%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO548+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 : n028.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 04:21:29 PM UTC 2026
% Result : Theorem 2.30s 1.99s
% Output : CNFRefutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 31
% Syntax : Number of formulae : 143 ( 32 unt; 0 def)
% Number of atoms : 346 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 324 ( 121 ~; 118 |; 53 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 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; 13 con; 0-4 aty)
% Number of variables : 627 ( 57 sgn 326 !; 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(exemplo6GDDFULL012008,conjecture,
! [X1,X2,X3,X8,X9,X13,X6,X19,X20,X21,X22,X23,X24] :
( ( circle(X8,X1,X2,X3)
& circle(X8,X1,X9,X23)
& perp(X13,X9,X1,X2)
& coll(X13,X1,X2)
& perp(X6,X9,X1,X3)
& coll(X6,X1,X3)
& circle(X8,X1,X19,X24)
& perp(X20,X19,X1,X2)
& coll(X20,X1,X2)
& perp(X21,X19,X1,X3)
& coll(X21,X1,X3)
& coll(X22,X20,X21)
& coll(X22,X13,X6) )
=> eqangle(X9,X1,X1,X19,X21,X22,X22,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012008) ).
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(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(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(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(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(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(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(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_31,plain,
! [X592,X593,X594,X595,X596,X597] :
( ~ perp(X592,X593,X594,X595)
| ~ perp(X594,X595,X596,X597)
| para(X592,X593,X596,X597) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
fof(c_0_32,plain,
! [X1034,X1035,X1036,X1037] :
( ~ circle(X1037,X1034,X1035,X1036)
| perp(esk12_4(X1034,X1035,X1036,X1037),X1034,X1034,X1037) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleX11])])])]) ).
fof(c_0_33,plain,
! [X588,X589,X590,X591] :
( ~ perp(X588,X589,X590,X591)
| perp(X590,X591,X588,X589) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
cnf(c_0_34,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
( perp(esk12_4(X2,X3,X4,X1),X2,X2,X1)
| ~ circle(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,negated_conjecture,
~ ! [X1,X2,X3,X8,X9,X13,X6,X19,X20,X21,X22,X23,X24] :
( ( circle(X8,X1,X2,X3)
& circle(X8,X1,X9,X23)
& perp(X13,X9,X1,X2)
& coll(X13,X1,X2)
& perp(X6,X9,X1,X3)
& coll(X6,X1,X3)
& circle(X8,X1,X19,X24)
& perp(X20,X19,X1,X2)
& coll(X20,X1,X2)
& perp(X21,X19,X1,X3)
& coll(X21,X1,X3)
& coll(X22,X20,X21)
& coll(X22,X13,X6) )
=> eqangle(X9,X1,X1,X19,X21,X22,X22,X6) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012008]) ).
cnf(c_0_38,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_34,c_0_35]) ).
cnf(c_0_39,plain,
( perp(X1,X2,esk12_4(X1,X3,X4,X2),X1)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
fof(c_0_40,negated_conjecture,
( circle(esk24_0,esk21_0,esk22_0,esk23_0)
& circle(esk24_0,esk21_0,esk25_0,esk32_0)
& perp(esk26_0,esk25_0,esk21_0,esk22_0)
& coll(esk26_0,esk21_0,esk22_0)
& perp(esk27_0,esk25_0,esk21_0,esk23_0)
& coll(esk27_0,esk21_0,esk23_0)
& circle(esk24_0,esk21_0,esk28_0,esk33_0)
& perp(esk29_0,esk28_0,esk21_0,esk22_0)
& coll(esk29_0,esk21_0,esk22_0)
& perp(esk30_0,esk28_0,esk21_0,esk23_0)
& coll(esk30_0,esk21_0,esk23_0)
& coll(esk31_0,esk29_0,esk30_0)
& coll(esk31_0,esk26_0,esk27_0)
& ~ eqangle(esk25_0,esk21_0,esk21_0,esk28_0,esk30_0,esk31_0,esk31_0,esk27_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
fof(c_0_41,plain,
! [X570,X571,X572,X573] :
( ~ para(X570,X571,X572,X573)
| para(X570,X571,X573,X572) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD4])]) ).
cnf(c_0_42,plain,
( para(X1,X2,X1,X2)
| ~ circle(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
circle(esk24_0,esk21_0,esk22_0,esk23_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_44,plain,
! [X641,X642,X643,X644,X645,X646,X647,X648] :
( ~ eqangle(X641,X642,X643,X644,X645,X646,X647,X648)
| eqangle(X643,X644,X641,X642,X647,X648,X645,X646) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_45,plain,
! [X795,X796,X797,X798,X799,X800] :
( ~ para(X795,X796,X797,X798)
| eqangle(X795,X796,X799,X800,X797,X798,X799,X800) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_46,plain,
! [X574,X575,X576,X577] :
( ~ para(X574,X575,X576,X577)
| para(X576,X577,X574,X575) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_47,plain,
( para(X1,X2,X4,X3)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
para(esk21_0,esk24_0,esk21_0,esk24_0),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_49,plain,
! [X789,X790,X791,X792,X793,X794] :
( ~ eqangle(X789,X790,X793,X794,X791,X792,X793,X794)
| para(X789,X790,X791,X792) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
cnf(c_0_50,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_44]) ).
cnf(c_0_51,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,negated_conjecture,
para(esk21_0,esk24_0,esk24_0,esk21_0),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
para(esk24_0,esk21_0,esk21_0,esk24_0),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_57,plain,
! [X924,X925,X926] :
( ~ para(X924,X925,X924,X926)
| coll(X924,X925,X926) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_58,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
para(esk24_0,esk21_0,esk24_0,esk21_0),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
fof(c_0_60,plain,
! [X563,X564,X565] :
( ~ coll(X563,X564,X565)
| coll(X564,X563,X565) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_61,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,negated_conjecture,
para(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_63,plain,
! [X560,X561,X562] :
( ~ coll(X560,X561,X562)
| coll(X560,X562,X561) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
cnf(c_0_64,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_66,plain,
! [X809,X810,X811,X812] :
( ~ eqangle(X811,X809,X811,X810,X812,X809,X812,X810)
| ~ coll(X811,X812,X810)
| cyclic(X809,X810,X811,X812) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_67,plain,
! [X566,X567,X568,X569] :
( ~ coll(X566,X567,X568)
| ~ coll(X566,X567,X569)
| coll(X568,X569,X566) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_68,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,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_66]) ).
cnf(c_0_71,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_72,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
fof(c_0_73,plain,
! [X620,X621,X622,X623] :
( ~ cyclic(X620,X621,X622,X623)
| cyclic(X620,X622,X621,X623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_74,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_51]) ).
cnf(c_0_75,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_72])]) ).
fof(c_0_76,plain,
! [X616,X617,X618,X619] :
( ~ cyclic(X616,X617,X618,X619)
| cyclic(X616,X617,X619,X618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_77,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_78,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_62])]),c_0_75])]) ).
fof(c_0_79,plain,
! [X624,X625,X626,X627] :
( ~ cyclic(X624,X625,X626,X627)
| cyclic(X625,X624,X626,X627) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_80,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_81,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
fof(c_0_82,plain,
! [X813,X814,X815,X816,X817,X818] :
( ~ cyclic(X813,X814,X815,X816)
| ~ cyclic(X813,X814,X815,X817)
| ~ cyclic(X813,X814,X815,X818)
| ~ eqangle(X815,X813,X815,X814,X818,X816,X818,X817)
| cong(X813,X814,X816,X817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD43])]) ).
fof(c_0_83,plain,
! [X863,X864,X865,X866] :
( ~ cyclic(X863,X864,X865,X866)
| ~ para(X863,X864,X865,X866)
| eqangle(X863,X866,X865,X866,X865,X866,X865,X864) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD54])]) ).
fof(c_0_84,plain,
! [X628,X629,X630,X631,X632] :
( ~ cyclic(X628,X629,X630,X631)
| ~ cyclic(X628,X629,X630,X632)
| cyclic(X629,X630,X631,X632) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_85,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_86,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
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_82]) ).
cnf(c_0_88,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_83]) ).
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_84]) ).
cnf(c_0_90,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_91,plain,
! [X927,X928,X929] :
( ~ cong(X927,X928,X927,X929)
| ~ coll(X927,X928,X929)
| midp(X927,X928,X929) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD67])]) ).
cnf(c_0_92,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_87,c_0_88]) ).
cnf(c_0_93,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_94,plain,
! [X824,X825,X826,X827,X828] :
( ~ midp(X827,X824,X825)
| ~ para(X827,X828,X825,X826)
| ~ coll(X828,X824,X826)
| midp(X828,X824,X826) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD45])]) ).
fof(c_0_95,plain,
! [X914,X915,X916,X917,X918] :
( ~ midp(X918,X914,X915)
| ~ para(X914,X916,X915,X917)
| ~ para(X914,X917,X915,X916)
| midp(X918,X916,X917) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD64])]) ).
cnf(c_0_96,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_97,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_92,c_0_78])]),c_0_93]),c_0_93]),c_0_93])]) ).
fof(c_0_98,plain,
! [X950,X951,X952,X953,X954,X955,X956,X957] :
( ~ eqangle(X950,X951,X952,X953,X954,X955,X956,X957)
| ~ para(X954,X955,X956,X957)
| para(X950,X951,X952,X953) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD73])]) ).
fof(c_0_99,plain,
! [X801,X802,X803,X804] :
( ~ cyclic(X801,X802,X803,X804)
| eqangle(X803,X801,X803,X802,X804,X801,X804,X802) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD41])]) ).
cnf(c_0_100,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_94]) ).
cnf(c_0_101,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_95]) ).
cnf(c_0_102,plain,
( midp(X1,X2,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_75])]) ).
cnf(c_0_103,negated_conjecture,
cong(X1,X1,X1,X1),
inference(spm,[status(thm)],[c_0_97,c_0_62]) ).
cnf(c_0_104,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_98]) ).
cnf(c_0_105,plain,
( eqangle(X3,X1,X3,X2,X4,X1,X4,X2)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
fof(c_0_106,plain,
! [X829,X830,X831] :
( ~ cong(X831,X829,X831,X830)
| eqangle(X831,X829,X829,X830,X829,X830,X831,X830) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD46])]) ).
cnf(c_0_107,plain,
( midp(X1,X2,X3)
| ~ midp(X4,X2,X5)
| ~ para(X4,X1,X5,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_75])]) ).
cnf(c_0_108,negated_conjecture,
para(X1,X2,X2,X1),
inference(spm,[status(thm)],[c_0_47,c_0_62]) ).
cnf(c_0_109,negated_conjecture,
( midp(X1,X2,X2)
| ~ midp(X1,X3,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_62]),c_0_62])]) ).
cnf(c_0_110,negated_conjecture,
midp(X1,X1,X1),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,plain,
( para(X1,X2,X1,X3)
| ~ cyclic(X2,X3,X1,X4)
| ~ para(X4,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,plain,
( eqangle(X1,X2,X2,X3,X2,X3,X1,X3)
| ~ cong(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
fof(c_0_113,plain,
! [X930,X931,X932] :
( ~ midp(X930,X931,X932)
| cong(X930,X931,X930,X932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD68])]) ).
cnf(c_0_114,negated_conjecture,
( midp(X1,X2,X3)
| ~ midp(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_115,negated_conjecture,
midp(X1,X2,X2),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_116,plain,
( para(X1,X2,X1,X3)
| ~ para(X4,X2,X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_93])]) ).
cnf(c_0_117,plain,
( para(X1,X1,X1,X2)
| ~ cong(X1,X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_112]) ).
cnf(c_0_118,plain,
( cong(X1,X2,X1,X3)
| ~ midp(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_119,negated_conjecture,
midp(X1,X1,X2),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,plain,
( para(X1,X2,X1,X3)
| ~ cong(X2,X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
cong(X1,X1,X1,X2),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( midp(X1,X2,X1)
| ~ midp(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_107,c_0_62]) ).
fof(c_0_123,plain,
! [X819,X820,X821,X822,X823] :
( ~ midp(X822,X819,X820)
| ~ midp(X823,X819,X821)
| para(X822,X823,X820,X821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD44])]) ).
cnf(c_0_124,plain,
para(X1,X2,X1,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
cnf(c_0_125,negated_conjecture,
midp(X1,X2,X1),
inference(spm,[status(thm)],[c_0_122,c_0_115]) ).
fof(c_0_126,plain,
! [X649,X650,X651,X652,X653,X654,X655,X656] :
( ~ eqangle(X649,X650,X651,X652,X653,X654,X655,X656)
| eqangle(X653,X654,X655,X656,X649,X650,X651,X652) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD20])]) ).
cnf(c_0_127,plain,
( para(X1,X4,X3,X5)
| ~ midp(X1,X2,X3)
| ~ midp(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_128,plain,
midp(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_124]),c_0_125])]) ).
cnf(c_0_129,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_126]) ).
fof(c_0_130,plain,
! [X657,X658,X659,X660,X661,X662,X663,X664] :
( ~ eqangle(X657,X658,X659,X660,X661,X662,X663,X664)
| eqangle(X657,X658,X661,X662,X659,X660,X663,X664) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD21])]) ).
cnf(c_0_131,plain,
para(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128]),c_0_128])]) ).
cnf(c_0_132,plain,
( eqangle(X1,X2,X3,X4,X5,X6,X3,X4)
| ~ para(X5,X6,X1,X2) ),
inference(spm,[status(thm)],[c_0_129,c_0_51]) ).
fof(c_0_133,plain,
! [X665,X666,X667,X668,X669,X670,X671,X672,X673,X674,X675,X676] :
( ~ eqangle(X665,X666,X667,X668,X669,X670,X671,X672)
| ~ eqangle(X669,X670,X671,X672,X673,X674,X675,X676)
| eqangle(X665,X666,X667,X668,X673,X674,X675,X676) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD22])]) ).
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_130]) ).
cnf(c_0_135,plain,
eqangle(X1,X2,X3,X4,X1,X2,X5,X6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_131])]) ).
cnf(c_0_136,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_131])]) ).
cnf(c_0_137,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_133]) ).
cnf(c_0_138,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_139,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(spm,[status(thm)],[c_0_134,c_0_136]) ).
cnf(c_0_140,negated_conjecture,
~ eqangle(esk25_0,esk21_0,esk21_0,esk28_0,esk30_0,esk31_0,esk31_0,esk27_0),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_141,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139])]) ).
cnf(c_0_142,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO548+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
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 18:02:45 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 2.30/1.99 % Version : CSE_E---1.7
% 2.30/1.99 % Problem : theBenchmark.p
% 2.30/1.99 % SZS status Theorem for theBenchmark.p
% 2.30/1.99 % SZS output start CNFRefutation
% See solution above
% 2.30/1.99 % Total time : 1.375s
%------------------------------------------------------------------------------