%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO660+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 : n031.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 04:21:49 PM UTC 2026
% Result : Theorem 1.84s 1.89s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 28
% Syntax : Number of formulae : 123 ( 23 unt; 0 def)
% Number of atoms : 299 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 286 ( 110 ~; 107 |; 40 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 493 ( 30 sgn 266 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(exemplo7Book00EE02E02319,conjecture,
! [X1,X2,X3,X4,X5,X6,X13] :
( ( perp(X3,X1,X3,X2)
& perp(X4,X3,X1,X2)
& coll(X4,X1,X2)
& coll(X5,X3,X4)
& coll(X6,X1,X2)
& eqangle(X2,X1,X1,X5,X5,X1,X1,X3)
& eqangle(X4,X3,X3,X6,X6,X3,X3,X2)
& coll(X13,X2,X3)
& coll(X13,X1,X5) )
=> para(X5,X6,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo7Book00EE02E02319) ).
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(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(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(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(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(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(ruleD54,axiom,
! [X1,X2,X3,X4] :
( ( cyclic(X1,X2,X3,X4)
& para(X1,X2,X3,X4) )
=> eqangle(X1,X4,X3,X4,X3,X4,X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD54) ).
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(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(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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD20) ).
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(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(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(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(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(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(c_0_28,negated_conjecture,
~ ! [X1,X2,X3,X4,X5,X6,X13] :
( ( perp(X3,X1,X3,X2)
& perp(X4,X3,X1,X2)
& coll(X4,X1,X2)
& coll(X5,X3,X4)
& coll(X6,X1,X2)
& eqangle(X2,X1,X1,X5,X5,X1,X1,X3)
& eqangle(X4,X3,X3,X6,X6,X3,X3,X2)
& coll(X13,X2,X3)
& coll(X13,X1,X5) )
=> para(X5,X6,X3,X2) ),
inference(assume_negation,[status(cth)],[exemplo7Book00EE02E02319]) ).
fof(c_0_29,plain,
! [X576,X577,X578,X579] :
( ~ perp(X576,X577,X578,X579)
| perp(X578,X579,X576,X577) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
fof(c_0_30,negated_conjecture,
( perp(esk23_0,esk21_0,esk23_0,esk22_0)
& perp(esk24_0,esk23_0,esk21_0,esk22_0)
& coll(esk24_0,esk21_0,esk22_0)
& coll(esk25_0,esk23_0,esk24_0)
& coll(esk26_0,esk21_0,esk22_0)
& eqangle(esk22_0,esk21_0,esk21_0,esk25_0,esk25_0,esk21_0,esk21_0,esk23_0)
& eqangle(esk24_0,esk23_0,esk23_0,esk26_0,esk26_0,esk23_0,esk23_0,esk22_0)
& coll(esk27_0,esk22_0,esk23_0)
& coll(esk27_0,esk21_0,esk25_0)
& ~ para(esk25_0,esk26_0,esk23_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,
! [X629,X630,X631,X632,X633,X634,X635,X636] :
( ~ eqangle(X629,X630,X631,X632,X633,X634,X635,X636)
| eqangle(X631,X632,X629,X630,X635,X636,X633,X634) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_32,plain,
! [X783,X784,X785,X786,X787,X788] :
( ~ para(X783,X784,X785,X786)
| eqangle(X783,X784,X787,X788,X785,X786,X787,X788) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_33,plain,
! [X580,X581,X582,X583,X584,X585] :
( ~ perp(X580,X581,X582,X583)
| ~ perp(X582,X583,X584,X585)
| para(X580,X581,X584,X585) ),
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(esk24_0,esk23_0,esk21_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X777,X778,X779,X780,X781,X782] :
( ~ eqangle(X777,X778,X781,X782,X779,X780,X781,X782)
| para(X777,X778,X779,X780) ),
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,
! [X562,X563,X564,X565] :
( ~ para(X562,X563,X564,X565)
| para(X564,X565,X562,X563) ),
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,esk24_0,esk23_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,esk24_0,esk23_0)
| ~ perp(X1,X2,esk21_0,esk22_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_46,plain,
! [X912,X913,X914] :
( ~ para(X912,X913,X912,X914)
| coll(X912,X913,X914) ),
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(esk24_0,esk23_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,
! [X551,X552,X553] :
( ~ coll(X551,X552,X553)
| coll(X552,X551,X553) ),
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,
! [X548,X549,X550] :
( ~ coll(X548,X549,X550)
| coll(X548,X550,X549) ),
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,
! [X797,X798,X799,X800] :
( ~ eqangle(X799,X797,X799,X798,X800,X797,X800,X798)
| ~ coll(X799,X800,X798)
| cyclic(X797,X798,X799,X800) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_56,plain,
! [X554,X555,X556,X557] :
( ~ coll(X554,X555,X556)
| ~ coll(X554,X555,X557)
| coll(X556,X557,X554) ),
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,
! [X608,X609,X610,X611] :
( ~ cyclic(X608,X609,X610,X611)
| cyclic(X608,X610,X609,X611) ),
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,
! [X604,X605,X606,X607] :
( ~ cyclic(X604,X605,X606,X607)
| cyclic(X604,X605,X607,X606) ),
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,
! [X612,X613,X614,X615] :
( ~ cyclic(X612,X613,X614,X615)
| cyclic(X613,X612,X614,X615) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_69,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
fof(c_0_71,plain,
! [X801,X802,X803,X804,X805,X806] :
( ~ cyclic(X801,X802,X803,X804)
| ~ cyclic(X801,X802,X803,X805)
| ~ cyclic(X801,X802,X803,X806)
| ~ eqangle(X803,X801,X803,X802,X806,X804,X806,X805)
| cong(X801,X802,X804,X805) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD43])]) ).
fof(c_0_72,plain,
! [X851,X852,X853,X854] :
( ~ cyclic(X851,X852,X853,X854)
| ~ para(X851,X852,X853,X854)
| eqangle(X851,X854,X853,X854,X853,X854,X853,X852) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD54])]) ).
fof(c_0_73,plain,
! [X616,X617,X618,X619,X620] :
( ~ cyclic(X616,X617,X618,X619)
| ~ cyclic(X616,X617,X618,X620)
| cyclic(X617,X618,X619,X620) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_74,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,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_71]) ).
cnf(c_0_77,plain,
( eqangle(X1,X4,X3,X4,X3,X4,X3,X2)
| ~ cyclic(X1,X2,X3,X4)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_78,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
fof(c_0_80,plain,
! [X915,X916,X917] :
( ~ cong(X915,X916,X915,X917)
| ~ coll(X915,X916,X917)
| midp(X915,X916,X917) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD67])]) ).
cnf(c_0_81,plain,
( cong(X1,X1,X1,X2)
| ~ cyclic(X1,X1,X3,X3)
| ~ cyclic(X1,X1,X3,X2)
| ~ cyclic(X1,X1,X3,X1)
| ~ cyclic(X3,X2,X3,X1)
| ~ para(X3,X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_79])]) ).
fof(c_0_83,plain,
! [X637,X638,X639,X640,X641,X642,X643,X644] :
( ~ eqangle(X637,X638,X639,X640,X641,X642,X643,X644)
| eqangle(X641,X642,X643,X644,X637,X638,X639,X640) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD20])]) ).
fof(c_0_84,plain,
! [X789,X790,X791,X792] :
( ~ cyclic(X789,X790,X791,X792)
| eqangle(X791,X789,X791,X790,X792,X789,X792,X790) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_85,plain,
! [X812,X813,X814,X815,X816] :
( ~ midp(X815,X812,X813)
| ~ para(X815,X816,X813,X814)
| ~ coll(X816,X812,X814)
| midp(X816,X812,X814) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
fof(c_0_86,plain,
! [X558,X559,X560,X561] :
( ~ para(X558,X559,X560,X561)
| para(X558,X559,X561,X560) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
fof(c_0_87,plain,
! [X902,X903,X904,X905,X906] :
( ~ midp(X906,X902,X903)
| ~ para(X902,X904,X903,X905)
| ~ para(X902,X905,X903,X904)
| midp(X906,X904,X905) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_88,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,plain,
( cong(X1,X1,X1,X2)
| ~ para(X3,X2,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_67])]),c_0_82]),c_0_82]),c_0_82])]) ).
fof(c_0_90,plain,
! [X938,X939,X940,X941,X942,X943,X944,X945] :
( ~ eqangle(X938,X939,X940,X941,X942,X943,X944,X945)
| ~ para(X942,X943,X944,X945)
| para(X938,X939,X940,X941) ),
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_83]) ).
cnf(c_0_92,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_93,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_94,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_95,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_87]) ).
cnf(c_0_96,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_64])]) ).
cnf(c_0_97,negated_conjecture,
cong(X1,X1,X1,X1),
inference(spm,[status(thm)],[c_0_89,c_0_51]) ).
cnf(c_0_98,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_99,plain,
( eqangle(X1,X2,X1,X3,X4,X2,X4,X3)
| ~ cyclic(X2,X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
fof(c_0_100,plain,
! [X817,X818,X819] :
( ~ cong(X819,X817,X819,X818)
| eqangle(X819,X817,X817,X818,X817,X818,X819,X818) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
cnf(c_0_101,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_64])]) ).
cnf(c_0_102,negated_conjecture,
para(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_94,c_0_51]) ).
cnf(c_0_103,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_51]),c_0_51])]) ).
cnf(c_0_104,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_105,plain,
( para(X1,X2,X1,X3)
| ~ cyclic(X2,X3,X4,X1)
| ~ para(X4,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,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_107,plain,
! [X918,X919,X920] :
( ~ midp(X918,X919,X920)
| cong(X918,X919,X918,X920) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_108,negated_conjecture,
( midp(X1,X2,X3)
| ~ midp(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,plain,
( para(X1,X2,X1,X3)
| ~ para(X4,X2,X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_82])]) ).
cnf(c_0_111,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_42,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(X1,X1,X2),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,plain,
( para(X1,X2,X1,X3)
| ~ cong(X2,X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
fof(c_0_116,plain,
! [X807,X808,X809,X810,X811] :
( ~ midp(X810,X807,X808)
| ~ midp(X811,X807,X809)
| para(X810,X811,X808,X809) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD44])]) ).
cnf(c_0_117,plain,
para(X1,X2,X1,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_118,plain,
( para(X1,X4,X3,X5)
| ~ midp(X1,X2,X3)
| ~ midp(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_119,plain,
midp(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_117]),c_0_109]),c_0_117])]) ).
cnf(c_0_120,negated_conjecture,
~ para(esk25_0,esk26_0,esk23_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_121,plain,
para(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_119])]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO660+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
% 0.15/0.32 % Computer : n031.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:07:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.84/1.89 % Version : CSE_E---1.7
% 1.84/1.89 % Problem : theBenchmark.p
% 1.84/1.89 % SZS status Theorem for theBenchmark.p
% 1.84/1.89 % SZS output start CNFRefutation
% See solution above
% 1.84/1.89 % Total time : 1.374s
%------------------------------------------------------------------------------