%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO637+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 01:21:43 PM UTC 2026
% Result : Theorem 22.51s 4.29s
% Output : CNFRefutation 22.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 156 ( 14 unt; 0 def)
% Number of atoms : 390 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 406 ( 172 ~; 166 |; 47 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 493 ( 0 sgn 473 !; 20 ?; 146 :)
% 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(f4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD4) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD5) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/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(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(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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD21) ).
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(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(f64,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X2,X3)
& midp(X4,X0,X1) )
=> para(X0,X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD63) ).
fof(f67,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD66) ).
fof(f74,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( para(X4,X5,X6,X7)
& eqangle(X0,X1,X2,X3,X4,X5,X6,X7) )
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD73) ).
fof(f86,axiom,
! [X0,X1,X2,X3] :
? [X4,X5] :
( ( perp(X1,X3,X0,X2)
& perp(X0,X3,X1,X2) )
=> ( perp(X1,X5,X2,X0)
& coll(X5,X2,X0)
& perp(X0,X4,X2,X1)
& coll(X4,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleX10) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( perp(X0,X3,X0,X6)
& perp(X2,X3,X2,X6)
& coll(X5,X0,X1)
& coll(X5,X3,X4)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2) )
=> cyclic(X0,X3,X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL81109101) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( perp(X0,X3,X0,X6)
& perp(X2,X3,X2,X6)
& coll(X5,X0,X1)
& coll(X5,X3,X4)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2) )
=> cyclic(X0,X3,X6,X5) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( perp(X0,X3,X0,X6)
& perp(X2,X3,X2,X6)
& coll(X5,X0,X1)
& coll(X5,X3,X4)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2)
& ~ cyclic(X0,X3,X6,X5) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( perp(X0,X3,X0,X6)
& perp(X2,X3,X2,X6)
& coll(X5,X0,X1)
& coll(X5,X3,X4)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2)
& ~ cyclic(X0,X3,X6,X5) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
? [X4,X5] :
( ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2)
| ( perp(X1,X5,X2,X0)
& coll(X5,X2,X0)
& perp(X0,X4,X2,X1)
& coll(X4,X2,X1) ) ),
inference(ennf_transformation,[],[f86]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
? [X4,X5] :
( ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2)
| ( perp(X1,X5,X2,X0)
& coll(X5,X2,X0)
& perp(X0,X4,X2,X1)
& coll(X4,X2,X1) ) ),
inference(flattening,[],[f106]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f67]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f150,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(f151,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f150]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(ennf_transformation,[],[f64]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(flattening,[],[f159]) ).
fof(f189,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(f190,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,[],[f189]) ).
fof(f194,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(f195,plain,
! [X0,X1,X2,X3,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(flattening,[],[f194]) ).
fof(f197,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(ennf_transformation,[],[f15]) ).
fof(f198,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f201,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f74]) ).
fof(f202,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| para(X0,X1,X2,X3) ),
inference(flattening,[],[f201]) ).
fof(f203,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(f207,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f208,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f216,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(f218,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(f220,plain,
( perp(sK0,sK3,sK0,sK6)
& perp(sK2,sK3,sK2,sK6)
& coll(sK5,sK0,sK1)
& coll(sK5,sK3,sK4)
& midp(sK4,sK2,sK1)
& circle(sK3,sK0,sK1,sK2)
& ~ cyclic(sK0,sK3,sK6,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f99]) ).
fof(f224,plain,
! [X0,X1,X2,X3] :
( ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2)
| ( perp(X1,sK11(X0,X1,X2,X3),X2,X0)
& coll(sK11(X0,X1,X2,X3),X2,X0)
& perp(X0,sK10(X0,X1,X2,X3),X2,X1)
& coll(sK10(X0,X1,X2,X3),X2,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X4,sK10(X0,X1,X2,X3)),skolemize(X5,sK11(X0,X1,X2,X3))],[f107]) ).
fof(f239,plain,
perp(sK0,sK3,sK0,sK6),
inference(cnf_transformation,[],[f220]) ).
fof(f241,plain,
coll(sK5,sK0,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f243,plain,
midp(sK4,sK2,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f245,plain,
~ cyclic(sK0,sK3,sK6,sK5),
inference(cnf_transformation,[],[f220]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2)
| coll(sK10(X0,X1,X2,X3),X2,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f269,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f272,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f273,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f286,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,[],[f151]) ).
fof(f287,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f288,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f153]) ).
fof(f294,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f160]) ).
fof(f311,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,[],[f190]) ).
fof(f314,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f195]) ).
fof(f316,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f197]) ).
fof(f317,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f198]) ).
fof(f319,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f202]) ).
fof(f320,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f203]) ).
fof(f323,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
fof(f324,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f208]) ).
fof(f330,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,[],[f216]) ).
fof(f332,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,[],[f218]) ).
tcf(c_49,negated_conjecture,
~ cyclic(sK0,sK3,sK6,sK5),
inference(cnf_transformation,[],[f245]) ).
tcf(c_51,negated_conjecture,
midp(sK4,sK2,sK1),
inference(cnf_transformation,[],[f243]) ).
tcf(c_53,negated_conjecture,
coll(sK5,sK0,sK1),
inference(cnf_transformation,[],[f241]) ).
tcf(c_55,negated_conjecture,
perp(sK0,sK3,sK0,sK6),
inference(cnf_transformation,[],[f239]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(sK10(X0,X2,X3,X1),X3,X2)
| ~ perp(X2,X1,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_96,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,[],[f286]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_121,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,[],[f311]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f316]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f317]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f319]) ).
tcf(c_130,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,[],[f320]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f324]) ).
tcf(c_140,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,[],[f330]) ).
tcf(c_142,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,[],[f332]) ).
tcf(c_2036,plain,
( coll(sK5,sK1,sK0)
| ~ coll(sK5,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_2049,plain,
! [X0: $i,X1: $i] :
( para(sK2,X0,sK1,X1)
| ~ midp(sK4,sK2,sK1)
| ~ midp(sK4,X0,X1) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_2077,plain,
( coll(sK10(sK0,sK0,sK6,sK3),sK6,sK0)
| ~ perp(sK0,sK3,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_2224,plain,
! [X0: $i] :
( coll(sK0,X0,sK5)
| ~ coll(sK5,sK1,sK0)
| ~ coll(sK5,sK1,X0) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2227,plain,
( coll(sK0,sK0,sK5)
| ~ coll(sK5,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_2224]) ).
tcf(c_2404,plain,
( coll(sK6,sK10(sK0,sK0,sK6,sK3),sK0)
| ~ coll(sK10(sK0,sK0,sK6,sK3),sK6,sK0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2512,plain,
( para(sK2,sK2,sK1,sK1)
| ~ midp(sK4,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_2049]) ).
tcf(c_2572,plain,
! [X0: $i,X1: $i] :
( eqangle(sK2,sK2,X0,X1,sK1,sK1,X0,X1)
| ~ para(sK2,sK2,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_2575,plain,
( eqangle(sK2,sK2,sK0,sK0,sK1,sK1,sK0,sK0)
| ~ para(sK2,sK2,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_2572]) ).
tcf(c_2577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X2,X3)
| ~ para(sK2,sK2,sK1,sK1)
| ~ eqangle(X0,X1,X2,X3,sK2,sK2,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_2578,plain,
( para(sK0,sK0,sK0,sK0)
| ~ para(sK2,sK2,sK1,sK1)
| ~ eqangle(sK0,sK0,sK0,sK0,sK2,sK2,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_2577]) ).
tcf(c_3962,plain,
! [X0: $i] :
( coll(sK0,X0,sK6)
| ~ coll(sK6,sK10(sK0,sK0,sK6,sK3),sK0)
| ~ coll(sK6,sK10(sK0,sK0,sK6,sK3),X0) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_3965,plain,
( coll(sK0,sK0,sK6)
| ~ coll(sK6,sK10(sK0,sK0,sK6,sK3),sK0) ),
inference(instantiation,[status(thm)],[c_3962]) ).
tcf(c_4264,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,sK5,sK0,X1)
| ~ coll(sK0,X1,sK5)
| ~ eqangle(sK0,X0,sK0,sK5,X1,X0,X1,sK5) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_4265,plain,
( cyclic(sK0,sK5,sK0,sK0)
| ~ coll(sK0,sK0,sK5)
| ~ eqangle(sK0,sK0,sK0,sK5,sK0,sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_4264]) ).
tcf(c_7391,plain,
! [X0: $i,X1: $i] :
( eqangle(X0,X1,sK2,sK2,X0,X1,sK1,sK1)
| ~ eqangle(sK2,sK2,X0,X1,sK1,sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_142]) ).
tcf(c_7396,plain,
( eqangle(sK0,sK0,sK2,sK2,sK0,sK0,sK1,sK1)
| ~ eqangle(sK2,sK2,sK0,sK0,sK1,sK1,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_7391]) ).
tcf(c_9424,plain,
! [X0: $i,X1: $i] :
( coll(sK3,X0,X1)
| ~ para(sK3,X0,sK3,X1) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_9425,plain,
( coll(sK3,sK0,sK0)
| ~ para(sK3,sK0,sK3,sK0) ),
inference(instantiation,[status(thm)],[c_9424]) ).
tcf(c_11073,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X2,sK3)
| ~ coll(sK3,X0,X2)
| ~ coll(sK3,X0,X1) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_11074,plain,
( coll(sK0,sK0,sK3)
| ~ coll(sK3,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_11073]) ).
tcf(c_25266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,X1,X2,X3,sK2,sK2,sK1,sK1)
| ~ eqangle(X0,X1,sK2,sK2,X2,X3,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_25267,plain,
( eqangle(sK0,sK0,sK0,sK0,sK2,sK2,sK1,sK1)
| ~ eqangle(sK0,sK0,sK2,sK2,sK0,sK0,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_25266]) ).
tcf(c_26798,plain,
perp(sK0,sK6,sK0,sK3),
inference(superposition,[status(thm)],[c_55,c_97]) ).
tcf(c_26876,plain,
perp(sK0,sK6,sK3,sK0),
inference(superposition,[status(thm)],[c_26798,c_98]) ).
tcf(c_27937,plain,
! [X0: $i,X1: $i] :
( para(sK0,sK3,X0,X1)
| ~ perp(sK0,sK6,X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_96]) ).
tcf(c_28116,plain,
para(sK0,sK3,sK3,sK0),
inference(superposition,[status(thm)],[c_26876,c_27937]) ).
tcf(c_28138,plain,
para(sK3,sK0,sK0,sK3),
inference(superposition,[status(thm)],[c_28116,c_133]) ).
tcf(c_28374,plain,
para(sK3,sK0,sK3,sK0),
inference(superposition,[status(thm)],[c_28138,c_134]) ).
tcf(c_38363,plain,
! [X0: $i] :
( cyclic(sK0,sK3,sK6,sK5)
| ~ cyclic(X0,sK0,sK3,sK5)
| ~ cyclic(X0,sK0,sK3,sK6) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_38364,plain,
( cyclic(sK0,sK3,sK6,sK5)
| ~ cyclic(sK0,sK0,sK3,sK5)
| ~ cyclic(sK0,sK0,sK3,sK6) ),
inference(instantiation,[status(thm)],[c_38363]) ).
tcf(c_40584,plain,
! [X0: $i] :
( cyclic(X0,sK0,sK3,sK6)
| ~ coll(sK3,sK6,sK0)
| ~ eqangle(sK3,X0,sK3,sK0,sK6,X0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_40585,plain,
( cyclic(sK0,sK0,sK3,sK6)
| ~ coll(sK3,sK6,sK0)
| ~ eqangle(sK3,sK0,sK3,sK0,sK6,sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_40584]) ).
tcf(c_48358,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,X1,sK0,sK3)
| ~ cyclic(X0,X1,sK3,sK0) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_48359,plain,
( cyclic(sK0,sK0,sK0,sK3)
| ~ cyclic(sK0,sK0,sK3,sK0) ),
inference(instantiation,[status(thm)],[c_48358]) ).
tcf(c_51458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,X1,sK0,sK3,X2,X3,sK0,sK3)
| ~ para(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_51459,plain,
( eqangle(sK0,sK0,sK0,sK3,sK0,sK0,sK0,sK3)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_51458]) ).
tcf(c_51841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,X1,X1,sK5,X2,X3,X1,sK5)
| ~ para(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_51842,plain,
( eqangle(sK0,sK0,sK0,sK5,sK0,sK0,sK0,sK5)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_51841]) ).
tcf(c_61383,plain,
! [X0: $i] :
( coll(sK3,sK6,sK0)
| ~ coll(sK0,X0,sK6)
| ~ coll(sK0,X0,sK3) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_61384,plain,
( coll(sK3,sK6,sK0)
| ~ coll(sK0,sK0,sK6)
| ~ coll(sK0,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_61383]) ).
tcf(c_61795,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,sK0,X2,sK3)
| ~ cyclic(X0,X1,sK0,sK3)
| ~ cyclic(X0,X1,sK0,X2) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_62217,plain,
! [X0: $i] :
( eqangle(sK3,X0,sK3,sK0,sK6,X0,sK6,sK0)
| ~ eqangle(sK3,X0,sK6,X0,sK3,sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_62218,plain,
( eqangle(sK3,sK0,sK3,sK0,sK6,sK0,sK6,sK0)
| ~ eqangle(sK3,sK0,sK6,sK0,sK3,sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_62217]) ).
tcf(c_62864,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,X1,sK3,sK0)
| ~ cyclic(X0,sK3,X1,sK0) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_62865,plain,
( cyclic(sK0,sK0,sK3,sK0)
| ~ cyclic(sK0,sK3,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_62864]) ).
tcf(c_62977,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,sK0,sK3,X1)
| ~ cyclic(X0,sK0,X1,sK3) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_64533,plain,
! [X0: $i,X1: $i] :
( cyclic(X1,sK3,X0,sK0)
| ~ coll(X0,sK0,sK3)
| ~ eqangle(X0,X1,X0,sK3,sK0,X1,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_64534,plain,
( cyclic(sK0,sK3,sK0,sK0)
| ~ coll(sK0,sK0,sK3)
| ~ eqangle(sK0,sK0,sK0,sK3,sK0,sK0,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_64533]) ).
tcf(c_65120,plain,
( eqangle(sK3,sK0,sK6,sK0,sK3,sK0,sK6,sK0)
| ~ para(sK3,sK0,sK3,sK0) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_66105,plain,
! [X0: $i,X1: $i] :
( cyclic(X1,sK0,sK5,sK3)
| ~ cyclic(X0,X1,sK0,sK5)
| ~ cyclic(X0,X1,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_61795]) ).
tcf(c_66106,plain,
( cyclic(sK0,sK0,sK5,sK3)
| ~ cyclic(sK0,sK0,sK0,sK5)
| ~ cyclic(sK0,sK0,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_66105]) ).
tcf(c_67973,plain,
! [X0: $i] :
( cyclic(X0,sK0,sK3,sK5)
| ~ cyclic(X0,sK0,sK5,sK3) ),
inference(instantiation,[status(thm)],[c_62977]) ).
tcf(c_67974,plain,
( cyclic(sK0,sK0,sK3,sK5)
| ~ cyclic(sK0,sK0,sK5,sK3) ),
inference(instantiation,[status(thm)],[c_67973]) ).
tcf(c_70686,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,X1,sK0,sK5)
| ~ cyclic(X0,X1,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_70687,plain,
( cyclic(sK0,sK0,sK0,sK5)
| ~ cyclic(sK0,sK0,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_70686]) ).
tcf(c_78221,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,X1,sK5,sK0)
| ~ cyclic(X0,sK5,X1,sK0) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_78222,plain,
( cyclic(sK0,sK0,sK5,sK0)
| ~ cyclic(sK0,sK5,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_78221]) ).
tcf(c_78223,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_78222,c_70687,c_67974,c_66106,c_65120,c_64534,c_62865,c_62218,c_61384,c_51842,c_51459,c_48359,c_40585,c_38364,c_28374,c_25267,c_11074,c_9425,c_7396,c_4265,c_3965,c_2578,c_2575,c_2512,c_2404,c_2227,c_2077,c_2036,c_49,c_55,c_51,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO637+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 12:37:49 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 22.51/4.29 % SZS status Started for theBenchmark.p
% 22.51/4.29 % SZS status Theorem for theBenchmark.p
% 22.51/4.29
% 22.51/4.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.51/4.29
% 22.51/4.29 % ------ iProver source info
% 22.51/4.29
% 22.51/4.29 % git: date: 2026-07-19 20:42:38 +0200
% 22.51/4.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.51/4.29 % git: non_committed_changes: false
% 22.51/4.29
% 22.51/4.29 % ------ Parsing...
% 22.51/4.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.51/4.29
% 22.51/4.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 22.51/4.29
% 22.51/4.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 22.51/4.29 % ------ Proving...
% 22.51/4.29 % ------ Problem Properties
% 22.51/4.29
% 22.51/4.29 %
% 22.51/4.29 % clauses 94
% 22.51/4.29 % conjectures 7
% 22.51/4.29 % EPR 61
% 22.51/4.29 % Horn 89
% 22.51/4.29 % unary 7
% 22.51/4.29 % binary 24
% 22.51/4.29 % lits 263
% 22.51/4.29 % lits eq 0
% 22.51/4.29 % fd_pure 0
% 22.51/4.29 % fd_pseudo 0
% 22.51/4.29 % fd_cond 0
% 22.51/4.29 % fd_pseudo_cond 0
% 22.51/4.29 % AC symbols 0
% 22.51/4.29
% 22.51/4.29 % ------ Schedule dynamic 5 is on
% 22.51/4.29
% 22.51/4.29 % ------ no equalities: superposition off
% 22.51/4.29
% 22.51/4.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.51/4.29
% 22.51/4.29
% 22.51/4.29 % ------
% 22.51/4.29 % Current options:
% 22.51/4.29 % ------
% 22.51/4.29
% 22.51/4.29
% 22.51/4.29 %
% 22.51/4.29
% 22.51/4.29 % ------ Proving...
% 22.51/4.29 %
% 22.51/4.29
% 22.51/4.29 % SZS status Theorem for theBenchmark.p
% 22.51/4.29
% 22.51/4.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.51/4.29
% 22.51/4.29
%------------------------------------------------------------------------------