%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO643+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 : n003.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 01:21:44 PM UTC 2026
% Result : Theorem 31.57s 9.23s
% Output : CNFRefutation 31.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 142 ( 19 unt; 0 def)
% Number of atoms : 352 ( 4 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 357 ( 147 ~; 141 |; 48 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-5 aty)
% Number of variables : 513 ( 0 sgn 488 !; 25 ?; 164 :)
% 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(f3,axiom,
! [X0,X1,X2,X3] :
( ( coll(X0,X1,X3)
& coll(X0,X1,X2) )
=> coll(X2,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD3) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD7) ).
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(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(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(f54,axiom,
! [X0,X1,X2,X3] :
( ( coll(X3,X0,X2)
& circle(X3,X0,X1,X2) )
=> perp(X0,X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD53) ).
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(f87,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X3,X0,X1,X2)
=> perp(X4,X0,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleX11) ).
fof(f91,axiom,
! [X0,X1,X2,X3,X4] :
? [X5] :
( ( coll(X1,X3,X4)
& perp(X0,X2,X2,X1) )
=> ( perp(X5,X0,X3,X4)
& coll(X5,X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleX15) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( circle(X9,X1,X0,X4)
& circle(X8,X1,X2,X5)
& circle(X7,X0,X2,X3)
& circle(X6,X3,X4,X5)
& coll(X5,X2,X3)
& coll(X5,X1,X4)
& coll(X4,X0,X3)
& coll(X2,X0,X1) )
=> cyclic(X8,X9,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL81109109F) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( circle(X9,X1,X0,X4)
& circle(X8,X1,X2,X5)
& circle(X7,X0,X2,X3)
& circle(X6,X3,X4,X5)
& coll(X5,X2,X3)
& coll(X5,X1,X4)
& coll(X4,X0,X3)
& coll(X2,X0,X1) )
=> cyclic(X8,X9,X7,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(f106,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f7]) ).
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(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(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(f174,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(ennf_transformation,[],[f54]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(flattening,[],[f174]) ).
fof(f197,plain,
! [X0,X1,X2] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f67]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
? [X4] :
( ~ circle(X3,X0,X1,X2)
| perp(X4,X0,X0,X3) ),
inference(ennf_transformation,[],[f87]) ).
fof(f241,plain,
! [X0,X1,X2,X3,X4] :
? [X5] :
( ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1)
| ( perp(X5,X0,X3,X4)
& coll(X5,X3,X4) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f242,plain,
! [X0,X1,X2,X3,X4] :
? [X5] :
( ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1)
| ( perp(X5,X0,X3,X4)
& coll(X5,X3,X4) ) ),
inference(flattening,[],[f241]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( circle(X9,X1,X0,X4)
& circle(X8,X1,X2,X5)
& circle(X7,X0,X2,X3)
& circle(X6,X3,X4,X5)
& coll(X5,X2,X3)
& coll(X5,X1,X4)
& coll(X4,X0,X3)
& coll(X2,X0,X1)
& ~ cyclic(X8,X9,X7,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( circle(X9,X1,X0,X4)
& circle(X8,X1,X2,X5)
& circle(X7,X0,X2,X3)
& circle(X6,X3,X4,X5)
& coll(X5,X2,X3)
& coll(X5,X1,X4)
& coll(X4,X0,X3)
& coll(X2,X0,X1)
& ~ cyclic(X8,X9,X7,X6) ),
inference(flattening,[],[f249]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( ~ circle(X3,X0,X1,X2)
| perp(sK11(X0,X1,X2,X3),X0,X0,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X2,X3))],[f234]) ).
fof(f266,plain,
! [X0,X1,X2,X3,X4] :
( ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1)
| ( perp(sK16(X0,X1,X2,X3,X4),X0,X3,X4)
& coll(sK16(X0,X1,X2,X3,X4),X3,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X5,sK16(X0,X1,X2,X3,X4))],[f242]) ).
fof(f270,plain,
( circle(sK29,sK21,sK20,sK24)
& circle(sK28,sK21,sK22,sK25)
& circle(sK27,sK20,sK22,sK23)
& circle(sK26,sK23,sK24,sK25)
& coll(sK25,sK22,sK23)
& coll(sK25,sK21,sK24)
& coll(sK24,sK20,sK23)
& coll(sK22,sK20,sK21)
& ~ cyclic(sK28,sK29,sK27,sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29]),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)],[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(f277,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f106]) ).
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(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(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(f324,plain,
! [X2,X3,X0,X1] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f175]) ).
fof(f337,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f197]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( ~ circle(X3,X0,X1,X2)
| perp(sK11(X0,X1,X2,X3),X0,X0,X3) ),
inference(cnf_transformation,[],[f262]) ).
fof(f377,plain,
! [X2,X3,X0,X1,X4] :
( ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1)
| perp(sK16(X0,X1,X2,X3,X4),X0,X3,X4) ),
inference(cnf_transformation,[],[f266]) ).
fof(f385,plain,
circle(sK28,sK21,sK22,sK25),
inference(cnf_transformation,[],[f270]) ).
fof(f386,plain,
circle(sK27,sK20,sK22,sK23),
inference(cnf_transformation,[],[f270]) ).
fof(f391,plain,
coll(sK22,sK20,sK21),
inference(cnf_transformation,[],[f270]) ).
fof(f392,plain,
~ cyclic(sK28,sK29,sK27,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_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f277]) ).
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_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_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_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X1,X2,X2,X3)
| ~ coll(X0,X1,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f324]) ).
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_148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(sK11(X1,X2,X3,X0),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f370]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( perp(sK16(X0,X2,X1,X3,X4),X0,X3,X4)
| ~ coll(X2,X3,X4)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f377]) ).
tcf(c_162,negated_conjecture,
~ cyclic(sK28,sK29,sK27,sK26),
inference(cnf_transformation,[],[f392]) ).
tcf(c_163,negated_conjecture,
coll(sK22,sK20,sK21),
inference(cnf_transformation,[],[f391]) ).
tcf(c_168,negated_conjecture,
circle(sK27,sK20,sK22,sK23),
inference(cnf_transformation,[],[f386]) ).
tcf(c_169,negated_conjecture,
circle(sK28,sK21,sK22,sK25),
inference(cnf_transformation,[],[f385]) ).
tcf(c_2295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(sK11(X1,X2,X3,X0),X1,X1,X0)
| ( X3 != sK23 )
| ( X2 != sK22 )
| ( X1 != sK20 )
| ( X0 != sK27 ) ),
inference(resolution_lifted,[status(thm)],[c_148,c_168]) ).
tcf(c_2296,plain,
perp(sK11(sK20,sK22,sK23,sK27),sK20,sK20,sK27),
inference(unflattening,[status(thm)],[c_2295]) ).
tcf(c_6895,plain,
( coll(sK22,sK21,sK20)
| ~ coll(sK22,sK20,sK21) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_6903,plain,
! [X0: $i] :
( coll(X0,sK21,sK22)
| ~ coll(sK22,sK20,sK21)
| ~ coll(sK22,sK20,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_6942,plain,
! [X0: $i] :
( coll(X0,sK20,sK22)
| ~ coll(sK22,sK21,sK20)
| ~ coll(sK22,sK21,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_6943,plain,
( coll(sK20,sK20,sK22)
| ~ coll(sK22,sK21,sK20) ),
inference(instantiation,[status(thm)],[c_6942]) ).
tcf(c_7046,plain,
( perp(sK11(sK20,sK22,sK23,sK27),sK20,sK27,sK20)
| ~ perp(sK11(sK20,sK22,sK23,sK27),sK20,sK20,sK27) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_7054,plain,
! [X0: $i,X1: $i] :
( perp(sK16(sK11(sK20,sK22,sK23,sK27),sK27,sK20,X0,X1),sK11(sK20,sK22,sK23,sK27),X0,X1)
| ~ coll(sK27,X0,X1)
| ~ perp(sK11(sK20,sK22,sK23,sK27),sK20,sK20,sK27) ),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_7872,plain,
( perp(sK27,sK20,sK11(sK20,sK22,sK23,sK27),sK20)
| ~ perp(sK11(sK20,sK22,sK23,sK27),sK20,sK27,sK20) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_7877,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK27,sK20)
| ~ perp(sK11(sK20,sK22,sK23,sK27),sK20,sK27,sK20)
| ~ perp(X0,X1,sK11(sK20,sK22,sK23,sK27),sK20) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_8861,plain,
( perp(sK16(sK11(sK20,sK22,sK23,sK27),sK27,sK20,sK21,sK22),sK11(sK20,sK22,sK23,sK27),sK21,sK22)
| ~ coll(sK27,sK21,sK22)
| ~ perp(sK11(sK20,sK22,sK23,sK27),sK20,sK20,sK27) ),
inference(instantiation,[status(thm)],[c_7054]) ).
tcf(c_8862,plain,
( coll(sK27,sK21,sK22)
| ~ coll(sK22,sK20,sK21)
| ~ coll(sK22,sK20,sK27) ),
inference(instantiation,[status(thm)],[c_6903]) ).
tcf(c_9140,plain,
( perp(sK21,sK22,sK16(sK11(sK20,sK22,sK23,sK27),sK27,sK20,sK21,sK22),sK11(sK20,sK22,sK23,sK27))
| ~ perp(sK16(sK11(sK20,sK22,sK23,sK27),sK27,sK20,sK21,sK22),sK11(sK20,sK22,sK23,sK27),sK21,sK22) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_9145,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK21,sK22)
| ~ perp(sK16(sK11(sK20,sK22,sK23,sK27),sK27,sK20,sK21,sK22),sK11(sK20,sK22,sK23,sK27),sK21,sK22)
| ~ perp(X0,X1,sK16(sK11(sK20,sK22,sK23,sK27),sK27,sK20,sK21,sK22),sK11(sK20,sK22,sK23,sK27)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_12246,plain,
( coll(sK22,sK20,sK27)
| ~ coll(sK22,sK27,sK20) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_13449,plain,
( para(sK27,sK20,sK27,sK20)
| ~ perp(sK27,sK20,sK11(sK20,sK22,sK23,sK27),sK20)
| ~ perp(sK11(sK20,sK22,sK23,sK27),sK20,sK27,sK20) ),
inference(instantiation,[status(thm)],[c_7877]) ).
tcf(c_18162,plain,
! [X0: $i] :
( coll(sK22,sK27,sK20)
| ~ coll(sK20,X0,sK22)
| ~ coll(sK20,X0,sK27) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_18163,plain,
( coll(sK22,sK27,sK20)
| ~ coll(sK20,sK20,sK22)
| ~ coll(sK20,sK20,sK27) ),
inference(instantiation,[status(thm)],[c_18162]) ).
tcf(c_19812,plain,
! [X0: $i,X1: $i] :
( coll(X1,sK20,sK27)
| ~ coll(sK27,X0,sK20)
| ~ coll(sK27,X0,X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_19813,plain,
( coll(sK20,sK20,sK27)
| ~ coll(sK27,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_19812]) ).
tcf(c_21336,plain,
! [X0: $i,X1: $i] :
( coll(sK27,X0,X1)
| ~ para(sK27,X0,sK27,X1) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_21337,plain,
( coll(sK27,sK20,sK20)
| ~ para(sK27,sK20,sK27,sK20) ),
inference(instantiation,[status(thm)],[c_21336]) ).
tcf(c_24577,plain,
( para(sK21,sK22,sK21,sK22)
| ~ perp(sK21,sK22,sK16(sK11(sK20,sK22,sK23,sK27),sK27,sK20,sK21,sK22),sK11(sK20,sK22,sK23,sK27))
| ~ perp(sK16(sK11(sK20,sK22,sK23,sK27),sK27,sK20,sK21,sK22),sK11(sK20,sK22,sK23,sK27),sK21,sK22) ),
inference(instantiation,[status(thm)],[c_9145]) ).
tcf(c_26365,plain,
( perp(sK21,sK22,sK22,sK25)
| ~ coll(sK28,sK21,sK25) ),
inference(superposition,[status(thm)],[c_169,c_102]) ).
tcf(c_26407,plain,
( perp(sK22,sK25,sK21,sK22)
| ~ coll(sK28,sK21,sK25) ),
inference(superposition,[status(thm)],[c_26365,c_56]) ).
tcf(c_26442,plain,
! [X0: $i,X1: $i] :
( para(sK21,sK22,X0,X1)
| ~ coll(sK28,sK21,sK25)
| ~ perp(sK22,sK25,X0,X1) ),
inference(superposition,[status(thm)],[c_26365,c_57]) ).
tcf(c_26630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X2,X3,X4,X5,X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_88,c_68]) ).
tcf(c_26650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X4,X5,X2,X3,X4,X5,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_26630,c_67]) ).
tcf(c_26674,plain,
( para(sK21,sK22,sK21,sK22)
| ~ coll(sK28,sK21,sK25) ),
inference(superposition,[status(thm)],[c_26407,c_26442]) ).
tcf(c_26951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(superposition,[status(thm)],[c_26650,c_87]) ).
tcf(c_28456,plain,
para(sK21,sK22,sK21,sK22),
inference(global_subsumption_just,[status(thm)],[c_26674,c_163,c_2296,c_6895,c_6943,c_7046,c_7872,c_8861,c_8862,c_9140,c_12246,c_13449,c_18163,c_19813,c_21337,c_24577]) ).
tcf(c_28466,plain,
! [X0: $i,X1: $i] : para(X0,X1,X0,X1),
inference(superposition,[status(thm)],[c_28456,c_26951]) ).
tcf(c_45178,plain,
! [X0: $i,X1: $i] : coll(X0,X1,X1),
inference(superposition,[status(thm)],[c_28466,c_115]) ).
tcf(c_45670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_88,c_67]) ).
tcf(c_45947,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1)
| ~ para(X0,X1,X0,X1) ),
inference(superposition,[status(thm)],[c_45670,c_91]) ).
tcf(c_45951,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45947,c_28466]) ).
tcf(c_45988,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X2,X0,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(superposition,[status(thm)],[c_45951,c_63]) ).
tcf(c_47934,plain,
! [X0: $i,X1: $i] : coll(X0,X1,X0),
inference(superposition,[status(thm)],[c_45178,c_50]) ).
tcf(c_49164,plain,
! [X0: $i,X1: $i] : coll(X0,X0,X1),
inference(superposition,[status(thm)],[c_47934,c_49]) ).
tcf(c_49229,plain,
! [X0: $i,X1: $i,X2: $i] : cyclic(X0,X1,X2,X1),
inference(backward_subsumption_resolution,[status(thm)],[c_45988,c_49164]) ).
tcf(c_51486,plain,
! [X0: $i,X1: $i,X2: $i] : cyclic(X0,X1,X2,X0),
inference(superposition,[status(thm)],[c_49229,c_64]) ).
tcf(c_52036,plain,
! [X0: $i,X1: $i,X2: $i] : cyclic(X0,X1,X0,X2),
inference(superposition,[status(thm)],[c_51486,c_62]) ).
tcf(c_52312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X0,X3,X2)
| ~ cyclic(X0,X1,X0,X2) ),
inference(superposition,[status(thm)],[c_52036,c_65]) ).
tcf(c_52316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[c_52312,c_52036]) ).
tcf(c_52317,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_162,c_52316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO643+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 12:40:35 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.40 Running first-order theorem proving
% 0.02/0.40 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
% 0.02/0.41
% 0.02/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.41
% 0.02/0.41 % Detected problem language: tptp
% 0.02/0.42 % Proving...
% 31.57/9.23 % SZS status Started for theBenchmark.p
% 31.57/9.23 % SZS status Theorem for theBenchmark.p
% 31.57/9.23
% 31.57/9.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.57/9.23
% 31.57/9.23 % ------ iProver source info
% 31.57/9.23
% 31.57/9.23 % git: date: 2026-07-19 20:42:38 +0200
% 31.57/9.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.57/9.23 % git: non_committed_changes: false
% 31.57/9.23
% 31.57/9.23 % ------ Parsing...
% 31.57/9.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.57/9.23
% 31.57/9.23 % ------ 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 %
% 31.57/9.23
% 31.57/9.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.57/9.23
% 31.57/9.23 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.57/9.23 % ------ Proving...
% 31.57/9.23 % ------ Problem Properties
% 31.57/9.23
% 31.57/9.23 %
% 31.57/9.23 % clauses 121
% 31.57/9.23 % conjectures 9
% 31.57/9.23 % EPR 84
% 31.57/9.23 % Horn 111
% 31.57/9.23 % unary 9
% 31.57/9.23 % binary 37
% 31.57/9.23 % lits 337
% 31.57/9.23 % lits eq 4
% 31.57/9.23 % fd_pure 0
% 31.57/9.23 % fd_pseudo 0
% 31.57/9.23 % fd_cond 0
% 31.57/9.23 % fd_pseudo_cond 4
% 31.57/9.23 % AC symbols 0
% 31.57/9.23
% 31.57/9.23 % ------ Input Options Time Limit: Unbounded
% 31.57/9.23
% 31.57/9.23
% 31.57/9.23 % ------
% 31.57/9.23 % Current options:
% 31.57/9.23 % ------
% 31.57/9.23
% 31.57/9.23
% 31.57/9.23 %
% 31.57/9.23
% 31.57/9.23 % ------ Proving...
% 31.57/9.23 %
% 31.57/9.23
% 31.57/9.23 % SZS status Theorem for theBenchmark.p
% 31.57/9.23
% 31.57/9.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.57/9.23
% 31.57/9.23
%------------------------------------------------------------------------------