%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO570+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 01:21:30 PM UTC 2026
% Result : Theorem 44.04s 11.77s
% Output : CNFRefutation 44.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 130 ( 21 unt; 0 def)
% Number of atoms : 326 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 329 ( 133 ~; 127 |; 47 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 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 : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 619 ( 0 sgn 601 !; 18 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
fof(f2,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD2) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD8) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X2,X3,X4,X5)
& perp(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD9) ).
fof(f14,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD19) ).
fof(f20,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD20) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD21) ).
fof(f22,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
& eqangle(X0,X1,X2,X3,X4,X5,X6,X7) )
=> eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD22) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD41) ).
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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD42b) ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
& cyclic(X0,X1,X2,X5)
& cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X3) )
=> cong(X0,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD43) ).
fof(f51,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X1,X2)
& circle(X3,X0,X1,X2) )
=> eqangle(X0,X1,X0,X2,X3,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD50) ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X3,X1,X3)
& cong(X0,X2,X1,X2) )
=> perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
fof(f67,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD66) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( coll(X7,X0,X1)
& perp(X7,X5,X0,X1)
& coll(X6,X2,X4)
& perp(X6,X5,X2,X4)
& coll(X5,X1,X4)
& coll(X5,X0,X2)
& circle(X3,X0,X4,X8)
& circle(X3,X0,X1,X2) )
=> eqangle(X0,X5,X5,X6,X7,X5,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL214032) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( coll(X7,X0,X1)
& perp(X7,X5,X0,X1)
& coll(X6,X2,X4)
& perp(X6,X5,X2,X4)
& coll(X5,X1,X4)
& coll(X5,X0,X2)
& circle(X3,X0,X4,X8)
& circle(X3,X0,X1,X2) )
=> eqangle(X0,X5,X5,X6,X7,X5,X5,X1) ),
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(f107,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f108]) ).
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(f124,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f20]) ).
fof(f125,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(ennf_transformation,[],[f21]) ).
fof(f126,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(flattening,[],[f126]) ).
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(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(f155,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4) ),
inference(ennf_transformation,[],[f44]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4) ),
inference(flattening,[],[f155]) ).
fof(f168,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X1,X2)
| ~ circle(X3,X0,X1,X2)
| eqangle(X0,X1,X0,X2,X3,X1,X3,X4) ),
inference(ennf_transformation,[],[f51]) ).
fof(f169,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X1,X2)
| ~ circle(X3,X0,X1,X2)
| eqangle(X0,X1,X0,X2,X3,X1,X3,X4) ),
inference(flattening,[],[f168]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f180]) ).
fof(f197,plain,
! [X0,X1,X2] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f67]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( coll(X7,X0,X1)
& perp(X7,X5,X0,X1)
& coll(X6,X2,X4)
& perp(X6,X5,X2,X4)
& coll(X5,X1,X4)
& coll(X5,X0,X2)
& circle(X3,X0,X4,X8)
& circle(X3,X0,X1,X2)
& ~ eqangle(X0,X5,X5,X6,X7,X5,X5,X1) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( coll(X7,X0,X1)
& perp(X7,X5,X0,X1)
& coll(X6,X2,X4)
& perp(X6,X5,X2,X4)
& coll(X5,X1,X4)
& coll(X5,X0,X2)
& circle(X3,X0,X4,X8)
& circle(X3,X0,X1,X2)
& ~ eqangle(X0,X5,X5,X6,X7,X5,X5,X1) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( coll(sK27,sK20,sK21)
& perp(sK27,sK25,sK20,sK21)
& coll(sK26,sK22,sK24)
& perp(sK26,sK25,sK22,sK24)
& coll(sK25,sK21,sK24)
& coll(sK25,sK20,sK22)
& circle(sK23,sK20,sK24,sK28)
& circle(sK23,sK20,sK21,sK22)
& ~ eqangle(sK20,sK25,sK25,sK26,sK27,sK25,sK25,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28]),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)],[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(f278,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f279,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f109]) ).
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(f290,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f124]) ).
fof(f291,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(cnf_transformation,[],[f125]) ).
fof(f292,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(cnf_transformation,[],[f127]) ).
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(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(f314,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4) ),
inference(cnf_transformation,[],[f156]) ).
fof(f321,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X1,X2)
| ~ circle(X3,X0,X1,X2)
| eqangle(X0,X1,X0,X2,X3,X1,X3,X4) ),
inference(cnf_transformation,[],[f169]) ).
fof(f327,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f181]) ).
fof(f337,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f197]) ).
fof(f387,plain,
perp(sK26,sK25,sK22,sK24),
inference(cnf_transformation,[],[f270]) ).
fof(f392,plain,
~ eqangle(sK20,sK25,sK25,sK26,sK27,sK25,sK25,sK21),
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_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f279]) ).
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_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f292]) ).
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_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_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( cong(X1,X2,X4,X5)
| ~ cyclic(X1,X2,X0,X5)
| ~ cyclic(X1,X2,X0,X4)
| ~ cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ midp(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f337]) ).
tcf(c_162,negated_conjecture,
~ eqangle(sK20,sK25,sK25,sK26,sK27,sK25,sK25,sK21),
inference(cnf_transformation,[],[f392]) ).
tcf(c_167,negated_conjecture,
perp(sK26,sK25,sK22,sK24),
inference(cnf_transformation,[],[f387]) ).
tcf(c_6381,plain,
( perp(sK22,sK24,sK26,sK25)
| ~ perp(sK26,sK25,sK22,sK24) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_6513,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK26,sK25)
| ~ perp(sK22,sK24,sK26,sK25)
| ~ perp(X0,X1,sK22,sK24) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_7661,plain,
( para(sK26,sK25,sK26,sK25)
| ~ perp(sK22,sK24,sK26,sK25)
| ~ perp(sK26,sK25,sK22,sK24) ),
inference(instantiation,[status(thm)],[c_6513]) ).
tcf(c_8152,plain,
! [X0: $i,X1: $i] :
( eqangle(sK26,sK25,X0,X1,sK26,sK25,X0,X1)
| ~ para(sK26,sK25,sK26,sK25) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_8601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_88,c_69]) ).
tcf(c_12309,plain,
! [X0: $i,X1: $i] :
( eqangle(X0,X1,sK26,sK25,X0,X1,sK26,sK25)
| ~ eqangle(sK26,sK25,X0,X1,sK26,sK25,X0,X1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_35473,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,X0,X1)
| ~ eqangle(X0,X1,sK26,sK25,X0,X1,sK26,sK25) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_46622,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,X0,X0)
| ~ coll(X0,X0,X2)
| ~ para(X0,X1,X0,X1) ),
inference(superposition,[status(thm)],[c_88,c_91]) ).
tcf(c_46715,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(X0,X1,X0,X1)
| ~ midp(X2,X1,X2)
| ~ circle(X0,X0,X1,X2) ),
inference(superposition,[status(thm)],[c_99,c_87]) ).
tcf(c_47170,plain,
! [X0: $i,X1: $i] : para(X0,X1,X0,X1),
inference(global_subsumption_just,[status(thm)],[c_46715,c_167,c_6381,c_7661,c_8152,c_12309,c_35473]) ).
tcf(c_47176,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_46622,c_47170]) ).
tcf(c_47185,plain,
! [X0: $i,X1: $i] : coll(X0,X1,X1),
inference(superposition,[status(thm)],[c_47170,c_115]) ).
tcf(c_48102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cong(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X1)
| ~ cyclic(X0,X1,X2,X0) ),
inference(superposition,[status(thm)],[c_89,c_92]) ).
tcf(c_48769,plain,
! [X0: $i,X1: $i] : coll(X0,X1,X0),
inference(superposition,[status(thm)],[c_47185,c_50]) ).
tcf(c_50213,plain,
! [X0: $i,X1: $i] : coll(X0,X0,X1),
inference(superposition,[status(thm)],[c_48769,c_49]) ).
tcf(c_50276,plain,
! [X0: $i,X1: $i,X2: $i] : cyclic(X0,X1,X2,X2),
inference(backward_subsumption_resolution,[status(thm)],[c_47176,c_50213]) ).
tcf(c_52779,plain,
! [X0: $i,X1: $i,X2: $i] : cyclic(X0,X1,X2,X1),
inference(superposition,[status(thm)],[c_50276,c_63]) ).
tcf(c_52805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cong(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_48102,c_52779]) ).
tcf(c_53231,plain,
! [X0: $i,X1: $i,X2: $i] : cyclic(X0,X1,X2,X0),
inference(superposition,[status(thm)],[c_52779,c_64]) ).
tcf(c_53237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cong(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52805,c_53231]) ).
tcf(c_53375,plain,
! [X0: $i,X1: $i,X2: $i] : cyclic(X0,X1,X0,X2),
inference(superposition,[status(thm)],[c_53231,c_62]) ).
tcf(c_53416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X0,X3,X2)
| ~ cyclic(X0,X1,X0,X2) ),
inference(superposition,[status(thm)],[c_53375,c_65]) ).
tcf(c_53420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[c_53416,c_53375]) ).
tcf(c_53424,plain,
! [X0: $i,X1: $i] : cong(X0,X1,X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[c_53237,c_53420]) ).
tcf(c_53618,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(X0,X0,X2,X1)
| ~ cong(X0,X1,X0,X1) ),
inference(superposition,[status(thm)],[c_53424,c_105]) ).
tcf(c_53644,plain,
! [X0: $i,X1: $i,X2: $i] : perp(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[c_53618,c_53424]) ).
tcf(c_53821,plain,
! [X0: $i,X1: $i,X2: $i] : perp(X0,X1,X2,X2),
inference(superposition,[status(thm)],[c_53644,c_56]) ).
tcf(c_53849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( para(X3,X4,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(superposition,[status(thm)],[c_53821,c_57]) ).
tcf(c_53879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[c_53849,c_53644]) ).
tcf(c_53938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5),
inference(backward_subsumption_resolution,[status(thm)],[c_8601,c_53879]) ).
tcf(c_55488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( eqangle(X6,X7,X8,X9,X2,X3,X4,X5)
| ~ eqangle(X0,X1,X0,X1,X2,X3,X4,X5) ),
inference(superposition,[status(thm)],[c_53938,c_70]) ).
tcf(c_55490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : eqangle(X0,X1,X0,X1,X2,X3,X4,X5),
inference(superposition,[status(thm)],[c_53938,c_68]) ).
tcf(c_55493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7),
inference(forward_subsumption_resolution,[status(thm)],[c_55488,c_55490]) ).
tcf(c_55494,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_162,c_55493]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO570+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.64 % Computer : n017.cluster.edu
% 0.17/0.64 % Model : x86_64 x86_64
% 0.17/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.64 % Memory : 8046.5625MB
% 0.17/0.64 % OS : Linux 6.8.0-71-generic
% 0.17/0.64 % CPULimit : 300
% 0.17/0.64 % WCLimit : 300
% 0.17/0.64 % DateTime : Wed Sep 23 12:21:33 UTC 2026
% 0.17/0.65 % CPUTime :
% 0.17/0.65 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.21/0.70 Running first-order theorem proving
% 0.21/0.70 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.71
% 0.21/0.71 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.71
% 0.21/0.71 % Detected problem language: tptp
% 0.21/0.73 % Proving...
% 44.04/11.77 % SZS status Started for theBenchmark.p
% 44.04/11.77 % SZS status Theorem for theBenchmark.p
% 44.04/11.77
% 44.04/11.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 44.04/11.77
% 44.04/11.77 % ------ iProver source info
% 44.04/11.77
% 44.04/11.77 % git: date: 2026-07-19 20:42:38 +0200
% 44.04/11.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 44.04/11.77 % git: non_committed_changes: false
% 44.04/11.77
% 44.04/11.77 % ------ Parsing...
% 44.04/11.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 44.04/11.77
% 44.04/11.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 44.04/11.77
% 44.04/11.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 44.04/11.77
% 44.04/11.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 44.04/11.77 % ------ Proving...
% 44.04/11.77 % ------ Problem Properties
% 44.04/11.77
% 44.04/11.77 %
% 44.04/11.77 % clauses 121
% 44.04/11.77 % conjectures 9
% 44.04/11.77 % EPR 84
% 44.04/11.77 % Horn 111
% 44.04/11.77 % unary 9
% 44.04/11.77 % binary 37
% 44.04/11.77 % lits 337
% 44.04/11.77 % lits eq 4
% 44.04/11.77 % fd_pure 0
% 44.04/11.77 % fd_pseudo 0
% 44.04/11.77 % fd_cond 0
% 44.04/11.77 % fd_pseudo_cond 4
% 44.04/11.77 % AC symbols 0
% 44.04/11.77
% 44.04/11.77 % ------ Input Options Time Limit: Unbounded
% 44.04/11.77
% 44.04/11.77
% 44.04/11.77 % ------
% 44.04/11.77 % Current options:
% 44.04/11.77 % ------
% 44.04/11.77
% 44.04/11.77
% 44.04/11.77 %
% 44.04/11.77
% 44.04/11.77 % ------ Proving...
% 44.04/11.77 %
% 44.04/11.77
% 44.04/11.77 % SZS status Theorem for theBenchmark.p
% 44.04/11.77
% 44.04/11.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 44.04/11.78
% 44.04/11.78
%------------------------------------------------------------------------------