%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO641+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 : n006.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 34.63s 6.58s
% Output : CNFRefutation 34.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 137 ( 19 unt; 0 def)
% Number of atoms : 357 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 382 ( 162 ~; 156 |; 48 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 400 ( 0 sgn 384 !; 16 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD43) ).
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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
fof(f65,axiom,
! [X0,X1,X2,X3,X4] :
( ( para(X0,X3,X1,X2)
& para(X0,X2,X1,X3)
& midp(X4,X0,X1) )
=> midp(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
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(f68,axiom,
! [X0,X1,X2] :
( ( coll(X0,X1,X2)
& cong(X0,X1,X0,X2) )
=> midp(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD67) ).
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(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(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( perp(X2,X4,X0,X6)
& perp(X0,X4,X2,X6)
& perp(X0,X2,X4,X6)
& perp(X1,X4,X0,X5)
& perp(X0,X4,X1,X5)
& perp(X0,X1,X4,X5)
& circle(X3,X0,X4,X7)
& circle(X3,X0,X1,X2) )
=> para(X5,X6,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL81109107) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( perp(X2,X4,X0,X6)
& perp(X0,X4,X2,X6)
& perp(X0,X2,X4,X6)
& perp(X1,X4,X0,X5)
& perp(X0,X4,X1,X5)
& perp(X0,X1,X4,X5)
& circle(X3,X0,X4,X7)
& circle(X3,X0,X1,X2) )
=> para(X5,X6,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( perp(X2,X4,X0,X6)
& perp(X0,X4,X2,X6)
& perp(X0,X2,X4,X6)
& perp(X1,X4,X0,X5)
& perp(X0,X4,X1,X5)
& perp(X0,X1,X4,X5)
& circle(X3,X0,X4,X7)
& circle(X3,X0,X1,X2)
& ~ para(X5,X6,X1,X2) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( perp(X2,X4,X0,X6)
& perp(X0,X4,X2,X6)
& perp(X0,X2,X4,X6)
& perp(X1,X4,X0,X5)
& perp(X0,X4,X1,X5)
& perp(X0,X1,X4,X5)
& circle(X3,X0,X4,X7)
& circle(X3,X0,X1,X2)
& ~ para(X5,X6,X1,X2) ),
inference(flattening,[],[f98]) ).
fof(f108,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(f109,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,[],[f108]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f67]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4] :
( ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1)
| midp(X4,X2,X3) ),
inference(ennf_transformation,[],[f65]) ).
fof(f116,plain,
! [X0,X1,X2,X3,X4] :
( ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1)
| midp(X4,X2,X3) ),
inference(flattening,[],[f115]) ).
fof(f123,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(f127,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(f128,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f127]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f149,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(f150,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f149]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(ennf_transformation,[],[f68]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(flattening,[],[f179]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f196,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(f198,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(f206,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(f207,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,[],[f206]) ).
fof(f208,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(f209,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,[],[f208]) ).
fof(f220,plain,
( perp(sK2,sK4,sK0,sK6)
& perp(sK0,sK4,sK2,sK6)
& perp(sK0,sK2,sK4,sK6)
& perp(sK1,sK4,sK0,sK5)
& perp(sK0,sK4,sK1,sK5)
& perp(sK0,sK1,sK4,sK5)
& circle(sK3,sK0,sK4,sK7)
& circle(sK3,sK0,sK1,sK2)
& ~ para(sK5,sK6,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f99]) ).
fof(f239,plain,
perp(sK2,sK4,sK0,sK6),
inference(cnf_transformation,[],[f220]) ).
fof(f241,plain,
perp(sK0,sK2,sK4,sK6),
inference(cnf_transformation,[],[f220]) ).
fof(f242,plain,
perp(sK1,sK4,sK0,sK5),
inference(cnf_transformation,[],[f220]) ).
fof(f244,plain,
perp(sK0,sK1,sK4,sK5),
inference(cnf_transformation,[],[f220]) ).
fof(f247,plain,
~ para(sK5,sK6,sK1,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f258,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,[],[f109]) ).
fof(f261,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f262,plain,
! [X2,X3,X0,X1,X4] :
( ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1)
| midp(X4,X2,X3) ),
inference(cnf_transformation,[],[f116]) ).
fof(f266,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f123]) ).
fof(f269,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,[],[f128]) ).
fof(f271,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f289,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f150]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f307,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f180]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f187]) ).
fof(f319,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,[],[f196]) ).
fof(f321,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,[],[f198]) ).
fof(f327,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,[],[f207]) ).
fof(f328,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,[],[f209]) ).
tcf(c_49,negated_conjecture,
~ para(sK5,sK6,sK1,sK2),
inference(cnf_transformation,[],[f247]) ).
tcf(c_52,negated_conjecture,
perp(sK0,sK1,sK4,sK5),
inference(cnf_transformation,[],[f244]) ).
tcf(c_54,negated_conjecture,
perp(sK1,sK4,sK0,sK5),
inference(cnf_transformation,[],[f242]) ).
tcf(c_55,negated_conjecture,
perp(sK0,sK2,sK4,sK6),
inference(cnf_transformation,[],[f241]) ).
tcf(c_57,negated_conjecture,
perp(sK2,sK4,sK0,sK6),
inference(cnf_transformation,[],[f239]) ).
tcf(c_68,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,[],[f258]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f261]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( midp(X4,X1,X3)
| ~ midp(X4,X0,X2)
| ~ para(X0,X3,X2,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f262]) ).
tcf(c_76,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,[],[f266]) ).
tcf(c_79,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,[],[f269]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_99,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,[],[f289]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_129,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,[],[f319]) ).
tcf(c_131,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,[],[f321]) ).
tcf(c_137,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,[],[f327]) ).
tcf(c_138,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,[],[f328]) ).
tcf(c_148,plain,
( coll(sK0,sK0,sK0)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_151,plain,
( midp(sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_154,plain,
( eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_163,plain,
( cyclic(sK0,sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_197,plain,
( cong(sK0,sK0,sK0,sK0)
| ~ cyclic(sK0,sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_2154,plain,
( perp(sK4,sK5,sK0,sK1)
| ~ perp(sK0,sK1,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_2250,plain,
! [X0: $i,X1: $i] :
( para(sK4,sK5,X0,X1)
| ~ perp(sK4,sK5,sK0,sK1)
| ~ perp(sK0,sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_2778,plain,
perp(sK4,sK5,sK0,sK1),
inference(superposition,[status(thm)],[c_52,c_102]) ).
tcf(c_2780,plain,
perp(sK0,sK5,sK1,sK4),
inference(superposition,[status(thm)],[c_54,c_102]) ).
tcf(c_2781,plain,
perp(sK4,sK6,sK0,sK2),
inference(superposition,[status(thm)],[c_55,c_102]) ).
tcf(c_2783,plain,
perp(sK0,sK6,sK2,sK4),
inference(superposition,[status(thm)],[c_57,c_102]) ).
tcf(c_4145,plain,
( para(sK5,sK6,sK1,sK2)
| ~ para(sK1,sK2,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_4544,plain,
( para(sK4,sK5,sK4,sK5)
| ~ perp(sK4,sK5,sK0,sK1)
| ~ perp(sK0,sK1,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_2250]) ).
tcf(c_5173,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK0,sK5)
| ~ perp(X0,X1,sK1,sK4) ),
inference(superposition,[status(thm)],[c_54,c_79]) ).
tcf(c_5176,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK0,sK6)
| ~ perp(X0,X1,sK2,sK4) ),
inference(superposition,[status(thm)],[c_57,c_79]) ).
tcf(c_5178,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK0,sK1)
| ~ perp(X0,X1,sK4,sK5) ),
inference(superposition,[status(thm)],[c_2778,c_79]) ).
tcf(c_5181,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK0,sK2)
| ~ perp(X0,X1,sK4,sK6) ),
inference(superposition,[status(thm)],[c_2781,c_79]) ).
tcf(c_6542,plain,
para(sK0,sK5,sK0,sK5),
inference(superposition,[status(thm)],[c_2780,c_5173]) ).
tcf(c_6816,plain,
para(sK0,sK6,sK0,sK6),
inference(superposition,[status(thm)],[c_2783,c_5176]) ).
tcf(c_6935,plain,
! [X0: $i,X1: $i] :
( eqangle(sK4,sK5,X0,X1,sK4,sK5,X0,X1)
| ~ para(sK4,sK5,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_6936,plain,
( eqangle(sK4,sK5,sK0,sK0,sK4,sK5,sK0,sK0)
| ~ para(sK4,sK5,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_6935]) ).
tcf(c_11060,plain,
! [X0: $i,X1: $i] :
( eqangle(X0,X1,sK4,sK5,X0,X1,sK4,sK5)
| ~ eqangle(sK4,sK5,X0,X1,sK4,sK5,X0,X1) ),
inference(instantiation,[status(thm)],[c_131]) ).
tcf(c_11064,plain,
( eqangle(sK0,sK0,sK4,sK5,sK0,sK0,sK4,sK5)
| ~ eqangle(sK4,sK5,sK0,sK0,sK4,sK5,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_11060]) ).
tcf(c_12583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X2,X3)
| ~ para(sK4,sK5,sK4,sK5)
| ~ eqangle(X0,X1,X2,X3,sK4,sK5,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_12584,plain,
( para(sK0,sK0,sK0,sK0)
| ~ para(sK4,sK5,sK4,sK5)
| ~ eqangle(sK0,sK0,sK0,sK0,sK4,sK5,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_12583]) ).
tcf(c_13367,plain,
para(sK0,sK1,sK0,sK1),
inference(superposition,[status(thm)],[c_52,c_5178]) ).
tcf(c_14833,plain,
! [X0: $i] :
( midp(X0,sK1,sK1)
| ~ midp(X0,sK0,sK0)
| ~ para(sK0,sK1,sK0,sK1) ),
inference(superposition,[status(thm)],[c_13367,c_72]) ).
tcf(c_14842,plain,
! [X0: $i] :
( midp(X0,sK5,sK5)
| ~ midp(X0,sK0,sK0)
| ~ para(sK0,sK5,sK0,sK5) ),
inference(superposition,[status(thm)],[c_6542,c_72]) ).
tcf(c_14846,plain,
! [X0: $i] :
( midp(X0,sK6,sK6)
| ~ midp(X0,sK0,sK0)
| ~ para(sK0,sK6,sK0,sK6) ),
inference(superposition,[status(thm)],[c_6816,c_72]) ).
tcf(c_14893,plain,
! [X0: $i] :
( midp(X0,sK6,sK6)
| ~ midp(X0,sK0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14846,c_6816]) ).
tcf(c_14905,plain,
! [X0: $i] :
( midp(X0,sK5,sK5)
| ~ midp(X0,sK0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14842,c_6542]) ).
tcf(c_14932,plain,
! [X0: $i] :
( midp(X0,sK1,sK1)
| ~ midp(X0,sK0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14833,c_13367]) ).
tcf(c_14985,plain,
( midp(sK0,sK1,sK1)
| ~ midp(sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_14932]) ).
tcf(c_14990,plain,
( midp(sK0,sK5,sK5)
| ~ midp(sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_14905]) ).
tcf(c_14993,plain,
( midp(sK0,sK6,sK6)
| ~ midp(sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_14893]) ).
tcf(c_16355,plain,
para(sK0,sK2,sK0,sK2),
inference(superposition,[status(thm)],[c_55,c_5181]) ).
tcf(c_16432,plain,
! [X0: $i] :
( midp(X0,sK2,sK2)
| ~ midp(X0,sK0,sK0)
| ~ para(sK0,sK2,sK0,sK2) ),
inference(superposition,[status(thm)],[c_16355,c_72]) ).
tcf(c_16441,plain,
! [X0: $i] :
( midp(X0,sK2,sK2)
| ~ midp(X0,sK0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16432,c_16355]) ).
tcf(c_16444,plain,
( midp(sK0,sK2,sK2)
| ~ midp(sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_16441]) ).
tcf(c_21871,plain,
! [X0: $i,X1: $i] :
( para(sK1,sK2,sK5,sK6)
| ~ perp(sK1,sK2,X0,X1)
| ~ perp(X0,X1,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_21872,plain,
( para(sK1,sK2,sK5,sK6)
| ~ perp(sK0,sK0,sK5,sK6)
| ~ perp(sK1,sK2,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_21871]) ).
tcf(c_22577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,X1,X2,X3,sK4,sK5,sK4,sK5)
| ~ eqangle(X0,X1,sK4,sK5,X2,X3,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_22578,plain,
( eqangle(sK0,sK0,sK0,sK0,sK4,sK5,sK4,sK5)
| ~ eqangle(sK0,sK0,sK4,sK5,sK0,sK0,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_22577]) ).
tcf(c_32472,plain,
! [X0: $i,X1: $i] :
( perp(sK1,sK2,X0,X1)
| ~ perp(X0,X1,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_32473,plain,
( perp(sK1,sK2,sK0,sK0)
| ~ perp(sK0,sK0,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_32472]) ).
tcf(c_34613,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,sK1,sK2)
| ~ cong(X0,sK2,X1,sK2)
| ~ cong(X0,sK1,X1,sK1) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_34614,plain,
( perp(sK0,sK0,sK1,sK2)
| ~ cong(sK0,sK2,sK0,sK2)
| ~ cong(sK0,sK1,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_34613]) ).
tcf(c_34639,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,sK5,sK6)
| ~ cong(X0,sK6,X1,sK6)
| ~ cong(X0,sK5,X1,sK5) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_34640,plain,
( perp(sK0,sK0,sK5,sK6)
| ~ cong(sK0,sK6,sK0,sK6)
| ~ cong(sK0,sK5,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_34639]) ).
tcf(c_36454,plain,
! [X0: $i] :
( cong(X0,sK1,X0,sK1)
| ~ midp(X0,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_36455,plain,
( cong(sK0,sK1,sK0,sK1)
| ~ midp(sK0,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_36454]) ).
tcf(c_43040,plain,
! [X0: $i] :
( cong(X0,sK2,X0,sK2)
| ~ midp(X0,sK2,sK2) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_43041,plain,
( cong(sK0,sK2,sK0,sK2)
| ~ midp(sK0,sK2,sK2) ),
inference(instantiation,[status(thm)],[c_43040]) ).
tcf(c_58456,plain,
! [X0: $i] :
( cong(X0,sK5,X0,sK5)
| ~ midp(X0,sK5,sK5) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_58457,plain,
( cong(sK0,sK5,sK0,sK5)
| ~ midp(sK0,sK5,sK5) ),
inference(instantiation,[status(thm)],[c_58456]) ).
tcf(c_61515,plain,
! [X0: $i,X1: $i] :
( cong(X0,sK6,X0,X1)
| ~ midp(X0,sK6,X1) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_71762,plain,
! [X0: $i] :
( cong(X0,sK6,X0,sK6)
| ~ midp(X0,sK6,sK6) ),
inference(instantiation,[status(thm)],[c_61515]) ).
tcf(c_71764,plain,
( cong(sK0,sK6,sK0,sK6)
| ~ midp(sK0,sK6,sK6) ),
inference(instantiation,[status(thm)],[c_71762]) ).
tcf(c_71765,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_71764,c_58457,c_43041,c_36455,c_34640,c_34614,c_32473,c_22578,c_21872,c_16444,c_14993,c_14990,c_14985,c_12584,c_11064,c_6936,c_4544,c_4145,c_2154,c_197,c_163,c_154,c_151,c_148,c_49,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO641+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.46 % Computer : n006.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Wed Sep 23 12:38:16 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.47 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 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
% 0.23/0.55
% 0.23/0.55 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.55
% 0.23/0.55 % Detected problem language: tptp
% 0.23/0.57 % Proving...
% 34.63/6.58 % SZS status Started for theBenchmark.p
% 34.63/6.58 % SZS status Theorem for theBenchmark.p
% 34.63/6.58
% 34.63/6.58 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 34.63/6.58
% 34.63/6.58 % ------ iProver source info
% 34.63/6.58
% 34.63/6.58 % git: date: 2026-07-19 20:42:38 +0200
% 34.63/6.58 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 34.63/6.58 % git: non_committed_changes: false
% 34.63/6.58
% 34.63/6.58 % ------ Parsing...
% 34.63/6.58 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 34.63/6.58
% 34.63/6.58 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 34.63/6.58
% 34.63/6.58 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 34.63/6.58 % ------ Proving...
% 34.63/6.58 % ------ Problem Properties
% 34.63/6.58
% 34.63/6.58 %
% 34.63/6.58 % clauses 96
% 34.63/6.58 % conjectures 9
% 34.63/6.58 % EPR 63
% 34.63/6.58 % Horn 91
% 34.63/6.58 % unary 9
% 34.63/6.58 % binary 24
% 34.63/6.58 % lits 265
% 34.63/6.58 % lits eq 0
% 34.63/6.58 % fd_pure 0
% 34.63/6.58 % fd_pseudo 0
% 34.63/6.58 % fd_cond 0
% 34.63/6.58 % fd_pseudo_cond 0
% 34.63/6.58 % AC symbols 0
% 34.63/6.58
% 34.63/6.58 % ------ Schedule dynamic 5 is on
% 34.63/6.58
% 34.63/6.58 % ------ no equalities: superposition off
% 34.63/6.58
% 34.63/6.58 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 34.63/6.58
% 34.63/6.58
% 34.63/6.58 % ------
% 34.63/6.58 % Current options:
% 34.63/6.58 % ------
% 34.63/6.58
% 34.63/6.58
% 34.63/6.58 %
% 34.63/6.58
% 34.63/6.58 % ------ Proving...
% 34.63/6.58 %
% 34.63/6.58
% 34.63/6.58 % SZS status Theorem for theBenchmark.p
% 34.63/6.58
% 34.63/6.58 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.63/6.58
% 34.63/6.58
%------------------------------------------------------------------------------