%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO595+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:21:35 PM UTC 2026
% Result : Theorem 33.72s 7.35s
% Output : CNFRefutation 33.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 163 ( 15 unt; 0 def)
% Number of atoms : 405 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 426 ( 184 ~; 181 |; 44 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 428 ( 0 sgn 406 !; 22 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
fof(f2,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD2) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( coll(X0,X1,X3)
& coll(X0,X1,X2) )
=> coll(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD3) ).
fof(f13,axiom,
! [X0,X1,X2,X3,X4] :
( ( cong(X4,X0,X4,X3)
& cong(X4,X0,X4,X2)
& cong(X4,X0,X4,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD13) ).
fof(f14,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD14) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD15) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X1,X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD16) ).
fof(f17,axiom,
! [X0,X1,X2,X3,X4] :
( ( cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X3) )
=> cyclic(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
fof(f19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD19) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD39) ).
fof(f40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD40) ).
fof(f41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD41) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ( ~ coll(X2,X3,X0)
& eqangle(X2,X0,X2,X1,X3,X0,X3,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD42a) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( coll(X2,X3,X1)
& eqangle(X2,X0,X2,X1,X3,X0,X3,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD42b) ).
fof(f69,axiom,
! [X0,X1,X2] :
( midp(X0,X1,X2)
=> cong(X0,X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD68) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ( circle(X4,X3,X6,X10)
& coll(X6,X0,X2)
& circle(X4,X3,X5,X9)
& coll(X5,X0,X1)
& circle(X4,X3,X7,X8)
& midp(X4,X0,X3)
& coll(X3,X1,X2)
& perp(X3,X0,X1,X2) )
=> cyclic(X1,X2,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416057) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ( circle(X4,X3,X6,X10)
& coll(X6,X0,X2)
& circle(X4,X3,X5,X9)
& coll(X5,X0,X1)
& circle(X4,X3,X7,X8)
& midp(X4,X0,X3)
& coll(X3,X1,X2)
& perp(X3,X0,X1,X2) )
=> cyclic(X1,X2,X5,X6) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(flattening,[],[f100]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4] :
( ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1)
| cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f13]) ).
fof(f116,plain,
! [X0,X1,X2,X3,X4] :
( ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1)
| cyclic(X0,X1,X2,X3) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f118,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(ennf_transformation,[],[f17]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(flattening,[],[f120]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
inference(ennf_transformation,[],[f19]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f39]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f40]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( coll(X2,X3,X0)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f42]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( coll(X2,X3,X0)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f43]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(flattening,[],[f153]) ).
fof(f200,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( circle(X4,X3,X6,X10)
& coll(X6,X0,X2)
& circle(X4,X3,X5,X9)
& coll(X5,X0,X1)
& circle(X4,X3,X7,X8)
& midp(X4,X0,X3)
& coll(X3,X1,X2)
& perp(X3,X0,X1,X2)
& ~ cyclic(X1,X2,X5,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( circle(X4,X3,X6,X10)
& coll(X6,X0,X2)
& circle(X4,X3,X5,X9)
& coll(X5,X0,X1)
& circle(X4,X3,X7,X8)
& midp(X4,X0,X3)
& coll(X3,X1,X2)
& perp(X3,X0,X1,X2)
& ~ cyclic(X1,X2,X5,X6) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( circle(sK24,sK23,sK26,sK30)
& coll(sK26,sK20,sK22)
& circle(sK24,sK23,sK25,sK29)
& coll(sK25,sK20,sK21)
& circle(sK24,sK23,sK27,sK28)
& midp(sK24,sK20,sK23)
& coll(sK23,sK21,sK22)
& perp(sK23,sK20,sK21,sK22)
& ~ cyclic(sK21,sK22,sK25,sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24),skolemize(X5,sK25),skolemize(X6,sK26),skolemize(X7,sK27),skolemize(X8,sK28),skolemize(X9,sK29),skolemize(X10,sK30)],[f250]) ).
fof(f271,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f272,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f273,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f283,plain,
! [X2,X3,X0,X1,X4] :
( ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1)
| cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f116]) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f285,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f118]) ).
fof(f286,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f119]) ).
fof(f287,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f121]) ).
fof(f289,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
inference(cnf_transformation,[],[f123]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f310,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f149]) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f312,plain,
! [X2,X3,X0,X1] :
( coll(X2,X3,X0)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f152]) ).
fof(f313,plain,
! [X2,X3,X0,X1] :
( ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f154]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f200]) ).
fof(f385,plain,
coll(sK26,sK20,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f389,plain,
midp(sK24,sK20,sK23),
inference(cnf_transformation,[],[f270]) ).
fof(f390,plain,
coll(sK23,sK21,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f392,plain,
~ cyclic(sK21,sK22,sK25,sK26),
inference(cnf_transformation,[],[f270]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( cyclic(X1,X3,X2,X4)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X0,X3,X1)
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X2,X0,X3)
| ~ coll(X0,X3,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f339]) ).
tcf(c_162,negated_conjecture,
~ cyclic(sK21,sK22,sK25,sK26),
inference(cnf_transformation,[],[f392]) ).
tcf(c_164,negated_conjecture,
coll(sK23,sK21,sK22),
inference(cnf_transformation,[],[f390]) ).
tcf(c_165,negated_conjecture,
midp(sK24,sK20,sK23),
inference(cnf_transformation,[],[f389]) ).
tcf(c_169,negated_conjecture,
coll(sK26,sK20,sK22),
inference(cnf_transformation,[],[f385]) ).
tcf(c_179,plain,
( eqangle(sK23,sK23,sK23,sK23,sK23,sK23,sK23,sK23)
| ~ cyclic(sK23,sK23,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_181,plain,
( para(sK23,sK23,sK23,sK23)
| ~ eqangle(sK23,sK23,sK23,sK23,sK23,sK23,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_2374,plain,
( coll(sK21,sK23,sK22)
| ~ coll(sK23,sK21,sK22) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_2377,plain,
! [X0: $i] :
( coll(X0,sK22,sK23)
| ~ coll(sK23,sK21,sK22)
| ~ coll(sK23,sK21,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_2381,plain,
( cong(sK24,sK20,sK24,sK23)
| ~ midp(sK24,sK20,sK23) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_2497,plain,
! [X0: $i,X1: $i] :
( cyclic(sK20,X1,X0,sK23)
| ~ cong(sK24,sK20,sK24,sK23)
| ~ cong(sK24,sK20,sK24,X1)
| ~ cong(sK24,sK20,sK24,X0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2498,plain,
( cyclic(sK20,sK23,sK23,sK23)
| ~ cong(sK24,sK20,sK24,sK23) ),
inference(instantiation,[status(thm)],[c_2497]) ).
tcf(c_2643,plain,
( coll(sK21,sK22,sK23)
| ~ coll(sK21,sK23,sK22) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_2668,plain,
( coll(sK22,sK22,sK23)
| ~ coll(sK23,sK21,sK22) ),
inference(instantiation,[status(thm)],[c_2377]) ).
tcf(c_2884,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,X2,sK23)
| ~ cyclic(sK20,X0,X1,sK23)
| ~ cyclic(sK20,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_2885,plain,
( cyclic(sK23,sK23,sK23,sK23)
| ~ cyclic(sK20,sK23,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_2884]) ).
tcf(c_2962,plain,
! [X0: $i] :
( coll(X0,sK23,sK21)
| ~ coll(sK21,sK22,sK23)
| ~ coll(sK21,sK22,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_2963,plain,
( coll(sK23,sK23,sK21)
| ~ coll(sK21,sK22,sK23) ),
inference(instantiation,[status(thm)],[c_2962]) ).
tcf(c_2979,plain,
! [X0: $i] :
( coll(X0,sK23,sK22)
| ~ coll(sK22,sK22,sK23)
| ~ coll(sK22,sK22,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_2980,plain,
( coll(sK23,sK23,sK22)
| ~ coll(sK22,sK22,sK23) ),
inference(instantiation,[status(thm)],[c_2979]) ).
tcf(c_3348,plain,
! [X0: $i] :
( cyclic(X0,sK21,sK22,sK26)
| ~ cyclic(X0,sK22,sK21,sK26) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_3349,plain,
( cyclic(sK23,sK21,sK22,sK26)
| ~ cyclic(sK23,sK22,sK21,sK26) ),
inference(instantiation,[status(thm)],[c_3348]) ).
tcf(c_3884,plain,
! [X0: $i,X1: $i] :
( cyclic(X1,sK22,sK21,sK26)
| ~ cyclic(X0,X1,sK22,sK26)
| ~ cyclic(X0,X1,sK22,sK21) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3885,plain,
( cyclic(sK23,sK22,sK21,sK26)
| ~ cyclic(sK23,sK23,sK22,sK26)
| ~ cyclic(sK23,sK23,sK22,sK21) ),
inference(instantiation,[status(thm)],[c_3884]) ).
tcf(c_4011,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,X2,sK26)
| ~ cyclic(X0,X1,sK26,X2) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_4012,plain,
( cyclic(sK23,sK23,sK23,sK26)
| ~ cyclic(sK23,sK23,sK26,sK23) ),
inference(instantiation,[status(thm)],[c_4011]) ).
tcf(c_4014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X2,X3,sK26)
| ~ cyclic(X0,X1,X2,sK26)
| ~ cyclic(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_6308,plain,
! [X0: $i] :
( coll(sK22,X0,sK23)
| ~ coll(sK23,sK21,X0) ),
inference(superposition,[status(thm)],[c_164,c_51]) ).
tcf(c_6310,plain,
! [X0: $i] :
( coll(sK22,X0,sK26)
| ~ coll(sK26,sK20,X0) ),
inference(superposition,[status(thm)],[c_169,c_51]) ).
tcf(c_7140,plain,
! [X0: $i] :
( ~ cyclic(X0,sK21,sK22,sK26)
| ~ cyclic(X0,sK21,sK22,sK25) ),
inference(resolution,[status(thm)],[c_162,c_65]) ).
tcf(c_7141,plain,
( ~ cyclic(sK23,sK21,sK22,sK26)
| ~ cyclic(sK23,sK21,sK22,sK25) ),
inference(instantiation,[status(thm)],[c_7140]) ).
tcf(c_7229,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,sK26,X2)
| ~ cyclic(X0,sK26,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_7230,plain,
( cyclic(sK23,sK23,sK26,sK23)
| ~ cyclic(sK23,sK26,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_7229]) ).
tcf(c_7384,plain,
coll(sK22,sK22,sK23),
inference(superposition,[status(thm)],[c_164,c_6308]) ).
tcf(c_7506,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,sK25,X2)
| ~ cyclic(X0,sK25,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_7507,plain,
( cyclic(sK23,sK23,sK25,sK23)
| ~ cyclic(sK23,sK25,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_7506]) ).
tcf(c_7518,plain,
! [X0: $i] :
( coll(sK23,X0,sK22)
| ~ coll(sK22,sK22,X0) ),
inference(superposition,[status(thm)],[c_7384,c_51]) ).
tcf(c_7575,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,sK22,X2)
| ~ cyclic(X0,sK22,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_7576,plain,
( cyclic(sK23,sK23,sK22,sK23)
| ~ cyclic(sK23,sK22,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_7575]) ).
tcf(c_7582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X2,sK22,X3)
| ~ cyclic(X0,X1,X2,sK22)
| ~ cyclic(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_8029,plain,
coll(sK22,sK22,sK26),
inference(superposition,[status(thm)],[c_169,c_6310]) ).
tcf(c_9729,plain,
! [X0: $i,X1: $i] :
( eqangle(X0,X1,X0,sK26,X0,X1,X0,sK26)
| ~ para(X0,X1,X0,X1) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_9731,plain,
( eqangle(sK23,sK23,sK23,sK26,sK23,sK23,sK23,sK26)
| ~ para(sK23,sK23,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_9729]) ).
tcf(c_10648,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X2,sK26)
| ~ coll(sK26,X0,X2)
| ~ coll(sK26,X0,X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_10649,plain,
( coll(sK23,sK23,sK26)
| ~ coll(sK26,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_10648]) ).
tcf(c_11690,plain,
coll(sK23,sK23,sK22),
inference(superposition,[status(thm)],[c_7384,c_7518]) ).
tcf(c_11691,plain,
coll(sK23,sK26,sK22),
inference(superposition,[status(thm)],[c_8029,c_7518]) ).
tcf(c_11777,plain,
coll(sK23,sK22,sK23),
inference(superposition,[status(thm)],[c_11690,c_49]) ).
tcf(c_11862,plain,
coll(sK23,sK22,sK26),
inference(superposition,[status(thm)],[c_11691,c_49]) ).
tcf(c_11986,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,X2,sK21)
| ~ cyclic(X0,X1,sK21,X2) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_11987,plain,
( cyclic(sK23,sK23,sK23,sK21)
| ~ cyclic(sK23,sK23,sK21,sK23) ),
inference(instantiation,[status(thm)],[c_11986]) ).
tcf(c_12073,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,sK26,X0,X2)
| ~ coll(X0,X2,sK26)
| ~ eqangle(X0,X1,X0,sK26,X2,X1,X2,sK26) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_12074,plain,
( cyclic(sK23,sK26,sK23,sK23)
| ~ coll(sK23,sK23,sK26)
| ~ eqangle(sK23,sK23,sK23,sK26,sK23,sK23,sK23,sK26) ),
inference(instantiation,[status(thm)],[c_12073]) ).
tcf(c_12689,plain,
! [X0: $i,X1: $i] :
( eqangle(X0,X1,X0,sK25,X0,X1,X0,sK25)
| ~ para(X0,X1,X0,X1) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_12691,plain,
( eqangle(sK23,sK23,sK23,sK25,sK23,sK23,sK23,sK25)
| ~ para(sK23,sK23,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_12689]) ).
tcf(c_13489,plain,
! [X0: $i,X1: $i] :
( eqangle(X0,X1,X0,sK22,X0,X1,X0,sK22)
| ~ para(X0,X1,X0,X1) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_13491,plain,
( eqangle(sK23,sK23,sK23,sK22,sK23,sK23,sK23,sK22)
| ~ para(sK23,sK23,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_13489]) ).
tcf(c_14549,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,sK25,X1,X2)
| ~ cyclic(sK25,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_14550,plain,
( cyclic(sK23,sK25,sK23,sK23)
| ~ cyclic(sK25,sK23,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_14549]) ).
tcf(c_14552,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,sK25,X0,X2)
| ~ coll(X0,X2,sK25)
| ~ eqangle(X0,X1,X0,sK25,X2,X1,X2,sK25) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_14553,plain,
( cyclic(sK23,sK25,sK23,sK23)
| ~ coll(sK23,sK23,sK25)
| ~ eqangle(sK23,sK23,sK23,sK25,sK23,sK23,sK23,sK25) ),
inference(instantiation,[status(thm)],[c_14552]) ).
tcf(c_14571,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,X2,sK25)
| ~ cyclic(X0,X1,sK25,X2) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_14572,plain,
( cyclic(sK23,sK23,sK23,sK25)
| ~ cyclic(sK23,sK23,sK25,sK23) ),
inference(instantiation,[status(thm)],[c_14571]) ).
tcf(c_14642,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,sK22,X0,X2)
| ~ coll(X0,X2,sK22)
| ~ eqangle(X0,X1,X0,sK22,X2,X1,X2,sK22) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_14643,plain,
( cyclic(sK23,sK22,sK23,sK23)
| ~ coll(sK23,sK23,sK22)
| ~ eqangle(sK23,sK23,sK23,sK22,sK23,sK23,sK23,sK22) ),
inference(instantiation,[status(thm)],[c_14642]) ).
tcf(c_14661,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,X2,sK22)
| ~ cyclic(X0,X1,sK22,X2) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_14662,plain,
( cyclic(sK23,sK23,sK23,sK22)
| ~ cyclic(sK23,sK23,sK22,sK23) ),
inference(instantiation,[status(thm)],[c_14661]) ).
tcf(c_15661,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,sK25)
| cyclic(sK25,X1,X0,X2)
| ~ eqangle(X0,sK25,X0,X1,X2,sK25,X2,X1) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_15662,plain,
( coll(sK23,sK23,sK25)
| cyclic(sK25,sK23,sK23,sK23)
| ~ eqangle(sK23,sK25,sK23,sK23,sK23,sK25,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_15661]) ).
tcf(c_16582,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,sK21,X0,X2)
| ~ coll(X0,X2,sK21)
| ~ eqangle(X0,X1,X0,sK21,X2,X1,X2,sK21) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_16583,plain,
( cyclic(sK23,sK21,sK23,sK23)
| ~ coll(sK23,sK23,sK21)
| ~ eqangle(sK23,sK23,sK23,sK21,sK23,sK23,sK23,sK21) ),
inference(instantiation,[status(thm)],[c_16582]) ).
tcf(c_18840,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,sK21,X2)
| ~ cyclic(X0,sK21,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_18841,plain,
( cyclic(sK23,sK23,sK21,sK23)
| ~ cyclic(sK23,sK21,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_18840]) ).
tcf(c_19169,plain,
! [X0: $i] :
( coll(sK26,X0,sK23)
| ~ coll(sK23,sK22,X0) ),
inference(superposition,[status(thm)],[c_11862,c_51]) ).
tcf(c_19201,plain,
( coll(sK26,sK23,sK23)
| ~ coll(sK23,sK22,sK23) ),
inference(instantiation,[status(thm)],[c_19169]) ).
tcf(c_23177,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,sK22,sK26)
| ~ cyclic(X0,X1,X2,sK26)
| ~ cyclic(X0,X1,X2,sK22) ),
inference(instantiation,[status(thm)],[c_4014]) ).
tcf(c_23178,plain,
( cyclic(sK23,sK23,sK22,sK26)
| ~ cyclic(sK23,sK23,sK23,sK26)
| ~ cyclic(sK23,sK23,sK23,sK22) ),
inference(instantiation,[status(thm)],[c_23177]) ).
tcf(c_24025,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,sK22,sK21)
| ~ cyclic(X0,X1,X2,sK22)
| ~ cyclic(X0,X1,X2,sK21) ),
inference(instantiation,[status(thm)],[c_7582]) ).
tcf(c_24026,plain,
( cyclic(sK23,sK23,sK22,sK21)
| ~ cyclic(sK23,sK23,sK23,sK22)
| ~ cyclic(sK23,sK23,sK23,sK21) ),
inference(instantiation,[status(thm)],[c_24025]) ).
tcf(c_25498,plain,
! [X0: $i,X1: $i] :
( eqangle(X0,X1,X0,sK21,X0,X1,X0,sK21)
| ~ para(X0,X1,X0,X1) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_25500,plain,
( eqangle(sK23,sK23,sK23,sK21,sK23,sK23,sK23,sK21)
| ~ para(sK23,sK23,sK23,sK23) ),
inference(instantiation,[status(thm)],[c_25498]) ).
tcf(c_26779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,sK25,X0,X1,X2,sK25,X2,X3)
| ~ eqangle(X0,X1,X0,sK25,X2,X3,X2,sK25) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_26780,plain,
( eqangle(sK23,sK25,sK23,sK23,sK23,sK25,sK23,sK23)
| ~ eqangle(sK23,sK23,sK23,sK25,sK23,sK23,sK23,sK25) ),
inference(instantiation,[status(thm)],[c_26779]) ).
tcf(c_29978,plain,
! [X0: $i,X1: $i] :
( cyclic(X1,sK21,sK22,sK25)
| ~ cyclic(X0,X1,sK21,sK25)
| ~ cyclic(X0,X1,sK21,sK22) ),
inference(instantiation,[status(thm)],[c_7582]) ).
tcf(c_29979,plain,
( cyclic(sK23,sK21,sK22,sK25)
| ~ cyclic(sK23,sK23,sK21,sK25)
| ~ cyclic(sK23,sK23,sK21,sK22) ),
inference(instantiation,[status(thm)],[c_29978]) ).
tcf(c_31049,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,sK21,sK25)
| ~ cyclic(X0,X1,X2,sK25)
| ~ cyclic(X0,X1,X2,sK21) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_31050,plain,
( cyclic(sK23,sK23,sK21,sK25)
| ~ cyclic(sK23,sK23,sK23,sK25)
| ~ cyclic(sK23,sK23,sK23,sK21) ),
inference(instantiation,[status(thm)],[c_31049]) ).
tcf(c_32599,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,X1,sK21,sK22)
| ~ cyclic(X0,X1,sK22,sK21) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_32600,plain,
( cyclic(sK23,sK23,sK21,sK22)
| ~ cyclic(sK23,sK23,sK22,sK21) ),
inference(instantiation,[status(thm)],[c_32599]) ).
tcf(c_32601,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_32600,c_31050,c_29979,c_26780,c_25500,c_24026,c_23178,c_19201,c_18841,c_16583,c_15662,c_14662,c_14643,c_14572,c_14553,c_14550,c_13491,c_12691,c_12074,c_11987,c_11777,c_10649,c_9731,c_7576,c_7507,c_7230,c_7141,c_4012,c_3885,c_3349,c_2980,c_2963,c_2885,c_2668,c_2643,c_2498,c_2381,c_2374,c_181,c_179,c_164,c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO595+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 12:30:34 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 33.72/7.35 % SZS status Started for theBenchmark.p
% 33.72/7.35 % SZS status Theorem for theBenchmark.p
% 33.72/7.35
% 33.72/7.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 33.72/7.35
% 33.72/7.35 % ------ iProver source info
% 33.72/7.35
% 33.72/7.35 % git: date: 2026-07-19 20:42:38 +0200
% 33.72/7.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 33.72/7.35 % git: non_committed_changes: false
% 33.72/7.35
% 33.72/7.35 % ------ Parsing...
% 33.72/7.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 33.72/7.35
% 33.72/7.35 % ------ Preprocessing...%
% 33.72/7.35
% 33.72/7.35 % ------ Preprocessing...%
% 33.72/7.35
% 33.72/7.35 % ------ Preprocessing...
% 33.72/7.35 % ------ Proving...
% 33.72/7.35 % ------ Problem Properties
% 33.72/7.35
% 33.72/7.35 %
% 33.72/7.35 % clauses 121
% 33.72/7.35 % conjectures 9
% 33.72/7.35 % EPR 84
% 33.72/7.35 % Horn 111
% 33.72/7.35 % unary 9
% 33.72/7.35 % binary 37
% 33.72/7.35 % lits 337
% 33.72/7.35 % lits eq 4
% 33.72/7.35 % fd_pure 0
% 33.72/7.35 % fd_pseudo 0
% 33.72/7.35 % fd_cond 0
% 33.72/7.35 % fd_pseudo_cond 4
% 33.72/7.35 % AC symbols 0
% 33.72/7.35
% 33.72/7.35 % ------ Input Options Time Limit: Unbounded
% 33.72/7.35
% 33.72/7.35
% 33.72/7.35 % ------
% 33.72/7.35 % Current options:
% 33.72/7.35 % ------
% 33.72/7.35
% 33.72/7.35
% 33.72/7.35 %
% 33.72/7.35
% 33.72/7.35 % ------ Proving...
% 33.72/7.35 %
% 33.72/7.35
% 33.72/7.35 % SZS status Theorem for theBenchmark.p
% 33.72/7.35
% 33.72/7.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 33.72/7.36
% 33.72/7.36
%------------------------------------------------------------------------------