%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO602+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 : n029.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 2.24s 1.97s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 35
% Syntax : Number of formulae : 175 ( 39 unt; 0 def)
% Number of atoms : 406 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 380 ( 149 ~; 146 |; 49 &)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 18 ( 18 usr; 17 con; 0-4 aty)
% Number of variables : 631 ( 30 sgn 340 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(exemplo6GDDFULL618064,conjecture,
! [X1,X2,X5,X6,X4,X7,X19,X20,X21,X22,X23,X24,X25,X26,X27,X28,X29] :
( ( circle(X2,X5,X21,X22)
& circle(X1,X5,X23,X24)
& circle(X2,X5,X6,X25)
& circle(X1,X5,X6,X26)
& coll(X4,X1,X2)
& coll(X4,X5,X6)
& circle(X2,X5,X7,X27)
& circle(X1,X5,X19,X28)
& coll(X19,X5,X7)
& coll(X20,X6,X7)
& circle(X1,X5,X20,X29) )
=> perp(X19,X20,X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL618064) ).
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(ruleD1,axiom,
! [X1,X2,X3] :
( coll(X1,X2,X3)
=> coll(X1,X3,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/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(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(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(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(ruleD11,axiom,
! [X1,X2,X7] :
( midp(X7,X2,X1)
=> midp(X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD11) ).
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(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(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(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(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(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(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(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(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(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(ruleD74,axiom,
! [X1,X2,X3,X4,X9,X10,X11,X12] :
( ( eqangle(X1,X2,X3,X4,X9,X10,X11,X12)
& perp(X9,X10,X11,X12) )
=> perp(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD74) ).
fof(ruleD57,axiom,
! [X1,X2,X9,X10] :
( ( cong(X1,X9,X2,X9)
& cong(X1,X10,X2,X10)
& cyclic(X1,X2,X9,X10) )
=> perp(X9,X1,X1,X10) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD57) ).
fof(ruleD7,axiom,
! [X1,X2,X3,X4] :
( perp(X1,X2,X3,X4)
=> perp(X1,X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD7) ).
fof(ruleD52,axiom,
! [X1,X2,X3,X7] :
( ( perp(X1,X2,X2,X3)
& midp(X7,X1,X3) )
=> cong(X1,X7,X2,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD52) ).
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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
fof(c_0_35,negated_conjecture,
~ ! [X1,X2,X5,X6,X4,X7,X19,X20,X21,X22,X23,X24,X25,X26,X27,X28,X29] :
( ( circle(X2,X5,X21,X22)
& circle(X1,X5,X23,X24)
& circle(X2,X5,X6,X25)
& circle(X1,X5,X6,X26)
& coll(X4,X1,X2)
& coll(X4,X5,X6)
& circle(X2,X5,X7,X27)
& circle(X1,X5,X19,X28)
& coll(X19,X5,X7)
& coll(X20,X6,X7)
& circle(X1,X5,X20,X29) )
=> perp(X19,X20,X7,X2) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618064]) ).
fof(c_0_36,plain,
! [X601,X602,X603,X604,X605,X606] :
( ~ perp(X601,X602,X603,X604)
| ~ perp(X603,X604,X605,X606)
| para(X601,X602,X605,X606) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
fof(c_0_37,plain,
! [X1043,X1044,X1045,X1046] :
( ~ circle(X1046,X1043,X1044,X1045)
| perp(esk12_4(X1043,X1044,X1045,X1046),X1043,X1043,X1046) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])]) ).
fof(c_0_38,plain,
! [X597,X598,X599,X600] :
( ~ perp(X597,X598,X599,X600)
| perp(X599,X600,X597,X598) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
fof(c_0_39,plain,
! [X569,X570,X571] :
( ~ coll(X569,X570,X571)
| coll(X569,X571,X570) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
fof(c_0_40,negated_conjecture,
( circle(esk22_0,esk23_0,esk29_0,esk30_0)
& circle(esk21_0,esk23_0,esk31_0,esk32_0)
& circle(esk22_0,esk23_0,esk24_0,esk33_0)
& circle(esk21_0,esk23_0,esk24_0,esk34_0)
& coll(esk25_0,esk21_0,esk22_0)
& coll(esk25_0,esk23_0,esk24_0)
& circle(esk22_0,esk23_0,esk26_0,esk35_0)
& circle(esk21_0,esk23_0,esk27_0,esk36_0)
& coll(esk27_0,esk23_0,esk26_0)
& coll(esk28_0,esk24_0,esk26_0)
& circle(esk21_0,esk23_0,esk28_0,esk37_0)
& ~ perp(esk27_0,esk28_0,esk26_0,esk22_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_41,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( perp(esk12_4(X2,X3,X4,X1),X2,X2,X1)
| ~ circle(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_44,plain,
! [X575,X576,X577,X578] :
( ~ coll(X575,X576,X577)
| ~ coll(X575,X576,X578)
| coll(X577,X578,X575) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_45,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
coll(esk27_0,esk23_0,esk26_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_47,plain,
! [X818,X819,X820,X821] :
( ~ eqangle(X820,X818,X820,X819,X821,X818,X821,X819)
| ~ coll(X820,X821,X819)
| cyclic(X818,X819,X820,X821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_48,plain,
! [X804,X805,X806,X807,X808,X809] :
( ~ para(X804,X805,X806,X807)
| eqangle(X804,X805,X808,X809,X806,X807,X808,X809) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
cnf(c_0_49,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_41,c_0_42]) ).
cnf(c_0_50,plain,
( perp(X1,X2,esk12_4(X1,X3,X4,X2),X1)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_51,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,negated_conjecture,
coll(esk27_0,esk26_0,esk23_0),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,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_47]) ).
cnf(c_0_54,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( para(X1,X2,X1,X2)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
circle(esk22_0,esk23_0,esk29_0,esk30_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_57,negated_conjecture,
( coll(X1,esk23_0,esk27_0)
| ~ coll(esk27_0,esk26_0,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_58,plain,
! [X629,X630,X631,X632] :
( ~ cyclic(X629,X630,X631,X632)
| cyclic(X629,X631,X630,X632) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_59,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
para(esk23_0,esk22_0,esk23_0,esk22_0),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
coll(esk23_0,esk23_0,esk27_0),
inference(spm,[status(thm)],[c_0_57,c_0_52]) ).
fof(c_0_62,plain,
! [X650,X651,X652,X653,X654,X655,X656,X657] :
( ~ eqangle(X650,X651,X652,X653,X654,X655,X656,X657)
| eqangle(X652,X653,X650,X651,X656,X657,X654,X655) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_63,plain,
! [X798,X799,X800,X801,X802,X803] :
( ~ eqangle(X798,X799,X802,X803,X800,X801,X802,X803)
| para(X798,X799,X800,X801) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
fof(c_0_64,plain,
! [X810,X811,X812,X813] :
( ~ cyclic(X810,X811,X812,X813)
| eqangle(X812,X810,X812,X811,X813,X810,X813,X811) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_65,plain,
! [X633,X634,X635,X636] :
( ~ cyclic(X633,X634,X635,X636)
| cyclic(X634,X633,X635,X636) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_66,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( cyclic(esk22_0,X1,esk23_0,esk23_0)
| ~ coll(esk23_0,esk23_0,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
coll(esk23_0,esk27_0,esk23_0),
inference(spm,[status(thm)],[c_0_45,c_0_61]) ).
cnf(c_0_69,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_62]) ).
cnf(c_0_70,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,negated_conjecture,
( cyclic(esk22_0,esk23_0,X1,esk23_0)
| ~ coll(esk23_0,esk23_0,X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( coll(X1,esk23_0,esk23_0)
| ~ coll(esk23_0,esk27_0,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_68]) ).
cnf(c_0_75,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_69,c_0_54]) ).
cnf(c_0_76,plain,
( para(X1,X2,X1,X2)
| ~ cyclic(X2,X3,X1,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( cyclic(esk23_0,esk22_0,X1,esk23_0)
| ~ coll(esk23_0,esk23_0,X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
coll(esk23_0,esk23_0,esk23_0),
inference(spm,[status(thm)],[c_0_74,c_0_68]) ).
fof(c_0_79,plain,
! [X933,X934,X935] :
( ~ para(X933,X934,X933,X935)
| coll(X933,X934,X935) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_80,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_70,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
para(esk23_0,esk23_0,esk23_0,esk23_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
fof(c_0_82,plain,
! [X572,X573,X574] :
( ~ coll(X572,X573,X574)
| coll(X573,X572,X574) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_83,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_84,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_86,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_88,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_87]) ).
cnf(c_0_89,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_88]),c_0_88])]) ).
fof(c_0_90,plain,
! [X625,X626,X627,X628] :
( ~ cyclic(X625,X626,X627,X628)
| cyclic(X625,X626,X628,X627) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_91,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_84])]),c_0_89])]) ).
fof(c_0_92,plain,
! [X859,X860,X861,X862,X863] :
( ~ circle(X862,X859,X860,X861)
| ~ coll(X863,X860,X861)
| ~ eqangle(X859,X860,X859,X861,X862,X860,X862,X863)
| midp(X863,X860,X861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD51])]) ).
cnf(c_0_93,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_94,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_66,c_0_91]) ).
cnf(c_0_95,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_92]) ).
fof(c_0_96,plain,
! [X637,X638,X639,X640,X641] :
( ~ cyclic(X637,X638,X639,X640)
| ~ cyclic(X637,X638,X639,X641)
| cyclic(X638,X639,X640,X641) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_97,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,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_95,c_0_71]) ).
cnf(c_0_99,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_100,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_72,c_0_97]) ).
cnf(c_0_101,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_98,c_0_87])]) ).
cnf(c_0_102,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_100])]) ).
fof(c_0_103,plain,
! [X613,X614,X615] :
( ~ midp(X615,X614,X613)
| midp(X615,X613,X614) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD11])]) ).
cnf(c_0_104,plain,
( midp(X1,X2,X1)
| ~ circle(X3,X4,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
fof(c_0_105,plain,
! [X975,X976,X977,X978,X979,X980,X981,X982] :
( ~ eqratio(X975,X976,X977,X978,X979,X980,X981,X982)
| ~ cong(X979,X980,X981,X982)
| cong(X975,X976,X977,X978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD75])]) ).
fof(c_0_106,plain,
! [X945,X946,X947,X948,X949,X950] :
( ~ midp(X949,X945,X946)
| ~ midp(X950,X947,X948)
| eqratio(X949,X945,X945,X946,X950,X947,X947,X948) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD70])]) ).
fof(c_0_107,plain,
! [X939,X940,X941] :
( ~ midp(X939,X940,X941)
| cong(X939,X940,X939,X941) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_108,plain,
( midp(X1,X3,X2)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_109,negated_conjecture,
midp(esk30_0,esk29_0,esk30_0),
inference(spm,[status(thm)],[c_0_104,c_0_56]) ).
cnf(c_0_110,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_105]) ).
cnf(c_0_111,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_106]) ).
cnf(c_0_112,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_113,negated_conjecture,
midp(esk30_0,esk30_0,esk29_0),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,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_110,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
cong(esk30_0,esk30_0,esk30_0,esk29_0),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,negated_conjecture,
circle(esk21_0,esk23_0,esk28_0,esk37_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_117,plain,
! [X936,X937,X938] :
( ~ cong(X936,X937,X936,X938)
| ~ coll(X936,X937,X938)
| midp(X936,X937,X938) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD67])]) ).
fof(c_0_118,plain,
! [X686,X687,X688,X689] :
( ~ cong(X686,X687,X688,X689)
| cong(X686,X687,X689,X688) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD23])]) ).
cnf(c_0_119,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_114,c_0_115]),c_0_113])]) ).
cnf(c_0_120,negated_conjecture,
midp(esk37_0,esk28_0,esk37_0),
inference(spm,[status(thm)],[c_0_104,c_0_116]) ).
fof(c_0_121,plain,
! [X838,X839,X840] :
( ~ cong(X840,X838,X840,X839)
| eqangle(X840,X838,X838,X839,X838,X839,X840,X839) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
fof(c_0_122,plain,
! [X923,X924,X925,X926,X927] :
( ~ midp(X927,X923,X924)
| ~ para(X923,X925,X924,X926)
| ~ para(X923,X926,X924,X925)
| midp(X927,X925,X926) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_123,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_124,plain,
( cong(X1,X2,X4,X3)
| ~ cong(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_125,negated_conjecture,
cong(esk37_0,esk28_0,esk28_0,esk37_0),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
fof(c_0_126,plain,
! [X579,X580,X581,X582] :
( ~ para(X579,X580,X581,X582)
| para(X579,X580,X582,X581) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_127,plain,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_128,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_122]) ).
cnf(c_0_129,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_89])]) ).
cnf(c_0_130,negated_conjecture,
cong(esk37_0,esk28_0,esk37_0,esk28_0),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
fof(c_0_131,plain,
! [X583,X584,X585,X586] :
( ~ para(X583,X584,X585,X586)
| para(X585,X586,X583,X584) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_132,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_133,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_127]) ).
cnf(c_0_134,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_84]),c_0_84])]) ).
cnf(c_0_135,negated_conjecture,
midp(esk37_0,esk28_0,esk28_0),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
fof(c_0_136,plain,
! [X833,X834,X835,X836,X837] :
( ~ midp(X836,X833,X834)
| ~ para(X836,X837,X834,X835)
| ~ coll(X837,X833,X835)
| midp(X837,X833,X835) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
cnf(c_0_137,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_138,plain,
( para(X1,X1,X2,X1)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
fof(c_0_139,plain,
! [X690,X691,X692,X693] :
( ~ cong(X690,X691,X692,X693)
| cong(X692,X693,X690,X691) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD24])]) ).
cnf(c_0_140,negated_conjecture,
midp(esk37_0,X1,X1),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
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_136]) ).
cnf(c_0_142,plain,
( para(X1,X2,X2,X2)
| ~ cong(X2,X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_143,plain,
( cong(X3,X4,X1,X2)
| ~ cong(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_144,negated_conjecture,
cong(esk37_0,X1,X1,X1),
inference(spm,[status(thm)],[c_0_119,c_0_140]) ).
cnf(c_0_145,plain,
( midp(X1,X2,X1)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X3,X2,X1)
| ~ coll(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_146,negated_conjecture,
cong(X1,X1,esk37_0,X1),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
fof(c_0_147,plain,
! [X967,X968,X969,X970,X971,X972,X973,X974] :
( ~ eqangle(X967,X968,X969,X970,X971,X972,X973,X974)
| ~ perp(X971,X972,X973,X974)
| perp(X967,X968,X969,X970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD74])]) ).
cnf(c_0_148,plain,
( midp(X1,X2,X1)
| ~ cong(X1,X1,X1,X3)
| ~ midp(X3,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_87])]) ).
cnf(c_0_149,negated_conjecture,
cong(X1,X1,X1,esk37_0),
inference(spm,[status(thm)],[c_0_124,c_0_146]) ).
cnf(c_0_150,plain,
( perp(X1,X2,X3,X4)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X7,X8)
| ~ perp(X5,X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
fof(c_0_151,plain,
! [X884,X885,X886,X887] :
( ~ cong(X884,X886,X885,X886)
| ~ cong(X884,X887,X885,X887)
| ~ cyclic(X884,X885,X886,X887)
| perp(X886,X884,X884,X887) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD57])]) ).
cnf(c_0_152,plain,
( coll(X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_133]) ).
cnf(c_0_153,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(esk37_0,X2,X1) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_154,plain,
( perp(X1,X2,X1,X3)
| ~ cyclic(X2,X3,X1,X4)
| ~ perp(X4,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_150,c_0_71]) ).
cnf(c_0_155,plain,
( perp(X2,X1,X1,X4)
| ~ cong(X1,X2,X3,X2)
| ~ cong(X1,X4,X3,X4)
| ~ cyclic(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_156,plain,
( cyclic(X1,X1,X1,X1)
| ~ cong(X1,X1,X1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_127]),c_0_152]) ).
cnf(c_0_157,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_153,c_0_140]) ).
cnf(c_0_158,plain,
( perp(X1,X2,X1,X3)
| ~ perp(X4,X2,X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_102])]) ).
cnf(c_0_159,plain,
( perp(X1,X1,X1,X1)
| ~ cong(X1,X1,X1,X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_160,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_134,c_0_157]) ).
fof(c_0_161,plain,
! [X593,X594,X595,X596] :
( ~ perp(X593,X594,X595,X596)
| perp(X593,X594,X596,X595) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD7])]) ).
cnf(c_0_162,plain,
( perp(X1,X2,X1,X2)
| ~ cong(X2,X2,X2,X2) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_163,negated_conjecture,
cong(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_112,c_0_160]) ).
fof(c_0_164,plain,
! [X864,X865,X866,X867] :
( ~ perp(X864,X865,X865,X866)
| ~ midp(X867,X864,X866)
| cong(X864,X867,X865,X867) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD52])]) ).
cnf(c_0_165,plain,
( perp(X1,X2,X4,X3)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_166,plain,
perp(X1,X2,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_163])]) ).
fof(c_0_167,plain,
! [X880,X881,X882,X883] :
( ~ cong(X880,X882,X881,X882)
| ~ cong(X880,X883,X881,X883)
| perp(X880,X881,X882,X883) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD56])]) ).
cnf(c_0_168,plain,
( cong(X1,X4,X2,X4)
| ~ perp(X1,X2,X2,X3)
| ~ midp(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_169,plain,
perp(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_170,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_171,plain,
cong(X1,X2,X3,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_160])]) ).
cnf(c_0_172,negated_conjecture,
~ perp(esk27_0,esk28_0,esk26_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_173,plain,
perp(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171]),c_0_171])]) ).
cnf(c_0_174,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO602+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 : n029.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 18:04:29 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.24/1.97 % Version : CSE_E---1.7
% 2.24/1.97 % Problem : theBenchmark.p
% 2.24/1.97 % SZS status Theorem for theBenchmark.p
% 2.24/1.97 % SZS output start CNFRefutation
% See solution above
% 2.24/1.98 % Total time : 1.371s
%------------------------------------------------------------------------------