%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO584+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 : n005.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 04:21:36 PM UTC 2026
% Result : Theorem 2.46s 2.03s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 30
% Syntax : Number of formulae : 144 ( 35 unt; 0 def)
% Number of atoms : 345 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 325 ( 124 ~; 121 |; 49 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-6 aty)
% Number of variables : 613 ( 60 sgn 310 !; 2 ?)
% 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(exemplo6GDDFULL416046,conjecture,
! [X1,X2,X3,X8,X4,X5,X10,X9,X19,X15,X20,X21] :
( ( circle(X8,X1,X2,X3)
& circle(X8,X1,X4,X20)
& circle(X8,X1,X5,X21)
& perp(X10,X5,X2,X3)
& coll(X10,X2,X3)
& perp(X9,X5,X1,X2)
& coll(X9,X1,X2)
& perp(X19,X5,X1,X4)
& coll(X19,X1,X4)
& perp(X15,X5,X3,X4)
& coll(X15,X3,X4) )
=> eqangle(X5,X9,X9,X19,X5,X10,X10,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416046) ).
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(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(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(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(ruleD11,axiom,
! [X1,X2,X7] :
( midp(X7,X2,X1)
=> midp(X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD11) ).
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(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(ruleX6,axiom,
! [X1,X2,X3,X4,X7,X17] :
? [X9] :
( ( midp(X7,X1,X2)
& midp(X17,X3,X4) )
=> ( midp(X9,X1,X4)
& para(X9,X7,X2,X4)
& para(X9,X17,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleX6) ).
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_30,plain,
! [X588,X589,X590,X591,X592,X593] :
( ~ perp(X588,X589,X590,X591)
| ~ perp(X590,X591,X592,X593)
| para(X588,X589,X592,X593) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
fof(c_0_31,plain,
! [X1030,X1031,X1032,X1033] :
( ~ circle(X1033,X1030,X1031,X1032)
| perp(esk12_4(X1030,X1031,X1032,X1033),X1030,X1030,X1033) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])]) ).
fof(c_0_32,plain,
! [X584,X585,X586,X587] :
( ~ perp(X584,X585,X586,X587)
| perp(X586,X587,X584,X585) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
cnf(c_0_33,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( perp(esk12_4(X2,X3,X4,X1),X2,X2,X1)
| ~ circle(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_36,negated_conjecture,
~ ! [X1,X2,X3,X8,X4,X5,X10,X9,X19,X15,X20,X21] :
( ( circle(X8,X1,X2,X3)
& circle(X8,X1,X4,X20)
& circle(X8,X1,X5,X21)
& perp(X10,X5,X2,X3)
& coll(X10,X2,X3)
& perp(X9,X5,X1,X2)
& coll(X9,X1,X2)
& perp(X19,X5,X1,X4)
& coll(X19,X1,X4)
& perp(X15,X5,X3,X4)
& coll(X15,X3,X4) )
=> eqangle(X5,X9,X9,X19,X5,X10,X10,X15) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416046]) ).
cnf(c_0_37,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_33,c_0_34]) ).
cnf(c_0_38,plain,
( perp(X1,X2,esk12_4(X1,X3,X4,X2),X1)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
fof(c_0_39,negated_conjecture,
( circle(esk24_0,esk21_0,esk22_0,esk23_0)
& circle(esk24_0,esk21_0,esk25_0,esk31_0)
& circle(esk24_0,esk21_0,esk26_0,esk32_0)
& perp(esk27_0,esk26_0,esk22_0,esk23_0)
& coll(esk27_0,esk22_0,esk23_0)
& perp(esk28_0,esk26_0,esk21_0,esk22_0)
& coll(esk28_0,esk21_0,esk22_0)
& perp(esk29_0,esk26_0,esk21_0,esk25_0)
& coll(esk29_0,esk21_0,esk25_0)
& perp(esk30_0,esk26_0,esk23_0,esk25_0)
& coll(esk30_0,esk23_0,esk25_0)
& ~ eqangle(esk26_0,esk28_0,esk28_0,esk29_0,esk26_0,esk27_0,esk27_0,esk30_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_40,plain,
! [X566,X567,X568,X569] :
( ~ para(X566,X567,X568,X569)
| para(X566,X567,X569,X568) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_41,plain,
( para(X1,X2,X1,X2)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
circle(esk24_0,esk21_0,esk22_0,esk23_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_43,plain,
! [X637,X638,X639,X640,X641,X642,X643,X644] :
( ~ eqangle(X637,X638,X639,X640,X641,X642,X643,X644)
| eqangle(X639,X640,X637,X638,X643,X644,X641,X642) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_44,plain,
! [X791,X792,X793,X794,X795,X796] :
( ~ para(X791,X792,X793,X794)
| eqangle(X791,X792,X795,X796,X793,X794,X795,X796) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_45,plain,
! [X570,X571,X572,X573] :
( ~ para(X570,X571,X572,X573)
| para(X572,X573,X570,X571) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_46,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
para(esk21_0,esk24_0,esk21_0,esk24_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_48,plain,
! [X785,X786,X787,X788,X789,X790] :
( ~ eqangle(X785,X786,X789,X790,X787,X788,X789,X790)
| para(X785,X786,X787,X788) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
cnf(c_0_49,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_43]) ).
cnf(c_0_50,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,negated_conjecture,
para(esk21_0,esk24_0,esk24_0,esk21_0),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
para(esk24_0,esk21_0,esk21_0,esk24_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_56,plain,
! [X920,X921,X922] :
( ~ para(X920,X921,X920,X922)
| coll(X920,X921,X922) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_57,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
para(esk24_0,esk21_0,esk24_0,esk21_0),
inference(spm,[status(thm)],[c_0_46,c_0_55]) ).
fof(c_0_59,plain,
! [X559,X560,X561] :
( ~ coll(X559,X560,X561)
| coll(X560,X559,X561) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_60,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
fof(c_0_62,plain,
! [X556,X557,X558] :
( ~ coll(X556,X557,X558)
| coll(X556,X558,X557) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
cnf(c_0_63,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_65,plain,
! [X805,X806,X807,X808] :
( ~ eqangle(X807,X805,X807,X806,X808,X805,X808,X806)
| ~ coll(X807,X808,X806)
| cyclic(X805,X806,X807,X808) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_66,plain,
! [X562,X563,X564,X565] :
( ~ coll(X562,X563,X564)
| ~ coll(X562,X563,X565)
| coll(X564,X565,X562) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_67,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_68,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,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_65]) ).
cnf(c_0_70,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_71,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
fof(c_0_72,plain,
! [X616,X617,X618,X619] :
( ~ cyclic(X616,X617,X618,X619)
| cyclic(X616,X618,X617,X619) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_73,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_50]) ).
cnf(c_0_74,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_71])]) ).
fof(c_0_75,plain,
! [X612,X613,X614,X615] :
( ~ cyclic(X612,X613,X614,X615)
| cyclic(X612,X613,X615,X614) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_76,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_61])]),c_0_74])]) ).
fof(c_0_78,plain,
! [X846,X847,X848,X849,X850] :
( ~ circle(X849,X846,X847,X848)
| ~ coll(X850,X847,X848)
| ~ eqangle(X846,X847,X846,X848,X849,X847,X849,X850)
| midp(X850,X847,X848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD51])]) ).
fof(c_0_79,plain,
! [X797,X798,X799,X800] :
( ~ cyclic(X797,X798,X799,X800)
| eqangle(X799,X797,X799,X798,X800,X797,X800,X798) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
fof(c_0_80,plain,
! [X620,X621,X622,X623] :
( ~ cyclic(X620,X621,X622,X623)
| cyclic(X621,X620,X622,X623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_81,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,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_78]) ).
cnf(c_0_84,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
fof(c_0_85,plain,
! [X624,X625,X626,X627,X628] :
( ~ cyclic(X624,X625,X626,X627)
| ~ cyclic(X624,X625,X626,X628)
| cyclic(X625,X626,X627,X628) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_86,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_87,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
fof(c_0_88,plain,
! [X820,X821,X822,X823,X824] :
( ~ midp(X823,X820,X821)
| ~ para(X823,X824,X821,X822)
| ~ coll(X824,X820,X822)
| midp(X824,X820,X822) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
cnf(c_0_89,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_83,c_0_84]) ).
cnf(c_0_90,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,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_88]) ).
cnf(c_0_93,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_89,c_0_68])]) ).
cnf(c_0_94,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_91])]) ).
cnf(c_0_95,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_74])]) ).
cnf(c_0_96,plain,
( midp(X1,X2,X1)
| ~ circle(X3,X4,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_97,negated_conjecture,
circle(esk24_0,esk21_0,esk26_0,esk32_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_98,plain,
! [X600,X601,X602] :
( ~ midp(X602,X601,X600)
| midp(X602,X600,X601) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD11])]) ).
cnf(c_0_99,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_95,c_0_61]) ).
cnf(c_0_100,negated_conjecture,
midp(esk32_0,esk26_0,esk32_0),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
fof(c_0_101,plain,
! [X946,X947,X948,X949,X950,X951,X952,X953] :
( ~ eqangle(X946,X947,X948,X949,X950,X951,X952,X953)
| ~ para(X950,X951,X952,X953)
| para(X946,X947,X948,X949) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD73])]) ).
fof(c_0_102,plain,
! [X825,X826,X827] :
( ~ cong(X827,X825,X827,X826)
| eqangle(X827,X825,X825,X826,X825,X826,X827,X826) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
fof(c_0_103,plain,
! [X926,X927,X928] :
( ~ midp(X926,X927,X928)
| cong(X926,X927,X926,X928) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_104,plain,
( midp(X1,X3,X2)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_105,negated_conjecture,
midp(X1,esk26_0,X1),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_106,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_101]) ).
cnf(c_0_107,plain,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_108,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_109,negated_conjecture,
midp(X1,X1,esk26_0),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_110,plain,
( para(X1,X2,X2,X3)
| ~ cong(X1,X2,X1,X3)
| ~ para(X2,X3,X1,X3) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,negated_conjecture,
cong(X1,X1,X1,esk26_0),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
fof(c_0_112,plain,
! [X910,X911,X912,X913,X914] :
( ~ midp(X914,X910,X911)
| ~ para(X910,X912,X911,X913)
| ~ para(X910,X913,X911,X912)
| midp(X914,X912,X913) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_113,negated_conjecture,
para(X1,X1,X1,esk26_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_61])]) ).
cnf(c_0_114,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_112]) ).
cnf(c_0_115,negated_conjecture,
( midp(X1,X2,esk26_0)
| ~ midp(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_113]) ).
fof(c_0_116,plain,
! [X996,X997,X998,X999,X1000,X1001] :
( ( midp(esk6_6(X996,X997,X998,X999,X1000,X1001),X996,X999)
| ~ midp(X1000,X996,X997)
| ~ midp(X1001,X998,X999) )
& ( para(esk6_6(X996,X997,X998,X999,X1000,X1001),X1000,X997,X999)
| ~ midp(X1000,X996,X997)
| ~ midp(X1001,X998,X999) )
& ( para(esk6_6(X996,X997,X998,X999,X1000,X1001),X1001,X996,X998)
| ~ midp(X1000,X996,X997)
| ~ midp(X1001,X998,X999) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX6])])])])]) ).
cnf(c_0_117,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_61]),c_0_61])]) ).
cnf(c_0_118,negated_conjecture,
midp(X1,esk26_0,esk26_0),
inference(spm,[status(thm)],[c_0_115,c_0_105]) ).
cnf(c_0_119,plain,
( para(esk6_6(X1,X2,X3,X4,X5,X6),X5,X2,X4)
| ~ midp(X5,X1,X2)
| ~ midp(X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_120,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_121,plain,
( midp(X1,X2,X3)
| ~ midp(esk6_6(X4,X5,X6,X3,X1,X7),X2,X5)
| ~ midp(X7,X6,X3)
| ~ midp(X1,X4,X5)
| ~ coll(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_92,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
midp(X1,X2,X1),
inference(spm,[status(thm)],[c_0_99,c_0_120]) ).
cnf(c_0_123,negated_conjecture,
para(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_61]) ).
cnf(c_0_124,plain,
( midp(X1,X2,X3)
| ~ midp(esk6_6(X4,X5,X6,X3,X1,X7),X2,X5)
| ~ midp(X7,X6,X3)
| ~ midp(X1,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_74])]) ).
cnf(c_0_125,negated_conjecture,
midp(X1,X2,esk26_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_122])]) ).
cnf(c_0_126,negated_conjecture,
( midp(X1,X2,X3)
| ~ midp(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_123]) ).
fof(c_0_127,plain,
! [X815,X816,X817,X818,X819] :
( ~ midp(X818,X815,X816)
| ~ midp(X819,X815,X817)
| para(X818,X819,X816,X817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD44])]) ).
cnf(c_0_128,negated_conjecture,
( midp(X1,X2,X3)
| ~ midp(X4,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_125])]) ).
cnf(c_0_129,negated_conjecture,
midp(esk26_0,X1,X2),
inference(spm,[status(thm)],[c_0_126,c_0_125]) ).
cnf(c_0_130,plain,
( para(X1,X4,X3,X5)
| ~ midp(X1,X2,X3)
| ~ midp(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_131,negated_conjecture,
midp(X1,X2,X3),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
fof(c_0_132,plain,
! [X653,X654,X655,X656,X657,X658,X659,X660] :
( ~ eqangle(X653,X654,X655,X656,X657,X658,X659,X660)
| eqangle(X653,X654,X657,X658,X655,X656,X659,X660) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD21])]) ).
cnf(c_0_133,plain,
para(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131]),c_0_131])]) ).
cnf(c_0_134,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_132]) ).
fof(c_0_135,plain,
! [X661,X662,X663,X664,X665,X666,X667,X668,X669,X670,X671,X672] :
( ~ eqangle(X661,X662,X663,X664,X665,X666,X667,X668)
| ~ eqangle(X665,X666,X667,X668,X669,X670,X671,X672)
| eqangle(X661,X662,X663,X664,X669,X670,X671,X672) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD22])]) ).
cnf(c_0_136,plain,
eqangle(X1,X2,X3,X4,X1,X2,X5,X6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_133])]) ).
cnf(c_0_137,plain,
( eqangle(X1,X2,X3,X4,X5,X6,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_134,c_0_50]) ).
cnf(c_0_138,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_135]) ).
cnf(c_0_139,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(spm,[status(thm)],[c_0_134,c_0_136]) ).
cnf(c_0_140,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_133])]) ).
cnf(c_0_141,negated_conjecture,
~ eqangle(esk26_0,esk28_0,esk28_0,esk29_0,esk26_0,esk27_0,esk27_0,esk30_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_142,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140])]) ).
cnf(c_0_143,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO584+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
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:03:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.46/2.03 % Version : CSE_E---1.7
% 2.46/2.03 % Problem : theBenchmark.p
% 2.46/2.03 % SZS status Theorem for theBenchmark.p
% 2.46/2.03 % SZS output start CNFRefutation
% See solution above
% 2.46/2.03 % Total time : 1.376s
%------------------------------------------------------------------------------