%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO606+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 : n006.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 04:21:39 PM UTC 2026
% Result : Theorem 3.55s 3.05s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 33
% Syntax : Number of formulae : 174 ( 42 unt; 0 def)
% Number of atoms : 396 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 364 ( 142 ~; 139 |; 49 &)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 19 ( 19 usr; 18 con; 0-4 aty)
% Number of variables : 649 ( 40 sgn 334 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(exemplo6GDDFULL618068,conjecture,
! [X1,X2,X9,X4,X5,X19,X6,X13,X20,X21,X22,X23,X24,X25,X26,X27,X28,X29] :
( ( perp(X9,X1,X9,X2)
& circle(X1,X9,X20,X21)
& circle(X2,X9,X22,X23)
& circle(X1,X9,X4,X24)
& circle(X1,X4,X5,X25)
& coll(X5,X4,X1)
& circle(X1,X9,X19,X26)
& circle(X2,X9,X19,X27)
& coll(X6,X4,X19)
& circle(X2,X9,X6,X28)
& circle(X2,X6,X13,X29)
& coll(X13,X6,X2) )
=> perp(X13,X6,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618068) ).
fof(ruleD9,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( perp(X1,X2,X3,X4)
& perp(X3,X4,X5,X6) )
=> para(X1,X2,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD9) ).
fof(ruleX11,axiom,
! [X1,X2,X3,X8] :
? [X9] :
( circle(X8,X1,X2,X3)
=> perp(X9,X1,X1,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleX11) ).
fof(ruleD8,axiom,
! [X1,X2,X3,X4] :
( perp(X1,X2,X3,X4)
=> perp(X3,X4,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD8) ).
fof(ruleD1,axiom,
! [X1,X2,X3] :
( coll(X1,X2,X3)
=> coll(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
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(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(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(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(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(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(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(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(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(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(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(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(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(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(ruleD11,axiom,
! [X1,X2,X7] :
( midp(X7,X2,X1)
=> midp(X7,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD11) ).
fof(ruleD68,axiom,
! [X1,X2,X3] :
( midp(X1,X2,X3)
=> cong(X1,X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD68) ).
fof(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(ruleD75,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12] :
( ( eqratio(X1,X2,X3,X4,X9,X10,X11,X12)
& cong(X9,X10,X11,X12) )
=> cong(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD75) ).
fof(ruleD70,axiom,
! [X1,X2,X3,X4,X7,X17] :
( ( midp(X7,X1,X2)
& midp(X17,X3,X4) )
=> eqratio(X7,X1,X1,X2,X17,X3,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD70) ).
fof(ruleD64,axiom,
! [X1,X2,X3,X4,X7] :
( ( midp(X7,X1,X2)
& para(X1,X3,X2,X4)
& para(X1,X4,X2,X3) )
=> midp(X7,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
fof(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(ruleD24,axiom,
! [X1,X2,X3,X4] :
( cong(X1,X2,X3,X4)
=> cong(X3,X4,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD24) ).
fof(ruleD23,axiom,
! [X1,X2,X3,X4] :
( cong(X1,X2,X3,X4)
=> cong(X1,X2,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD23) ).
fof(ruleD67,axiom,
! [X1,X2,X3] :
( ( cong(X1,X2,X1,X3)
& coll(X1,X2,X3) )
=> midp(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD67) ).
fof(ruleD56,axiom,
! [X1,X2,X9,X10] :
( ( cong(X1,X9,X2,X9)
& cong(X1,X10,X2,X10) )
=> perp(X1,X2,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
fof(c_0_33,negated_conjecture,
~ ! [X1,X2,X9,X4,X5,X19,X6,X13,X20,X21,X22,X23,X24,X25,X26,X27,X28,X29] :
( ( perp(X9,X1,X9,X2)
& circle(X1,X9,X20,X21)
& circle(X2,X9,X22,X23)
& circle(X1,X9,X4,X24)
& circle(X1,X4,X5,X25)
& coll(X5,X4,X1)
& circle(X1,X9,X19,X26)
& circle(X2,X9,X19,X27)
& coll(X6,X4,X19)
& circle(X2,X9,X6,X28)
& circle(X2,X6,X13,X29)
& coll(X13,X6,X2) )
=> perp(X13,X6,X4,X5) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618068]) ).
fof(c_0_34,plain,
! [X602,X603,X604,X605,X606,X607] :
( ~ perp(X602,X603,X604,X605)
| ~ perp(X604,X605,X606,X607)
| para(X602,X603,X606,X607) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
fof(c_0_35,plain,
! [X1044,X1045,X1046,X1047] :
( ~ circle(X1047,X1044,X1045,X1046)
| perp(esk12_4(X1044,X1045,X1046,X1047),X1044,X1044,X1047) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])]) ).
fof(c_0_36,plain,
! [X598,X599,X600,X601] :
( ~ perp(X598,X599,X600,X601)
| perp(X600,X601,X598,X599) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
fof(c_0_37,plain,
! [X570,X571,X572] :
( ~ coll(X570,X571,X572)
| coll(X570,X572,X571) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
fof(c_0_38,negated_conjecture,
( perp(esk23_0,esk21_0,esk23_0,esk22_0)
& circle(esk21_0,esk23_0,esk29_0,esk30_0)
& circle(esk22_0,esk23_0,esk31_0,esk32_0)
& circle(esk21_0,esk23_0,esk24_0,esk33_0)
& circle(esk21_0,esk24_0,esk25_0,esk34_0)
& coll(esk25_0,esk24_0,esk21_0)
& circle(esk21_0,esk23_0,esk26_0,esk35_0)
& circle(esk22_0,esk23_0,esk26_0,esk36_0)
& coll(esk27_0,esk24_0,esk26_0)
& circle(esk22_0,esk23_0,esk27_0,esk37_0)
& circle(esk22_0,esk27_0,esk28_0,esk38_0)
& coll(esk28_0,esk27_0,esk22_0)
& ~ perp(esk28_0,esk27_0,esk24_0,esk25_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_39,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_40,plain,
( perp(esk12_4(X2,X3,X4,X1),X2,X2,X1)
| ~ circle(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_42,plain,
! [X576,X577,X578,X579] :
( ~ coll(X576,X577,X578)
| ~ coll(X576,X577,X579)
| coll(X578,X579,X576) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_43,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,negated_conjecture,
coll(esk28_0,esk27_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_45,plain,
! [X819,X820,X821,X822] :
( ~ eqangle(X821,X819,X821,X820,X822,X819,X822,X820)
| ~ coll(X821,X822,X820)
| cyclic(X819,X820,X821,X822) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_46,plain,
! [X805,X806,X807,X808,X809,X810] :
( ~ para(X805,X806,X807,X808)
| eqangle(X805,X806,X809,X810,X807,X808,X809,X810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
cnf(c_0_47,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_39,c_0_40]) ).
cnf(c_0_48,plain,
( perp(X1,X2,esk12_4(X1,X3,X4,X2),X1)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_49,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,negated_conjecture,
coll(esk28_0,esk22_0,esk27_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,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_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(X1,X2,X1,X2)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
circle(esk22_0,esk27_0,esk28_0,esk38_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_55,negated_conjecture,
( coll(X1,esk27_0,esk28_0)
| ~ coll(esk28_0,esk22_0,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_56,plain,
! [X630,X631,X632,X633] :
( ~ cyclic(X630,X631,X632,X633)
| cyclic(X630,X632,X631,X633) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_57,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
para(esk27_0,esk22_0,esk27_0,esk22_0),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
coll(esk27_0,esk27_0,esk28_0),
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
fof(c_0_60,plain,
! [X651,X652,X653,X654,X655,X656,X657,X658] :
( ~ eqangle(X651,X652,X653,X654,X655,X656,X657,X658)
| eqangle(X653,X654,X651,X652,X657,X658,X655,X656) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_61,plain,
! [X799,X800,X801,X802,X803,X804] :
( ~ eqangle(X799,X800,X803,X804,X801,X802,X803,X804)
| para(X799,X800,X801,X802) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
fof(c_0_62,plain,
! [X811,X812,X813,X814] :
( ~ cyclic(X811,X812,X813,X814)
| eqangle(X813,X811,X813,X812,X814,X811,X814,X812) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_63,plain,
! [X634,X635,X636,X637] :
( ~ cyclic(X634,X635,X636,X637)
| cyclic(X635,X634,X636,X637) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_64,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( cyclic(esk22_0,X1,esk27_0,esk27_0)
| ~ coll(esk27_0,esk27_0,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
coll(esk27_0,esk28_0,esk27_0),
inference(spm,[status(thm)],[c_0_43,c_0_59]) ).
cnf(c_0_67,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_60]) ).
cnf(c_0_68,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( cyclic(esk22_0,esk27_0,X1,esk27_0)
| ~ coll(esk27_0,esk27_0,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( coll(X1,esk27_0,esk27_0)
| ~ coll(esk27_0,esk28_0,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_66]) ).
cnf(c_0_73,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_67,c_0_52]) ).
cnf(c_0_74,plain,
( para(X1,X2,X1,X2)
| ~ cyclic(X2,X3,X1,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
( cyclic(esk27_0,esk22_0,X1,esk27_0)
| ~ coll(esk27_0,esk27_0,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
coll(esk27_0,esk27_0,esk27_0),
inference(spm,[status(thm)],[c_0_72,c_0_66]) ).
fof(c_0_77,plain,
! [X934,X935,X936] :
( ~ para(X934,X935,X934,X936)
| coll(X934,X935,X936) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_78,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_68,c_0_73]) ).
cnf(c_0_79,negated_conjecture,
para(esk27_0,esk27_0,esk27_0,esk27_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
fof(c_0_80,plain,
! [X573,X574,X575] :
( ~ coll(X573,X574,X575)
| coll(X574,X573,X575) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_81,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_82,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_83,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_84,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_86,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_85]) ).
cnf(c_0_87,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_86]),c_0_86])]) ).
fof(c_0_88,plain,
! [X626,X627,X628,X629] :
( ~ cyclic(X626,X627,X628,X629)
| cyclic(X626,X627,X629,X628) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_89,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_82])]),c_0_87])]) ).
fof(c_0_90,plain,
! [X860,X861,X862,X863,X864] :
( ~ circle(X863,X860,X861,X862)
| ~ coll(X864,X861,X862)
| ~ eqangle(X860,X861,X860,X862,X863,X861,X863,X864)
| midp(X864,X861,X862) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD51])]) ).
cnf(c_0_91,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_92,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_64,c_0_89]) ).
cnf(c_0_93,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_90]) ).
fof(c_0_94,plain,
! [X638,X639,X640,X641,X642] :
( ~ cyclic(X638,X639,X640,X641)
| ~ cyclic(X638,X639,X640,X642)
| cyclic(X639,X640,X641,X642) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_95,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
fof(c_0_96,plain,
! [X659,X660,X661,X662,X663,X664,X665,X666] :
( ~ eqangle(X659,X660,X661,X662,X663,X664,X665,X666)
| eqangle(X663,X664,X665,X666,X659,X660,X661,X662) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD20])]) ).
cnf(c_0_97,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_93,c_0_69]) ).
cnf(c_0_98,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_99,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_70,c_0_95]) ).
fof(c_0_100,plain,
! [X960,X961,X962,X963,X964,X965,X966,X967] :
( ~ eqangle(X960,X961,X962,X963,X964,X965,X966,X967)
| ~ para(X964,X965,X966,X967)
| para(X960,X961,X962,X963) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD73])]) ).
cnf(c_0_101,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_96]) ).
fof(c_0_102,plain,
! [X839,X840,X841] :
( ~ cong(X841,X839,X841,X840)
| eqangle(X841,X839,X839,X840,X839,X840,X841,X840) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
cnf(c_0_103,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_97,c_0_85])]) ).
cnf(c_0_104,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_99])]) ).
cnf(c_0_105,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_100]) ).
cnf(c_0_106,plain,
( eqangle(X1,X2,X1,X3,X4,X2,X4,X3)
| ~ cyclic(X2,X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_69]) ).
fof(c_0_107,plain,
! [X584,X585,X586,X587] :
( ~ para(X584,X585,X586,X587)
| para(X586,X587,X584,X585) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_108,plain,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
fof(c_0_109,plain,
! [X614,X615,X616] :
( ~ midp(X616,X615,X614)
| midp(X616,X614,X615) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD11])]) ).
cnf(c_0_110,plain,
( midp(X1,X2,X1)
| ~ circle(X3,X4,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).
cnf(c_0_111,plain,
( para(X1,X2,X1,X3)
| ~ cyclic(X2,X3,X4,X1)
| ~ para(X4,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_113,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_108]) ).
fof(c_0_114,plain,
! [X940,X941,X942] :
( ~ midp(X940,X941,X942)
| cong(X940,X941,X940,X942) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_115,plain,
( midp(X1,X3,X2)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_116,negated_conjecture,
midp(esk38_0,esk28_0,esk38_0),
inference(spm,[status(thm)],[c_0_110,c_0_54]) ).
cnf(c_0_117,plain,
( para(X1,X2,X1,X3)
| ~ para(X4,X2,X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_104])]) ).
cnf(c_0_118,plain,
( para(X1,X2,X1,X1)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_119,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_120,negated_conjecture,
midp(esk38_0,esk38_0,esk28_0),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
fof(c_0_121,plain,
! [X580,X581,X582,X583] :
( ~ para(X580,X581,X582,X583)
| para(X580,X581,X583,X582) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_122,plain,
( para(X1,X2,X1,X3)
| ~ cong(X3,X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_123,negated_conjecture,
cong(esk38_0,esk38_0,esk38_0,esk28_0),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_124,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_125,negated_conjecture,
para(X1,esk28_0,X1,esk38_0),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,negated_conjecture,
para(X1,esk28_0,esk38_0,X1),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
fof(c_0_127,plain,
! [X976,X977,X978,X979,X980,X981,X982,X983] :
( ~ eqratio(X976,X977,X978,X979,X980,X981,X982,X983)
| ~ cong(X980,X981,X982,X983)
| cong(X976,X977,X978,X979) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD75])]) ).
fof(c_0_128,plain,
! [X946,X947,X948,X949,X950,X951] :
( ~ midp(X950,X946,X947)
| ~ midp(X951,X948,X949)
| eqratio(X950,X946,X946,X947,X951,X948,X948,X949) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD70])]) ).
fof(c_0_129,plain,
! [X924,X925,X926,X927,X928] :
( ~ midp(X928,X924,X925)
| ~ para(X924,X926,X925,X927)
| ~ para(X924,X927,X925,X926)
| midp(X928,X926,X927) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_130,negated_conjecture,
para(esk38_0,X1,X1,esk28_0),
inference(spm,[status(thm)],[c_0_112,c_0_126]) ).
cnf(c_0_131,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_127]) ).
cnf(c_0_132,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_128]) ).
cnf(c_0_133,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_129]) ).
cnf(c_0_134,negated_conjecture,
para(esk38_0,X1,esk28_0,X1),
inference(spm,[status(thm)],[c_0_124,c_0_130]) ).
cnf(c_0_135,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_131,c_0_132]) ).
cnf(c_0_136,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,esk38_0,esk28_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_134])]) ).
fof(c_0_137,plain,
! [X834,X835,X836,X837,X838] :
( ~ midp(X837,X834,X835)
| ~ para(X837,X838,X835,X836)
| ~ coll(X838,X834,X836)
| midp(X838,X834,X836) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
fof(c_0_138,plain,
! [X691,X692,X693,X694] :
( ~ cong(X691,X692,X693,X694)
| cong(X693,X694,X691,X692) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD24])]) ).
cnf(c_0_139,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_135,c_0_123]),c_0_120])]) ).
cnf(c_0_140,negated_conjecture,
midp(esk38_0,X1,X1),
inference(spm,[status(thm)],[c_0_136,c_0_120]) ).
cnf(c_0_141,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_137]) ).
cnf(c_0_142,plain,
( para(X1,X1,X2,X1)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_113]) ).
fof(c_0_143,plain,
! [X687,X688,X689,X690] :
( ~ cong(X687,X688,X689,X690)
| cong(X687,X688,X690,X689) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD23])]) ).
cnf(c_0_144,plain,
( cong(X3,X4,X1,X2)
| ~ cong(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_145,negated_conjecture,
cong(esk38_0,X1,X1,X1),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
fof(c_0_146,plain,
! [X937,X938,X939] :
( ~ cong(X937,X938,X937,X939)
| ~ coll(X937,X938,X939)
| midp(X937,X938,X939) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD67])]) ).
cnf(c_0_147,plain,
( midp(X1,X2,X1)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X1,X2,X3)
| ~ coll(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_148,plain,
( cong(X1,X2,X4,X3)
| ~ cong(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_149,negated_conjecture,
cong(X1,X1,esk38_0,X1),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_151,plain,
( midp(X1,X2,X1)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_85])]) ).
cnf(c_0_152,negated_conjecture,
cong(X1,X1,X1,esk38_0),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_153,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_87])]) ).
cnf(c_0_154,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X1,X2,esk38_0) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_155,negated_conjecture,
midp(X1,X1,esk38_0),
inference(spm,[status(thm)],[c_0_153,c_0_152]) ).
cnf(c_0_156,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_87])]) ).
cnf(c_0_157,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_82]),c_0_82])]) ).
cnf(c_0_158,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_159,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_156,c_0_82]) ).
cnf(c_0_160,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_161,negated_conjecture,
midp(X1,X2,X1),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_162,negated_conjecture,
midp(X1,X1,X2),
inference(spm,[status(thm)],[c_0_115,c_0_161]) ).
cnf(c_0_163,plain,
( para(X1,X2,X1,X3)
| ~ cong(X2,X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_117,c_0_113]) ).
cnf(c_0_164,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_119,c_0_162]) ).
cnf(c_0_165,plain,
para(X1,X2,X1,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]) ).
cnf(c_0_166,plain,
midp(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_165]),c_0_161])]) ).
fof(c_0_167,plain,
! [X881,X882,X883,X884] :
( ~ cong(X881,X883,X882,X883)
| ~ cong(X881,X884,X882,X884)
| perp(X881,X882,X883,X884) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD56])]) ).
cnf(c_0_168,negated_conjecture,
cong(X1,X2,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_166])]) ).
cnf(c_0_169,plain,
( perp(X1,X3,X2,X4)
| ~ cong(X1,X2,X3,X2)
| ~ cong(X1,X4,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_170,negated_conjecture,
cong(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_148,c_0_168]) ).
cnf(c_0_171,negated_conjecture,
~ perp(esk28_0,esk27_0,esk24_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_172,plain,
perp(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170]),c_0_170])]) ).
cnf(c_0_173,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO606+1 : TPTP v9.2.1. Released v7.5.0.
% 0.08/0.14 % 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
% 0.16/0.35 % Computer : n006.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Mon May 4 18:04:16 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.36 % start to proof: theBenchmark
% 3.55/3.05 % Version : CSE_E---1.7
% 3.55/3.05 % Problem : theBenchmark.p
% 3.55/3.05 % SZS status Theorem for theBenchmark.p
% 3.55/3.05 % SZS output start CNFRefutation
% See solution above
% 3.55/3.05 % Total time : 2.373s
%------------------------------------------------------------------------------