%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO612+1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 04:21:41 PM UTC 2026
% Result : Theorem 1.95s 1.85s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 14 unt; 0 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 137 ( 47 ~; 44 |; 29 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 266 ( 18 sgn 154 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(exemplo6GDDFULL618074,conjecture,
! [X1,X2,X3,X8,X13,X4,X5,X6,X19] :
( ( circle(X8,X1,X2,X3)
& perp(X13,X3,X1,X2)
& coll(X13,X1,X2)
& circle(X8,X3,X4,X19)
& coll(X4,X3,X13)
& perp(X5,X4,X1,X3)
& coll(X5,X1,X3)
& perp(X6,X4,X2,X3)
& coll(X6,X2,X3) )
=> cyclic(X1,X5,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618074) ).
fof(ruleD8,axiom,
! [X1,X2,X3,X4] :
( perp(X1,X2,X3,X4)
=> perp(X3,X4,X1,X2) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD5) ).
fof(ruleD66,axiom,
! [X1,X2,X3] :
( para(X1,X2,X1,X3)
=> coll(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD66) ).
fof(ruleD2,axiom,
! [X1,X2,X3] :
( coll(X1,X2,X3)
=> coll(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD2) ).
fof(ruleD1,axiom,
! [X1,X2,X3] :
( coll(X1,X2,X3)
=> coll(X1,X3,X2) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2,X3,X8,X13,X4,X5,X6,X19] :
( ( circle(X8,X1,X2,X3)
& perp(X13,X3,X1,X2)
& coll(X13,X1,X2)
& circle(X8,X3,X4,X19)
& coll(X4,X3,X13)
& perp(X5,X4,X1,X3)
& coll(X5,X1,X3)
& perp(X6,X4,X2,X3)
& coll(X6,X2,X3) )
=> cyclic(X1,X5,X6,X2) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618074]) ).
fof(c_0_17,plain,
! [X579,X580,X581,X582] :
( ~ perp(X579,X580,X581,X582)
| perp(X581,X582,X579,X580) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD8])]) ).
fof(c_0_18,negated_conjecture,
( circle(esk24_0,esk21_0,esk22_0,esk23_0)
& perp(esk25_0,esk23_0,esk21_0,esk22_0)
& coll(esk25_0,esk21_0,esk22_0)
& circle(esk24_0,esk23_0,esk26_0,esk29_0)
& coll(esk26_0,esk23_0,esk25_0)
& perp(esk27_0,esk26_0,esk21_0,esk23_0)
& coll(esk27_0,esk21_0,esk23_0)
& perp(esk28_0,esk26_0,esk22_0,esk23_0)
& coll(esk28_0,esk22_0,esk23_0)
& ~ cyclic(esk21_0,esk27_0,esk28_0,esk22_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_19,plain,
! [X632,X633,X634,X635,X636,X637,X638,X639] :
( ~ eqangle(X632,X633,X634,X635,X636,X637,X638,X639)
| eqangle(X634,X635,X632,X633,X638,X639,X636,X637) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD19])]) ).
fof(c_0_20,plain,
! [X786,X787,X788,X789,X790,X791] :
( ~ para(X786,X787,X788,X789)
| eqangle(X786,X787,X790,X791,X788,X789,X790,X791) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD40])]) ).
fof(c_0_21,plain,
! [X583,X584,X585,X586,X587,X588] :
( ~ perp(X583,X584,X585,X586)
| ~ perp(X585,X586,X587,X588)
| para(X583,X584,X587,X588) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD9])]) ).
cnf(c_0_22,plain,
( perp(X3,X4,X1,X2)
| ~ perp(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
perp(esk28_0,esk26_0,esk22_0,esk23_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X780,X781,X782,X783,X784,X785] :
( ~ eqangle(X780,X781,X784,X785,X782,X783,X784,X785)
| para(X780,X781,X782,X783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD39])]) ).
cnf(c_0_25,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_19]) ).
cnf(c_0_26,plain,
( eqangle(X1,X2,X5,X6,X3,X4,X5,X6)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_27,plain,
! [X565,X566,X567,X568] :
( ~ para(X565,X566,X567,X568)
| para(X567,X568,X565,X566) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD5])]) ).
cnf(c_0_28,plain,
( para(X1,X2,X5,X6)
| ~ perp(X1,X2,X3,X4)
| ~ perp(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
perp(esk22_0,esk23_0,esk28_0,esk26_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( para(X1,X2,X5,X6)
| ~ eqangle(X1,X2,X3,X4,X5,X6,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( eqangle(X1,X2,X3,X4,X1,X2,X5,X6)
| ~ para(X3,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( para(X3,X4,X1,X2)
| ~ para(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( para(X1,X2,esk28_0,esk26_0)
| ~ perp(X1,X2,esk22_0,esk23_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_34,plain,
! [X915,X916,X917] :
( ~ para(X915,X916,X915,X917)
| coll(X915,X916,X917) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD66])]) ).
cnf(c_0_35,plain,
( para(X1,X2,X1,X2)
| ~ para(X3,X4,X3,X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( para(esk28_0,esk26_0,X1,X2)
| ~ perp(X1,X2,esk22_0,esk23_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_37,plain,
! [X554,X555,X556] :
( ~ coll(X554,X555,X556)
| coll(X555,X554,X556) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD2])]) ).
cnf(c_0_38,plain,
( coll(X1,X2,X3)
| ~ para(X1,X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
para(X1,X2,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_23])]) ).
fof(c_0_40,plain,
! [X551,X552,X553] :
( ~ coll(X551,X552,X553)
| coll(X551,X553,X552) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD1])]) ).
cnf(c_0_41,plain,
( coll(X2,X1,X3)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,negated_conjecture,
coll(X1,X2,X2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_43,plain,
! [X800,X801,X802,X803] :
( ~ eqangle(X802,X800,X802,X801,X803,X800,X803,X801)
| ~ coll(X802,X803,X801)
| cyclic(X800,X801,X802,X803) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD42b])]) ).
fof(c_0_44,plain,
! [X557,X558,X559,X560] :
( ~ coll(X557,X558,X559)
| ~ coll(X557,X558,X560)
| coll(X559,X560,X557) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD3])]) ).
cnf(c_0_45,plain,
( coll(X1,X3,X2)
| ~ coll(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,negated_conjecture,
coll(X1,X2,X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,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_43]) ).
cnf(c_0_48,plain,
( coll(X3,X4,X1)
| ~ coll(X1,X2,X3)
| ~ coll(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,negated_conjecture,
coll(X1,X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_50,plain,
! [X611,X612,X613,X614] :
( ~ cyclic(X611,X612,X613,X614)
| cyclic(X611,X613,X612,X614) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD15])]) ).
cnf(c_0_51,plain,
( cyclic(X1,X2,X3,X3)
| ~ para(X3,X1,X3,X1)
| ~ coll(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_26]) ).
cnf(c_0_52,negated_conjecture,
coll(X1,X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_49])]) ).
fof(c_0_53,plain,
! [X607,X608,X609,X610] :
( ~ cyclic(X607,X608,X609,X610)
| cyclic(X607,X608,X610,X609) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD14])]) ).
cnf(c_0_54,plain,
( cyclic(X1,X3,X2,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
cyclic(X1,X2,X3,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_39])]),c_0_52])]) ).
fof(c_0_56,plain,
! [X615,X616,X617,X618] :
( ~ cyclic(X615,X616,X617,X618)
| cyclic(X616,X615,X617,X618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD16])]) ).
cnf(c_0_57,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,plain,
cyclic(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_59,plain,
! [X619,X620,X621,X622,X623] :
( ~ cyclic(X619,X620,X621,X622)
| ~ cyclic(X619,X620,X621,X623)
| cyclic(X620,X621,X622,X623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ruleD17])]) ).
cnf(c_0_60,plain,
( cyclic(X2,X1,X3,X4)
| ~ cyclic(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,plain,
cyclic(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
( cyclic(X2,X3,X4,X5)
| ~ cyclic(X1,X2,X3,X4)
| ~ cyclic(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_63,plain,
cyclic(X1,X2,X1,X3),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
~ cyclic(esk21_0,esk27_0,esk28_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_65,plain,
cyclic(X1,X2,X3,X4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_63])]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GEO612+1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.09/0.26 % Computer : n002.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8042.1875MB
% 0.09/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Mon May 4 18:04:31 EDT 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.27 % start to proof: theBenchmark
% 1.95/1.85 % Version : CSE_E---1.7
% 1.95/1.85 % Problem : theBenchmark.p
% 1.95/1.85 % SZS status Theorem for theBenchmark.p
% 1.95/1.85 % SZS output start CNFRefutation
% See solution above
% 1.95/1.86 % Total time : 1.369s
%------------------------------------------------------------------------------