%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO549+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 : n027.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 04:21:30 PM UTC 2026
% Result : Theorem 3.97s 3.26s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 29
% Syntax : Number of formulae : 131 ( 29 unt; 0 def)
% Number of atoms : 323 ( 0 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 298 ( 106 ~; 103 |; 59 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 17 ( 17 usr; 16 con; 0-4 aty)
% Number of variables : 575 ( 54 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(exemplo6GDDFULL012009,conjecture,
! [X1,X2,X4,X8,X3,X9,X6,X19,X20,X21,X22,X23,X7,X24,X25,X26] :
( ( circle(X8,X1,X2,X4)
& circle(X8,X1,X3,X24)
& circle(X8,X1,X9,X25)
& perp(X6,X9,X1,X3)
& coll(X6,X1,X3)
& circle(X8,X1,X19,X26)
& perp(X20,X19,X1,X3)
& coll(X20,X1,X3)
& perp(X21,X19,X1,X4)
& coll(X21,X1,X4)
& perp(X22,X9,X1,X4)
& coll(X22,X1,X4)
& perp(X23,X9,X1,X2)
& coll(X23,X1,X2)
& perp(X7,X19,X1,X2)
& coll(X7,X1,X2) )
=> eqangle(X6,X23,X23,X22,X20,X7,X7,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012009) ).
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(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(ruleD43,axiom,
! [X1,X2,X3,X9,X10,X15] :
( ( cyclic(X1,X2,X3,X9)
& cyclic(X1,X2,X3,X10)
& cyclic(X1,X2,X3,X15)
& eqangle(X3,X1,X3,X2,X15,X9,X15,X10) )
=> cong(X1,X2,X9,X10) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD43) ).
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(ruleD17,axiom,
! [X1,X2,X3,X4,X5] :
( ( cyclic(X1,X2,X3,X4)
& cyclic(X1,X2,X3,X5) )
=> cyclic(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
fof(ruleD45,axiom,
! [X1,X2,X3,X5,X6] :
( ( midp(X5,X1,X2)
& para(X5,X6,X2,X3)
& coll(X6,X1,X3) )
=> midp(X6,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD45) ).
fof(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(ruleD46,axiom,
! [X1,X2,X8] :
( cong(X8,X1,X8,X2)
=> eqangle(X8,X1,X1,X2,X1,X2,X8,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD46) ).
fof(ruleD11,axiom,
! [X1,X2,X7] :
( midp(X7,X2,X1)
=> midp(X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD11) ).
fof(ruleD68,axiom,
! [X1,X2,X3] :
( midp(X1,X2,X3)
=> cong(X1,X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD68) ).
fof(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(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/sandbox/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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD22) ).
fof(c_0_29,plain,
! [X597,X598,X599,X600,X601,X602] :
( ~ perp(X597,X598,X599,X600)
| ~ perp(X599,X600,X601,X602)
| para(X597,X598,X601,X602) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
fof(c_0_30,plain,
! [X1039,X1040,X1041,X1042] :
( ~ circle(X1042,X1039,X1040,X1041)
| perp(esk12_4(X1039,X1040,X1041,X1042),X1039,X1039,X1042) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])]) ).
fof(c_0_31,plain,
! [X593,X594,X595,X596] :
( ~ perp(X593,X594,X595,X596)
| perp(X595,X596,X593,X594) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
cnf(c_0_32,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( perp(esk12_4(X2,X3,X4,X1),X2,X2,X1)
| ~ circle(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_35,negated_conjecture,
~ ! [X1,X2,X4,X8,X3,X9,X6,X19,X20,X21,X22,X23,X7,X24,X25,X26] :
( ( circle(X8,X1,X2,X4)
& circle(X8,X1,X3,X24)
& circle(X8,X1,X9,X25)
& perp(X6,X9,X1,X3)
& coll(X6,X1,X3)
& circle(X8,X1,X19,X26)
& perp(X20,X19,X1,X3)
& coll(X20,X1,X3)
& perp(X21,X19,X1,X4)
& coll(X21,X1,X4)
& perp(X22,X9,X1,X4)
& coll(X22,X1,X4)
& perp(X23,X9,X1,X2)
& coll(X23,X1,X2)
& perp(X7,X19,X1,X2)
& coll(X7,X1,X2) )
=> eqangle(X6,X23,X23,X22,X20,X7,X7,X21) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012009]) ).
cnf(c_0_36,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_32,c_0_33]) ).
cnf(c_0_37,plain,
( perp(X1,X2,esk12_4(X1,X3,X4,X2),X1)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
fof(c_0_38,negated_conjecture,
( circle(esk24_0,esk21_0,esk22_0,esk23_0)
& circle(esk24_0,esk21_0,esk25_0,esk34_0)
& circle(esk24_0,esk21_0,esk26_0,esk35_0)
& perp(esk27_0,esk26_0,esk21_0,esk25_0)
& coll(esk27_0,esk21_0,esk25_0)
& circle(esk24_0,esk21_0,esk28_0,esk36_0)
& perp(esk29_0,esk28_0,esk21_0,esk25_0)
& coll(esk29_0,esk21_0,esk25_0)
& perp(esk30_0,esk28_0,esk21_0,esk23_0)
& coll(esk30_0,esk21_0,esk23_0)
& perp(esk31_0,esk26_0,esk21_0,esk23_0)
& coll(esk31_0,esk21_0,esk23_0)
& perp(esk32_0,esk26_0,esk21_0,esk22_0)
& coll(esk32_0,esk21_0,esk22_0)
& perp(esk33_0,esk28_0,esk21_0,esk22_0)
& coll(esk33_0,esk21_0,esk22_0)
& ~ eqangle(esk27_0,esk32_0,esk32_0,esk31_0,esk29_0,esk33_0,esk33_0,esk30_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_39,plain,
! [X575,X576,X577,X578] :
( ~ para(X575,X576,X577,X578)
| para(X575,X576,X578,X577) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_40,plain,
( para(X1,X2,X1,X2)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
circle(esk24_0,esk21_0,esk22_0,esk23_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_42,plain,
! [X646,X647,X648,X649,X650,X651,X652,X653] :
( ~ eqangle(X646,X647,X648,X649,X650,X651,X652,X653)
| eqangle(X648,X649,X646,X647,X652,X653,X650,X651) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_43,plain,
! [X800,X801,X802,X803,X804,X805] :
( ~ para(X800,X801,X802,X803)
| eqangle(X800,X801,X804,X805,X802,X803,X804,X805) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_44,plain,
! [X579,X580,X581,X582] :
( ~ para(X579,X580,X581,X582)
| para(X581,X582,X579,X580) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_45,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
para(esk21_0,esk24_0,esk21_0,esk24_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_47,plain,
! [X794,X795,X796,X797,X798,X799] :
( ~ eqangle(X794,X795,X798,X799,X796,X797,X798,X799)
| para(X794,X795,X796,X797) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
cnf(c_0_48,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_42]) ).
cnf(c_0_49,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
para(esk21_0,esk24_0,esk24_0,esk21_0),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
para(esk24_0,esk21_0,esk21_0,esk24_0),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_55,plain,
! [X929,X930,X931] :
( ~ para(X929,X930,X929,X931)
| coll(X929,X930,X931) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_56,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
para(esk24_0,esk21_0,esk24_0,esk21_0),
inference(spm,[status(thm)],[c_0_45,c_0_54]) ).
fof(c_0_58,plain,
! [X568,X569,X570] :
( ~ coll(X568,X569,X570)
| coll(X569,X568,X570) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_59,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_61,plain,
! [X565,X566,X567] :
( ~ coll(X565,X566,X567)
| coll(X565,X567,X566) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
cnf(c_0_62,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
fof(c_0_64,plain,
! [X814,X815,X816,X817] :
( ~ eqangle(X816,X814,X816,X815,X817,X814,X817,X815)
| ~ coll(X816,X817,X815)
| cyclic(X814,X815,X816,X817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_65,plain,
! [X571,X572,X573,X574] :
( ~ coll(X571,X572,X573)
| ~ coll(X571,X572,X574)
| coll(X573,X574,X571) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_66,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,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_64]) ).
cnf(c_0_69,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
fof(c_0_71,plain,
! [X625,X626,X627,X628] :
( ~ cyclic(X625,X626,X627,X628)
| cyclic(X625,X627,X626,X628) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_72,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_49]) ).
cnf(c_0_73,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_70])]) ).
fof(c_0_74,plain,
! [X621,X622,X623,X624] :
( ~ cyclic(X621,X622,X623,X624)
| cyclic(X621,X622,X624,X623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_75,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_60])]),c_0_73])]) ).
fof(c_0_77,plain,
! [X629,X630,X631,X632] :
( ~ cyclic(X629,X630,X631,X632)
| cyclic(X630,X629,X631,X632) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_78,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_79,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
fof(c_0_80,plain,
! [X818,X819,X820,X821,X822,X823] :
( ~ cyclic(X818,X819,X820,X821)
| ~ cyclic(X818,X819,X820,X822)
| ~ cyclic(X818,X819,X820,X823)
| ~ eqangle(X820,X818,X820,X819,X823,X821,X823,X822)
| cong(X818,X819,X821,X822) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD43])]) ).
fof(c_0_81,plain,
! [X806,X807,X808,X809] :
( ~ cyclic(X806,X807,X808,X809)
| eqangle(X808,X806,X808,X807,X809,X806,X809,X807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_82,plain,
! [X633,X634,X635,X636,X637] :
( ~ cyclic(X633,X634,X635,X636)
| ~ cyclic(X633,X634,X635,X637)
| cyclic(X634,X635,X636,X637) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_83,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_84,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
fof(c_0_85,plain,
! [X829,X830,X831,X832,X833] :
( ~ midp(X832,X829,X830)
| ~ para(X832,X833,X830,X831)
| ~ coll(X833,X829,X831)
| midp(X833,X829,X831) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
fof(c_0_86,plain,
! [X932,X933,X934] :
( ~ cong(X932,X933,X932,X934)
| ~ coll(X932,X933,X934)
| midp(X932,X933,X934) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD67])]) ).
cnf(c_0_87,plain,
( cong(X1,X2,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5)
| ~ cyclic(X1,X2,X3,X6)
| ~ eqangle(X3,X1,X3,X2,X6,X4,X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_88,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_89,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_90,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,plain,
( midp(X4,X2,X5)
| ~ midp(X1,X2,X3)
| ~ para(X1,X4,X3,X5)
| ~ coll(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_92,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,plain,
( cong(X1,X2,X1,X2)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X2)
| ~ cyclic(X1,X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_94,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_90])]) ).
fof(c_0_95,plain,
! [X955,X956,X957,X958,X959,X960,X961,X962] :
( ~ eqangle(X955,X956,X957,X958,X959,X960,X961,X962)
| ~ para(X959,X960,X961,X962)
| para(X955,X956,X957,X958) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD73])]) ).
cnf(c_0_96,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_73])]) ).
cnf(c_0_97,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_73])]) ).
cnf(c_0_98,plain,
cong(X1,X2,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_79])]),c_0_94]),c_0_94])]) ).
cnf(c_0_99,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_95]) ).
fof(c_0_100,plain,
! [X834,X835,X836] :
( ~ cong(X836,X834,X836,X835)
| eqangle(X836,X834,X834,X835,X834,X835,X836,X835) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
fof(c_0_101,plain,
! [X609,X610,X611] :
( ~ midp(X611,X610,X609)
| midp(X611,X609,X610) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD11])]) ).
cnf(c_0_102,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_96,c_0_60]) ).
cnf(c_0_103,plain,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,plain,
( para(X1,X2,X1,X3)
| ~ cyclic(X2,X3,X1,X4)
| ~ para(X4,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_99,c_0_88]) ).
cnf(c_0_105,plain,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_106,plain,
! [X935,X936,X937] :
( ~ midp(X935,X936,X937)
| cong(X935,X936,X935,X937) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_107,plain,
( midp(X1,X3,X2)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_108,negated_conjecture,
midp(X1,X2,X1),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,plain,
( para(X1,X2,X1,X3)
| ~ para(X4,X2,X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_94])]) ).
cnf(c_0_110,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_105]) ).
cnf(c_0_111,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_112,negated_conjecture,
midp(X1,X1,X2),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_113,plain,
( para(X1,X2,X1,X3)
| ~ cong(X2,X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
fof(c_0_115,plain,
! [X824,X825,X826,X827,X828] :
( ~ midp(X827,X824,X825)
| ~ midp(X828,X824,X826)
| para(X827,X828,X825,X826) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD44])]) ).
cnf(c_0_116,plain,
para(X1,X2,X1,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_117,plain,
( para(X1,X4,X3,X5)
| ~ midp(X1,X2,X3)
| ~ midp(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_118,plain,
midp(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_116]),c_0_108])]) ).
fof(c_0_119,plain,
! [X662,X663,X664,X665,X666,X667,X668,X669] :
( ~ eqangle(X662,X663,X664,X665,X666,X667,X668,X669)
| eqangle(X662,X663,X666,X667,X664,X665,X668,X669) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD21])]) ).
cnf(c_0_120,plain,
para(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118]),c_0_118])]) ).
cnf(c_0_121,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_119]) ).
fof(c_0_122,plain,
! [X670,X671,X672,X673,X674,X675,X676,X677,X678,X679,X680,X681] :
( ~ eqangle(X670,X671,X672,X673,X674,X675,X676,X677)
| ~ eqangle(X674,X675,X676,X677,X678,X679,X680,X681)
| eqangle(X670,X671,X672,X673,X678,X679,X680,X681) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD22])]) ).
cnf(c_0_123,plain,
eqangle(X1,X2,X3,X4,X1,X2,X5,X6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_120])]) ).
cnf(c_0_124,plain,
( eqangle(X1,X2,X3,X4,X5,X6,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_121,c_0_49]) ).
cnf(c_0_125,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_122]) ).
cnf(c_0_126,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(spm,[status(thm)],[c_0_121,c_0_123]) ).
cnf(c_0_127,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_120])]) ).
cnf(c_0_128,negated_conjecture,
~ eqangle(esk27_0,esk32_0,esk32_0,esk31_0,esk29_0,esk33_0,esk33_0,esk30_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_129,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127])]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO549+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 : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:02:35 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.97/3.26 % Version : CSE_E---1.7
% 3.97/3.26 % Problem : theBenchmark.p
% 3.97/3.26 % SZS status Theorem for theBenchmark.p
% 3.97/3.26 % SZS output start CNFRefutation
% See solution above
% 3.97/3.27 % Total time : 2.373s
%------------------------------------------------------------------------------