_87,plain,
! [X621,X622,X623,X624,X625] :
( ~ cyclic(X621,X622,X623,X624)
| ~ cyclic(X621,X622,X623,X625)
| cyclic(X622,X623,X624,X625) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_88,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_89,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
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_85,c_0_86]) ).
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_87]) ).
cnf(c_0_92,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
fof(c_0_93,plain,
! [X822,X823,X824] :
( ~ cong(X824,X822,X824,X823)
| eqangle(X824,X822,X822,X823,X822,X823,X824,X823) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
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_70])]) ).
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,
! [X817,X818,X819,X820,X821] :
( ~ midp(X820,X817,X818)
| ~ para(X820,X821,X818,X819)
| ~ coll(X821,X817,X819)
| midp(X821,X817,X819) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
cnf(c_0_97,plain,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_98,plain,
! [X597,X598,X599] :
( ~ midp(X599,X598,X597)
| midp(X599,X597,X598) ),
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,negated_conjecture,
circle(esk24_0,esk22_0,esk28_0,esk30_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_101,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_102,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_97]) ).
fof(c_0_103,plain,
! [X923,X924,X925] :
( ~ midp(X923,X924,X925)
| cong(X923,X924,X923,X925) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_104,plain,
( midp(X1,X3,X2)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_105,negated_conjecture,
midp(esk30_0,esk28_0,esk30_0),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_106,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X1,X2,X1)
| ~ coll(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,negated_conjecture,
midp(esk30_0,esk30_0,esk28_0),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
fof(c_0_109,plain,
! [X959,X960,X961,X962,X963,X964,X965,X966] :
( ~ eqratio(X959,X960,X961,X962,X963,X964,X965,X966)
| ~ cong(X963,X964,X965,X966)
| cong(X959,X960,X961,X962) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD75])]) ).
fof(c_0_110,plain,
! [X929,X930,X931,X932,X933,X934] :
( ~ midp(X933,X929,X930)
| ~ midp(X934,X931,X932)
| eqratio(X933,X929,X929,X930,X934,X931,X931,X932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD70])]) ).
cnf(c_0_111,negated_conjecture,
midp(esk25_0,esk22_0,esk25_0),
inference(spm,[status(thm)],[c_0_99,c_0_44]) ).
fof(c_0_112,plain,
! [X907,X908,X909,X910,X911] :
( ~ midp(X911,X907,X908)
| ~ para(X907,X909,X908,X910)
| ~ para(X907,X910,X908,X909)
| midp(X911,X909,X910) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_113,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X1,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_76])]) ).
cnf(c_0_114,negated_conjecture,
cong(esk30_0,esk30_0,esk30_0,esk28_0),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_115,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_109]) ).
cnf(c_0_116,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_110]) ).
cnf(c_0_117,negated_conjecture,
midp(esk25_0,esk25_0,esk22_0),
inference(spm,[status(thm)],[c_0_104,c_0_111]) ).
cnf(c_0_118,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_112]) ).
cnf(c_0_119,negated_conjecture,
( midp(esk30_0,X1,esk28_0)
| ~ midp(esk30_0,X1,esk30_0) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_120,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_115,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
cong(esk25_0,esk25_0,esk25_0,esk22_0),
inference(spm,[status(thm)],[c_0_107,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_63]),c_0_63])]) ).
cnf(c_0_123,negated_conjecture,
midp(esk30_0,esk28_0,esk28_0),
inference(spm,[status(thm)],[c_0_119,c_0_105]) ).
fof(c_0_124,plain,
! [X674,X675,X676,X677] :
( ~ cong(X674,X675,X676,X677)
| cong(X676,X677,X674,X675) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD24])]) ).
cnf(c_0_125,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_120,c_0_121]),c_0_117])]) ).
cnf(c_0_126,negated_conjecture,
midp(esk30_0,X1,X1),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_127,plain,
( para(X1,X1,X2,X1)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_102]) ).
fof(c_0_128,plain,
! [X670,X671,X672,X673] :
( ~ cong(X670,X671,X672,X673)
| cong(X670,X671,X673,X672) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD23])]) ).
cnf(c_0_129,plain,
( cong(X3,X4,X1,X2)
| ~ cong(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_130,negated_conjecture,
cong(esk30_0,X1,X1,X1),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
fof(c_0_131,plain,
! [X920,X921,X922] :
( ~ cong(X920,X921,X920,X922)
| ~ coll(X920,X921,X922)
| midp(X920,X921,X922) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD67])]) ).
cnf(c_0_132,plain,
( midp(X1,X2,X1)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X1,X2,X3)
| ~ coll(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_127]) ).
cnf(c_0_133,plain,
( cong(X1,X2,X4,X3)
| ~ cong(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_134,negated_conjecture,
cong(X1,X1,esk30_0,X1),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_136,plain,
( midp(X1,X2,X1)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_70])]) ).
cnf(c_0_137,negated_conjecture,
cong(X1,X1,X1,esk30_0),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_138,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_76])]) ).
cnf(c_0_139,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X1,X2,esk30_0) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_140,negated_conjecture,
midp(X1,X1,esk30_0),
inference(spm,[status(thm)],[c_0_138,c_0_137]) ).
fof(c_0_141,plain,
! [X943,X944,X945,X946,X947,X948,X949,X950] :
( ~ eqangle(X943,X944,X945,X946,X947,X948,X949,X950)
| ~ para(X947,X948,X949,X950)
| para(X943,X944,X945,X946) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD73])]) ).
cnf(c_0_142,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_76])]) ).
cnf(c_0_143,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_144,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_141]) ).
cnf(c_0_145,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_142,c_0_63]) ).
cnf(c_0_146,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_122,c_0_143]) ).
cnf(c_0_147,plain,
( para(X1,X2,X1,X3)
| ~ cyclic(X2,X3,X1,X4)
| ~ para(X4,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_144,c_0_86]) ).
cnf(c_0_148,negated_conjecture,
midp(X1,X2,X1),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_149,plain,
( para(X1,X2,X1,X3)
| ~ para(X4,X2,X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_95])]) ).
cnf(c_0_150,negated_conjecture,
midp(X1,X1,X2),
inference(spm,[status(thm)],[c_0_104,c_0_148]) ).
cnf(c_0_151,plain,
( para(X1,X2,X1,X3)
| ~ cong(X2,X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_149,c_0_102]) ).
cnf(c_0_152,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_107,c_0_150]) ).
fof(c_0_153,plain,
! [X812,X813,X814,X815,X816] :
( ~ midp(X815,X812,X813)
| ~ midp(X816,X812,X814)
| para(X815,X816,X813,X814) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD44])]) ).
cnf(c_0_154,plain,
para(X1,X2,X1,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_152])]) ).
cnf(c_0_155,plain,
( para(X1,X4,X3,X5)
| ~ midp(X1,X2,X3)
| ~ midp(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_156,plain,
midp(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_154]),c_0_148])]) ).
cnf(c_0_157,negated_conjecture,
~ para(esk23_0,esk28_0,esk27_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_158,plain,
para(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156]),c_0_156])]) ).
cnf(c_0_159,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_158])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GEO559+1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 18:02:46 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.62/1.74 % Version : CSE_E---1.7
% 1.62/1.74 % Problem : theBenchmark.p
% 1.62/1.74 % SZS status Theorem for theBenchmark.p
% 1.62/1.74 % SZS output start CNFRefutation
% See solution above
% 1.62/1.75 % Total time : 1.364s
%------------------------------------------------------------------------------