%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO570+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 : 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 04:21:33 PM UTC 2026
% Result : Theorem 2.10s 1.94s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 28
% Syntax : Number of formulae : 137 ( 32 unt; 0 def)
% Number of atoms : 309 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 283 ( 111 ~; 108 |; 35 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 587 ( 56 sgn 294 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(exemplo6GDDFULL214032,conjecture,
! [X2,X3,X15,X8,X19,X1,X7,X17,X20] :
( ( circle(X8,X2,X3,X15)
& circle(X8,X2,X19,X20)
& coll(X1,X2,X15)
& coll(X1,X3,X19)
& perp(X7,X1,X15,X19)
& coll(X7,X15,X19)
& perp(X17,X1,X2,X3)
& coll(X17,X2,X3) )
=> eqangle(X2,X1,X1,X7,X17,X1,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214032) ).
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(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(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(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(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(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(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(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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD73) ).
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(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(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(ruleD44,axiom,
! [X1,X2,X3,X5,X6] :
( ( midp(X5,X1,X2)
& midp(X6,X1,X3) )
=> para(X5,X6,X2,X3) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD22) ).
fof(c_0_28,negated_conjecture,
~ ! [X2,X3,X15,X8,X19,X1,X7,X17,X20] :
( ( circle(X8,X2,X3,X15)
& circle(X8,X2,X19,X20)
& coll(X1,X2,X15)
& coll(X1,X3,X19)
& perp(X7,X1,X15,X19)
& coll(X7,X15,X19)
& perp(X17,X1,X2,X3)
& coll(X17,X2,X3) )
=> eqangle(X2,X1,X1,X7,X17,X1,X1,X3) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214032]) ).
fof(c_0_29,plain,
! [X580,X581,X582,X583] :
( ~ perp(X580,X581,X582,X583)
| perp(X582,X583,X580,X581) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
fof(c_0_30,negated_conjecture,
( circle(esk24_0,esk21_0,esk22_0,esk23_0)
& circle(esk24_0,esk21_0,esk25_0,esk29_0)
& coll(esk26_0,esk21_0,esk23_0)
& coll(esk26_0,esk22_0,esk25_0)
& perp(esk27_0,esk26_0,esk23_0,esk25_0)
& coll(esk27_0,esk23_0,esk25_0)
& perp(esk28_0,esk26_0,esk21_0,esk22_0)
& coll(esk28_0,esk21_0,esk22_0)
& ~ eqangle(esk21_0,esk26_0,esk26_0,esk27_0,esk28_0,esk26_0,esk26_0,esk22_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_31,plain,
! [X633,X634,X635,X636,X637,X638,X639,X640] :
( ~ eqangle(X633,X634,X635,X636,X637,X638,X639,X640)
| eqangle(X635,X636,X633,X634,X639,X640,X637,X638) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_32,plain,
! [X787,X788,X789,X790,X791,X792] :
( ~ para(X787,X788,X789,X790)
| eqangle(X787,X788,X791,X792,X789,X790,X791,X792) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_33,plain,
! [X584,X585,X586,X587,X588,X589] :
( ~ perp(X584,X585,X586,X587)
| ~ perp(X586,X587,X588,X589)
| para(X584,X585,X588,X589) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
cnf(c_0_34,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
perp(esk28_0,esk26_0,esk21_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X781,X782,X783,X784,X785,X786] :
( ~ eqangle(X781,X782,X785,X786,X783,X784,X785,X786)
| para(X781,X782,X783,X784) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
cnf(c_0_37,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_31]) ).
cnf(c_0_38,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X566,X567,X568,X569] :
( ~ para(X566,X567,X568,X569)
| para(X568,X569,X566,X567) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_40,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
perp(esk21_0,esk22_0,esk28_0,esk26_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( para(X1,X2,esk28_0,esk26_0)
| ~ perp(X1,X2,esk21_0,esk22_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_46,plain,
! [X916,X917,X918] :
( ~ para(X916,X917,X916,X918)
| coll(X916,X917,X918) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_47,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( para(esk28_0,esk26_0,X1,X2)
| ~ perp(X1,X2,esk21_0,esk22_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_49,plain,
! [X555,X556,X557] :
( ~ coll(X555,X556,X557)
| coll(X556,X555,X557) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_50,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,negated_conjecture,
para(X1,X2,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_35])]) ).
fof(c_0_52,plain,
! [X552,X553,X554] :
( ~ coll(X552,X553,X554)
| coll(X552,X554,X553) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
cnf(c_0_53,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_55,plain,
! [X801,X802,X803,X804] :
( ~ eqangle(X803,X801,X803,X802,X804,X801,X804,X802)
| ~ coll(X803,X804,X802)
| cyclic(X801,X802,X803,X804) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_56,plain,
! [X558,X559,X560,X561] :
( ~ coll(X558,X559,X560)
| ~ coll(X558,X559,X561)
| coll(X560,X561,X558) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_57,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,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_55]) ).
cnf(c_0_60,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
fof(c_0_62,plain,
! [X612,X613,X614,X615] :
( ~ cyclic(X612,X613,X614,X615)
| cyclic(X612,X614,X613,X615) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_63,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_38]) ).
cnf(c_0_64,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_61])]) ).
fof(c_0_65,plain,
! [X608,X609,X610,X611] :
( ~ cyclic(X608,X609,X610,X611)
| cyclic(X608,X609,X611,X610) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_66,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_51])]),c_0_64])]) ).
fof(c_0_68,plain,
! [X842,X843,X844,X845,X846] :
( ~ circle(X845,X842,X843,X844)
| ~ coll(X846,X843,X844)
| ~ eqangle(X842,X843,X842,X844,X845,X843,X845,X846)
| midp(X846,X843,X844) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD51])]) ).
fof(c_0_69,plain,
! [X793,X794,X795,X796] :
( ~ cyclic(X793,X794,X795,X796)
| eqangle(X795,X793,X795,X794,X796,X793,X796,X794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_70,plain,
! [X616,X617,X618,X619] :
( ~ cyclic(X616,X617,X618,X619)
| cyclic(X617,X616,X618,X619) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_71,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,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_68]) ).
cnf(c_0_74,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_75,plain,
! [X620,X621,X622,X623,X624] :
( ~ cyclic(X620,X621,X622,X623)
| ~ cyclic(X620,X621,X622,X624)
| cyclic(X621,X622,X623,X624) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_76,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
fof(c_0_78,plain,
! [X816,X817,X818,X819,X820] :
( ~ midp(X819,X816,X817)
| ~ para(X819,X820,X817,X818)
| ~ coll(X820,X816,X818)
| midp(X820,X816,X818) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
cnf(c_0_79,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_73,c_0_74]) ).
cnf(c_0_80,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_81,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,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_78]) ).
cnf(c_0_83,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_79,c_0_58])]) ).
cnf(c_0_84,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_81])]) ).
fof(c_0_85,plain,
! [X641,X642,X643,X644,X645,X646,X647,X648] :
( ~ eqangle(X641,X642,X643,X644,X645,X646,X647,X648)
| eqangle(X645,X646,X647,X648,X641,X642,X643,X644) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD20])]) ).
fof(c_0_86,plain,
! [X821,X822,X823] :
( ~ cong(X823,X821,X823,X822)
| eqangle(X823,X821,X821,X822,X821,X822,X823,X822) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
cnf(c_0_87,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_64])]) ).
cnf(c_0_88,plain,
( midp(X1,X2,X1)
| ~ circle(X3,X4,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
cnf(c_0_89,negated_conjecture,
circle(esk24_0,esk21_0,esk25_0,esk29_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_90,plain,
! [X942,X943,X944,X945,X946,X947,X948,X949] :
( ~ eqangle(X942,X943,X944,X945,X946,X947,X948,X949)
| ~ para(X946,X947,X948,X949)
| para(X942,X943,X944,X945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD73])]) ).
cnf(c_0_91,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_85]) ).
cnf(c_0_92,plain,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_93,plain,
! [X922,X923,X924] :
( ~ midp(X922,X923,X924)
| cong(X922,X923,X922,X924) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_94,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_87,c_0_51]) ).
cnf(c_0_95,negated_conjecture,
midp(esk29_0,esk25_0,esk29_0),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
fof(c_0_96,plain,
! [X562,X563,X564,X565] :
( ~ para(X562,X563,X564,X565)
| para(X562,X563,X565,X564) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_97,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_90]) ).
cnf(c_0_98,plain,
( eqangle(X1,X2,X3,X2,X3,X1,X1,X2)
| ~ cong(X3,X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_99,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_100,negated_conjecture,
midp(X1,esk25_0,X1),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
fof(c_0_102,plain,
! [X906,X907,X908,X909,X910] :
( ~ midp(X910,X906,X907)
| ~ para(X906,X908,X907,X909)
| ~ para(X906,X909,X907,X908)
| midp(X910,X908,X909) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_103,plain,
( para(X1,X2,X3,X2)
| ~ cong(X3,X1,X3,X2)
| ~ para(X3,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
cong(X1,esk25_0,X1,X1),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_105,negated_conjecture,
para(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_101,c_0_51]) ).
cnf(c_0_106,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_102]) ).
cnf(c_0_107,negated_conjecture,
para(esk25_0,X1,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105])]) ).
cnf(c_0_108,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,esk25_0,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_107])]) ).
cnf(c_0_109,plain,
( eqangle(X1,X2,X1,X3,X4,X2,X4,X3)
| ~ cyclic(X2,X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_74]) ).
cnf(c_0_110,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_51]),c_0_51])]) ).
cnf(c_0_111,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_108,c_0_100]) ).
cnf(c_0_112,plain,
( para(X1,X2,X1,X3)
| ~ cyclic(X2,X3,X4,X1)
| ~ para(X4,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_97,c_0_109]) ).
cnf(c_0_113,negated_conjecture,
( midp(X1,X2,X3)
| ~ midp(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_105]) ).
cnf(c_0_114,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,plain,
( para(X1,X2,X1,X3)
| ~ para(X4,X2,X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_84])]) ).
cnf(c_0_116,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_92]) ).
cnf(c_0_117,negated_conjecture,
midp(X1,X1,X2),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,plain,
( para(X1,X2,X1,X3)
| ~ cong(X2,X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_119,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_99,c_0_117]) ).
fof(c_0_120,plain,
! [X811,X812,X813,X814,X815] :
( ~ midp(X814,X811,X812)
| ~ midp(X815,X811,X813)
| para(X814,X815,X812,X813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD44])]) ).
cnf(c_0_121,plain,
para(X1,X2,X1,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119])]) ).
cnf(c_0_122,plain,
( para(X1,X4,X3,X5)
| ~ midp(X1,X2,X3)
| ~ midp(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_123,plain,
midp(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_121]),c_0_114]),c_0_121])]) ).
fof(c_0_124,plain,
! [X649,X650,X651,X652,X653,X654,X655,X656] :
( ~ eqangle(X649,X650,X651,X652,X653,X654,X655,X656)
| eqangle(X649,X650,X653,X654,X651,X652,X655,X656) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD21])]) ).
cnf(c_0_125,plain,
para(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_123])]) ).
cnf(c_0_126,plain,
( eqangle(X1,X2,X3,X4,X5,X6,X3,X4)
| ~ para(X5,X6,X1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_38]) ).
fof(c_0_127,plain,
! [X657,X658,X659,X660,X661,X662,X663,X664,X665,X666,X667,X668] :
( ~ eqangle(X657,X658,X659,X660,X661,X662,X663,X664)
| ~ eqangle(X661,X662,X663,X664,X665,X666,X667,X668)
| eqangle(X657,X658,X659,X660,X665,X666,X667,X668) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD22])]) ).
cnf(c_0_128,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_124]) ).
cnf(c_0_129,plain,
eqangle(X1,X2,X3,X4,X1,X2,X5,X6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_125])]) ).
cnf(c_0_130,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_125])]) ).
cnf(c_0_131,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_127]) ).
cnf(c_0_132,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_133,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(spm,[status(thm)],[c_0_128,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
~ eqangle(esk21_0,esk26_0,esk26_0,esk27_0,esk28_0,esk26_0,esk26_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_135,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133])]) ).
cnf(c_0_136,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO570+1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % 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
% 0.15/0.34 % Computer : n011.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 18:03:02 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 2.10/1.94 % Version : CSE_E---1.7
% 2.10/1.94 % Problem : theBenchmark.p
% 2.10/1.94 % SZS status Theorem for theBenchmark.p
% 2.10/1.94 % SZS output start CNFRefutation
% See solution above
% 2.10/1.94 % Total time : 1.373s
%------------------------------------------------------------------------------