%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN067-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Thu Sep 24 03:15:07 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.60s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 82
% Syntax : Number of formulae : 304 ( 2 unt; 36 def)
% Number of atoms : 1459 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 2004 ( 849 ~;1119 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 39 ( 38 usr; 37 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-1 aty)
% Number of variables : 458 ( 458 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X7,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [X7,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [X7,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [X7,X2,X1] :
( big_p(f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [X7,X2,X1] :
( big_r(X1,f5(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [X7,X2,X1] :
( big_r(f5(X1),f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [X7,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [X7,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [X7,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
! [X7,X2,X1] :
( big_p(f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
! [X7,X2,X1] :
( big_r(X1,f5(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [X7,X2,X1] :
( big_r(f5(X1),f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
! [X7,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [X7,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
! [X7,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [X7,X2,X1] :
( big_p(f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
! [X7,X2,X1] :
( big_r(X1,f5(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
! [X7,X2,X1] :
( big_r(f5(X1),f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
! [X8,X7,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
! [X8,X7,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
! [X8,X7,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
! [X8,X7,X2,X1] :
( big_p(f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
! [X8,X7,X2,X1] :
( big_r(X1,f5(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
! [X8,X7,X2,X1] :
( big_r(f5(X1),f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
! [X8,X7,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X7,f1(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
! [X8,X7,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X7,f1(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
! [X8,X7,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X7,f1(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
! [X8,X7,X2,X1] :
( big_p(f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X7,f1(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X8,X7,X2,X1] :
( big_r(X1,f5(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X7,f1(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
! [X8,X7,X2,X1] :
( big_r(f5(X1),f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X7,f1(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
! [X8,X7,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
! [X8,X7,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
! [X8,X7,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X8,X7,X2,X1] :
( big_p(f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
! [X8,X7,X2,X1] :
( big_r(X1,f5(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
! [X8,X7,X2,X1] :
( big_r(f5(X1),f6(X1))
| ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X7),f2(X7))
| ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( big_p(a)
| big_p(a)
| big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( big_p(c3)
| ~ big_p(c4)
| big_p(c1)
| ~ big_p(c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( big_r(c4,c3)
| ~ big_p(c4)
| big_p(c1)
| ~ big_p(c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
! [X3,X4,X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(c4,X6)
| ~ big_p(X5)
| ~ big_r(X4,X3)
| ~ big_r(c4,X4)
| ~ big_p(X3)
| big_p(c1)
| ~ big_p(c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
( big_p(c3)
| ~ big_p(c4)
| big_r(c2,c1)
| ~ big_p(c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
( big_r(c4,c3)
| ~ big_p(c4)
| big_r(c2,c1)
| ~ big_p(c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
! [X3,X4,X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(c4,X6)
| ~ big_p(X5)
| ~ big_r(X4,X3)
| ~ big_r(c4,X4)
| ~ big_p(X3)
| big_r(c2,c1)
| ~ big_p(c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,negated_conjecture,
! [X9,X10] :
( big_p(c3)
| ~ big_p(c4)
| ~ big_r(X10,X9)
| ~ big_r(c2,X10)
| ~ big_p(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,negated_conjecture,
! [X9,X10] :
( big_r(c4,c3)
| ~ big_p(c4)
| ~ big_r(X10,X9)
| ~ big_r(c2,X10)
| ~ big_p(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,negated_conjecture,
! [X9,X10,X3,X4,X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(c4,X6)
| ~ big_p(X5)
| ~ big_r(X4,X3)
| ~ big_r(c4,X4)
| ~ big_p(X3)
| ~ big_r(X10,X9)
| ~ big_r(c2,X10)
| ~ big_p(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,plain,
! [X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f86,plain,
! [X0,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f88,plain,
! [X0,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f90,plain,
! [X0,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_p(f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [X1] :
( big_p(f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f92,plain,
! [X0,X1,X2] :
( big_p(f6(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_p(f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [X1] :
( big_r(X1,f5(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f94,plain,
! [X0,X1,X2] :
( big_r(X2,f5(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_p(f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
! [X1] :
( big_r(f5(X1),f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f96,plain,
! [X0,X1,X2] :
( big_r(f5(X2),f6(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_p(f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f98,plain,
! [X0,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X0,f1(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f100,plain,
! [X0,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X0,f1(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f102,plain,
! [X0,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(X0,f1(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [X1] :
( big_p(f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f104,plain,
! [X0,X1,X2] :
( big_p(f6(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_r(X0,f1(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
! [X1] :
( big_r(X1,f5(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f106,plain,
! [X0,X1,X2] :
( big_r(X2,f5(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_r(X0,f1(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
! [X1] :
( big_r(f5(X1),f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f108,plain,
! [X0,X1,X2] :
( big_r(f5(X2),f6(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_r(X0,f1(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f110,plain,
! [X0,X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X0),f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f112,plain,
! [X0,X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X0),f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f114,plain,
! [X0,X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| big_r(f1(X0),f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [X1] :
( big_p(f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f116,plain,
! [X0,X1,X2] :
( big_p(f6(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_r(f1(X0),f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X1] :
( big_r(X1,f5(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f118,plain,
! [X0,X1,X2] :
( big_r(X2,f5(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_r(f1(X0),f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
! [X1] :
( big_r(f5(X1),f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| big_p(X7)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f120,plain,
! [X0,X1,X2] :
( big_r(f5(X2),f6(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| big_r(f1(X0),f2(X0))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f122,plain,
! [X0,X1,X2] :
( big_p(f4(X2))
| big_p(X2)
| ~ big_p(a)
| big_p(f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f124,plain,
! [X0,X1,X2] :
( big_r(X2,f3(X2))
| big_p(X2)
| ~ big_p(a)
| big_p(f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f126,plain,
! [X0,X1,X2] :
( big_r(f3(X2),f4(X2))
| big_p(X2)
| ~ big_p(a)
| big_p(f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [X1] :
( big_p(f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( big_p(f6(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X1] :
( big_r(X1,f5(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f130,plain,
! [X0,X1,X2,X3] :
( big_r(X3,f5(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [X1] :
( big_r(f5(X1),f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_p(f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( big_r(f5(X3),f6(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_p(f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f134,plain,
! [X0,X1,X2] :
( big_p(f4(X2))
| big_p(X2)
| ~ big_p(a)
| big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f136,plain,
! [X0,X1,X2] :
( big_r(X2,f3(X2))
| big_p(X2)
| ~ big_p(a)
| big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f138,plain,
! [X0,X1,X2] :
( big_r(f3(X2),f4(X2))
| big_p(X2)
| ~ big_p(a)
| big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [X1] :
( big_p(f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( big_p(f6(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [X1] :
( big_r(X1,f5(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f142,plain,
! [X0,X1,X2,X3] :
( big_r(X3,f5(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [X1] :
( big_r(f5(X1),f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(X7,f1(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( big_r(f5(X3),f6(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [X1] :
( big_p(f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f146,plain,
! [X0,X1,X2] :
( big_p(f4(X2))
| big_p(X2)
| ~ big_p(a)
| big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [X1] :
( big_r(X1,f3(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f148,plain,
! [X0,X1,X2] :
( big_r(X2,f3(X2))
| big_p(X2)
| ~ big_p(a)
| big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f149,plain,
! [X1] :
( big_r(f3(X1),f4(X1))
| big_p(X1)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f150,plain,
! [X0,X1,X2] :
( big_r(f3(X2),f4(X2))
| big_p(X2)
| ~ big_p(a)
| big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f151,plain,
! [X1] :
( big_p(f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( big_p(f6(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
! [X1] :
( big_r(X1,f5(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( big_r(X3,f5(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
! [X1] :
( big_r(f5(X1),f6(X1))
| ! [X2] :
( ~ big_r(X1,X2)
| ~ big_p(X2)
| ~ big_p(a)
| ! [X7] :
( big_r(f1(X7),f2(X7))
| ! [X8] :
( ~ big_r(X7,X8)
| ~ big_p(X8)
| ~ big_p(a) ) ) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( big_r(f5(X3),f6(X3))
| ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_p(a)
| big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
( big_p(a)
| big_p(a)
| big_p(a) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f178,plain,
( big_p(c3)
| ~ big_p(c4)
| big_p(c1)
| ~ big_p(c2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f179,plain,
( big_r(c4,c3)
| ~ big_p(c4)
| big_p(c1)
| ~ big_p(c2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f187,plain,
! [X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(c4,X6)
| ~ big_p(X5)
| ! [X3,X4] :
( ~ big_r(X4,X3)
| ~ big_r(c4,X4)
| ~ big_p(X3)
| big_p(c1)
| ~ big_p(c2) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( ~ big_r(X3,X2)
| ~ big_r(c4,X3)
| ~ big_p(X2)
| ~ big_r(X1,X0)
| ~ big_r(c4,X1)
| ~ big_p(X0)
| big_p(c1)
| ~ big_p(c2) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f194,plain,
( big_p(c3)
| ~ big_p(c4)
| big_r(c2,c1)
| ~ big_p(c2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f195,plain,
( big_r(c4,c3)
| ~ big_p(c4)
| big_r(c2,c1)
| ~ big_p(c2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f203,plain,
! [X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(c4,X6)
| ~ big_p(X5)
| ! [X3,X4] :
( ~ big_r(X4,X3)
| ~ big_r(c4,X4)
| ~ big_p(X3)
| big_r(c2,c1)
| ~ big_p(c2) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f204,plain,
! [X0,X1,X2,X3] :
( ~ big_r(X3,X2)
| ~ big_r(c4,X3)
| ~ big_p(X2)
| ~ big_r(X1,X0)
| ~ big_r(c4,X1)
| ~ big_p(X0)
| big_r(c2,c1)
| ~ big_p(c2) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f215,plain,
( big_p(c3)
| ~ big_p(c4)
| ! [X9,X10] :
( ~ big_r(X10,X9)
| ~ big_r(c2,X10)
| ~ big_p(X9) ) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f216,plain,
! [X0,X1] :
( big_p(c3)
| ~ big_p(c4)
| ~ big_r(X1,X0)
| ~ big_r(c2,X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
( big_r(c4,c3)
| ~ big_p(c4)
| ! [X9,X10] :
( ~ big_r(X10,X9)
| ~ big_r(c2,X10)
| ~ big_p(X9) ) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f218,plain,
! [X0,X1] :
( big_r(c4,c3)
| ~ big_p(c4)
| ~ big_r(X1,X0)
| ~ big_r(c2,X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f227,plain,
! [X5,X6] :
( ~ big_r(X6,X5)
| ~ big_r(c4,X6)
| ~ big_p(X5)
| ! [X3,X4] :
( ~ big_r(X4,X3)
| ~ big_r(c4,X4)
| ~ big_p(X3)
| ! [X9,X10] :
( ~ big_r(X10,X9)
| ~ big_r(c2,X10)
| ~ big_p(X9) ) ) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f228,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ big_r(X5,X4)
| ~ big_r(c4,X5)
| ~ big_p(X4)
| ~ big_r(X3,X2)
| ~ big_r(c4,X3)
| ~ big_p(X2)
| ~ big_r(X1,X0)
| ~ big_r(c2,X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f229,definition,
( sQ0_spl
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f232,definition,
! [X0] :
( sQ1_spl
<=> ( big_p(f2(X0))
| big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f233,plain,
! [X0] :
( ~ sQ1_spl
| big_p(f2(X0))
| big_p(X0) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,definition,
! [X1] :
( sQ2_spl
<=> ( big_p(f4(X1))
| big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f236,plain,
! [X0] :
( ~ sQ2_spl
| big_p(f4(X0))
| big_p(X0) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f229,f232,f235]) ).
fof(f239,definition,
! [X1] :
( sQ3_spl
<=> ( big_r(X1,f3(X1))
| big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f240,plain,
! [X0] :
( ~ sQ3_spl
| big_r(X0,f3(X0))
| big_p(X0) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( sQ3_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f88,f229,f232,f239]) ).
fof(f243,definition,
! [X1] :
( sQ4_spl
<=> ( big_r(f3(X1),f4(X1))
| big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f244,plain,
! [X0] :
( ~ sQ4_spl
| big_r(f3(X0),f4(X0))
| big_p(X0) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,plain,
( sQ4_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f90,f229,f232,f243]) ).
fof(f247,definition,
! [X1,X2] :
( sQ5_spl
<=> ( big_p(f6(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f248,plain,
! [X0,X1] :
( ~ sQ5_spl
| big_p(f6(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sQ5_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f92,f229,f232,f247]) ).
fof(f251,definition,
! [X1,X2] :
( sQ6_spl
<=> ( big_r(X2,f5(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f252,plain,
! [X0,X1] :
( ~ sQ6_spl
| big_r(X1,f5(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( sQ6_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f94,f229,f232,f251]) ).
fof(f255,definition,
! [X1,X2] :
( sQ7_spl
<=> ( big_r(f5(X2),f6(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f256,plain,
! [X0,X1] :
( ~ sQ7_spl
| big_r(f5(X1),f6(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( sQ7_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f96,f229,f232,f255]) ).
fof(f259,definition,
! [X0] :
( sQ8_spl
<=> ( big_r(X0,f1(X0))
| big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f260,plain,
! [X0] :
( ~ sQ8_spl
| big_r(X0,f1(X0))
| big_p(X0) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( sQ2_spl
| sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f98,f229,f259,f235]) ).
fof(f263,plain,
( sQ3_spl
| sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f100,f229,f259,f239]) ).
fof(f264,plain,
( sQ4_spl
| sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f102,f229,f259,f243]) ).
fof(f265,plain,
( sQ5_spl
| sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f104,f229,f259,f247]) ).
fof(f266,plain,
( sQ6_spl
| sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f106,f229,f259,f251]) ).
fof(f267,plain,
( sQ7_spl
| sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f108,f229,f259,f255]) ).
fof(f268,definition,
! [X0] :
( sQ9_spl
<=> ( big_r(f1(X0),f2(X0))
| big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f269,plain,
! [X0] :
( ~ sQ9_spl
| big_r(f1(X0),f2(X0))
| big_p(X0) ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,plain,
( sQ2_spl
| sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f110,f229,f268,f235]) ).
fof(f272,plain,
( sQ3_spl
| sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f112,f229,f268,f239]) ).
fof(f273,plain,
( sQ4_spl
| sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f114,f229,f268,f243]) ).
fof(f274,plain,
( sQ5_spl
| sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f116,f229,f268,f247]) ).
fof(f275,plain,
( sQ6_spl
| sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f118,f229,f268,f251]) ).
fof(f276,plain,
( sQ7_spl
| sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f120,f229,f268,f255]) ).
fof(f277,definition,
! [X0,X1] :
( sQ10_spl
<=> ( big_p(f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f278,plain,
! [X0,X1] :
( ~ sQ10_spl
| big_p(f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( sQ2_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f122,f229,f277,f235]) ).
fof(f281,plain,
( sQ3_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f124,f229,f277,f239]) ).
fof(f282,plain,
( sQ4_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f126,f229,f277,f243]) ).
fof(f283,plain,
( sQ5_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f128,f229,f277,f247]) ).
fof(f284,plain,
( sQ6_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f130,f229,f277,f251]) ).
fof(f285,plain,
( sQ7_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f132,f229,f277,f255]) ).
fof(f286,definition,
! [X0,X1] :
( sQ11_spl
<=> ( big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f287,plain,
! [X0,X1] :
( ~ sQ11_spl
| big_r(X1,f1(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( sQ2_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f134,f229,f286,f235]) ).
fof(f290,plain,
( sQ3_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f136,f229,f286,f239]) ).
fof(f291,plain,
( sQ4_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f138,f229,f286,f243]) ).
fof(f292,plain,
( sQ5_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f140,f229,f286,f247]) ).
fof(f293,plain,
( sQ6_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f142,f229,f286,f251]) ).
fof(f294,plain,
( sQ7_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f144,f229,f286,f255]) ).
fof(f295,definition,
! [X0,X1] :
( sQ12_spl
<=> ( big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f296,plain,
! [X0,X1] :
( ~ sQ12_spl
| big_r(f1(X1),f2(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( sQ2_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f146,f229,f295,f235]) ).
fof(f299,plain,
( sQ3_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f148,f229,f295,f239]) ).
fof(f300,plain,
( sQ4_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f150,f229,f295,f243]) ).
fof(f301,plain,
( sQ5_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f152,f229,f295,f247]) ).
fof(f302,plain,
( sQ6_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f154,f229,f295,f251]) ).
fof(f303,plain,
( sQ7_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f156,f229,f295,f255]) ).
fof(f304,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f157,f229]) ).
fof(f305,definition,
( sQ13_spl
<=> big_p(c3) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ13_spl
| big_p(c3) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f309,definition,
( sQ14_spl
<=> big_r(c4,c3) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( ~ sQ14_spl
| big_r(c4,c3) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f313,definition,
! [X0,X1] :
( sQ15_spl
<=> ( ~ big_r(X1,X0)
| ~ big_r(c4,X1)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f314,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ big_r(X1,X0)
| ~ big_r(c4,X1)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f317,definition,
( sQ16_spl
<=> big_p(c4) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f328,definition,
( sQ17_spl
<=> big_p(c2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f331,definition,
( sQ18_spl
<=> big_p(c1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ18_spl
| big_p(c1) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f339,plain,
( sQ13_spl
| ~ sQ16_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f178,f328,f331,f317,f305]) ).
fof(f340,plain,
( sQ14_spl
| ~ sQ16_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f179,f328,f331,f317,f309]) ).
fof(f345,plain,
( sQ15_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f188,f328,f331,f313]) ).
fof(f346,definition,
( sQ19_spl
<=> big_r(c2,c1) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( ~ sQ19_spl
| big_r(c2,c1) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f354,plain,
( sQ13_spl
| ~ sQ16_spl
| sQ19_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f194,f328,f346,f317,f305]) ).
fof(f355,plain,
( sQ14_spl
| ~ sQ16_spl
| sQ19_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f195,f328,f346,f317,f309]) ).
fof(f360,plain,
( sQ15_spl
| sQ19_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f204,f328,f346,f313]) ).
fof(f361,definition,
! [X0,X1] :
( sQ20_spl
<=> ( ~ big_r(X1,X0)
| ~ big_r(c2,X1)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f362,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ big_r(X1,X0)
| ~ big_r(c2,X1)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f369,plain,
( sQ13_spl
| ~ sQ16_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f216,f361,f317,f305]) ).
fof(f370,plain,
( sQ14_spl
| ~ sQ16_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f218,f361,f317,f309]) ).
fof(f375,plain,
( sQ15_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f228,f361,f313]) ).
fof(f376,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ8_spl
| ~ big_r(f1(c4),X0)
| ~ big_p(X0)
| big_p(c4) ),
inference(resolution,[status(thm)],[f260,f314]) ).
fof(f377,definition,
! [X0] :
( sQ21_spl
<=> ( ~ big_r(f1(c4),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f378,plain,
! [X0] :
( ~ sQ21_spl
| ~ big_r(f1(c4),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,plain,
( ~ sQ15_spl
| ~ sQ8_spl
| sQ21_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f376,f317,f377,f259,f313]) ).
fof(f383,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ3_spl
| ~ big_r(f3(c4),X0)
| ~ big_p(X0)
| big_p(c4) ),
inference(resolution,[status(thm)],[f240,f314]) ).
fof(f388,definition,
! [X0] :
( sQ23_spl
<=> ( ~ big_r(f3(c4),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f389,plain,
! [X0] :
( ~ sQ23_spl
| ~ big_r(f3(c4),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| sQ23_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f383,f317,f388,f239,f313]) ).
fof(f394,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ20_spl
| big_p(c2)
| ~ big_r(f1(c2),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f362,f260]) ).
fof(f395,definition,
! [X0] :
( sQ24_spl
<=> ( ~ big_r(f1(c2),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f396,plain,
! [X0] :
( ~ sQ24_spl
| ~ big_r(f1(c2),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| sQ17_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f394,f395,f328,f361,f259]) ).
fof(f400,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ11_spl
| ~ big_r(f1(c2),X1)
| ~ big_p(X1)
| ~ big_r(c2,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f287,f362]) ).
fof(f401,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ sQ11_spl
| ~ big_r(f1(c4),X1)
| ~ big_p(X1)
| ~ big_r(c4,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f287,f314]) ).
fof(f402,definition,
! [X0] :
( sQ25_spl
<=> ( ~ big_r(c2,X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f403,plain,
! [X0] :
( ~ sQ25_spl
| ~ big_r(c2,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( ~ sQ20_spl
| ~ sQ11_spl
| sQ24_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f400,f402,f395,f286,f361]) ).
fof(f406,definition,
! [X0] :
( sQ26_spl
<=> ( ~ big_r(c4,X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f407,plain,
! [X0] :
( ~ sQ26_spl
| ~ big_r(c4,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| sQ21_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f401,f406,f377,f286,f313]) ).
fof(f425,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ24_spl
| ~ big_r(c2,X0)
| ~ big_p(X0)
| ~ big_p(f2(c2)) ),
inference(resolution,[status(thm)],[f396,f296]) ).
fof(f426,plain,
( ~ sQ9_spl
| ~ sQ24_spl
| big_p(c2)
| ~ big_p(f2(c2)) ),
inference(resolution,[status(thm)],[f396,f269]) ).
fof(f428,definition,
( sQ29_spl
<=> big_p(f2(c2)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( sQ29_spl
| ~ big_p(f2(c2)) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| sQ25_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f425,f428,f402,f395,f295]) ).
fof(f432,plain,
( ~ sQ9_spl
| ~ sQ24_spl
| sQ17_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f426,f428,f328,f395,f268]) ).
fof(f440,plain,
! [X0] :
( ~ sQ10_spl
| sQ29_spl
| ~ big_r(c2,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f430,f278]) ).
fof(f441,plain,
( ~ sQ1_spl
| sQ29_spl
| big_p(c2) ),
inference(resolution,[status(thm)],[f430,f233]) ).
fof(f442,plain,
( ~ sQ1_spl
| sQ29_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f441,f328,f428,f232]) ).
fof(f444,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ sQ6_spl
| ~ big_r(f5(c4),X1)
| ~ big_p(X1)
| ~ big_r(c4,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f252,f314]) ).
fof(f452,definition,
! [X1] :
( sQ34_spl
<=> ( ~ big_r(f5(c4),X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f453,plain,
! [X0] :
( ~ sQ34_spl
| ~ big_r(f5(c4),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| sQ34_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f444,f406,f452,f251,f313]) ).
fof(f456,plain,
( ~ sQ19_spl
| ~ sQ25_spl
| ~ big_p(c1) ),
inference(resolution,[status(thm)],[f403,f347]) ).
fof(f457,plain,
( ~ sQ19_spl
| ~ sQ25_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f332]) ).
fof(f458,plain,
( ~ sQ19_spl
| ~ sQ25_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f459,plain,
( ~ sQ14_spl
| ~ sQ26_spl
| ~ big_p(c3) ),
inference(resolution,[status(thm)],[f407,f310]) ).
fof(f460,plain,
( ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f459,f306]) ).
fof(f461,plain,
( ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f460]) ).
fof(f492,plain,
( ~ sQ26_spl
| ~ sQ3_spl
| ~ big_p(f3(c4))
| big_p(c4) ),
inference(resolution,[status(thm)],[f240,f407]) ).
fof(f502,definition,
( sQ41_spl
<=> big_p(f3(c4)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ41_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f492,f317,f502,f239,f406]) ).
fof(f518,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ20_spl
| big_p(c2)
| ~ big_r(f3(c2),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f362,f240]) ).
fof(f519,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ20_spl
| ~ big_r(c2,X1)
| ~ big_p(X1)
| ~ big_r(f5(c2),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f362,f252]) ).
fof(f521,definition,
! [X0] :
( sQ43_spl
<=> ( ~ big_r(f3(c2),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f522,plain,
! [X0] :
( ~ sQ43_spl
| ~ big_r(f3(c2),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| sQ17_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f518,f521,f328,f361,f239]) ).
fof(f525,definition,
! [X0] :
( sQ44_spl
<=> ( ~ big_r(f5(c2),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f526,plain,
! [X0] :
( ~ sQ44_spl
| ~ big_r(f5(c2),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| sQ25_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f519,f525,f402,f361,f251]) ).
fof(f530,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ21_spl
| ~ big_r(c4,X0)
| ~ big_p(X0)
| ~ big_p(f2(c4)) ),
inference(resolution,[status(thm)],[f378,f296]) ).
fof(f531,plain,
( ~ sQ9_spl
| ~ sQ21_spl
| big_p(c4)
| ~ big_p(f2(c4)) ),
inference(resolution,[status(thm)],[f378,f269]) ).
fof(f535,definition,
( sQ45_spl
<=> big_p(f2(c4)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( sQ45_spl
| ~ big_p(f2(c4)) ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f538,plain,
( ~ sQ12_spl
| ~ sQ21_spl
| sQ26_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f530,f535,f406,f377,f295]) ).
fof(f539,plain,
( ~ sQ9_spl
| ~ sQ21_spl
| sQ16_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f531,f535,f317,f377,f268]) ).
fof(f552,plain,
! [X0] :
( ~ sQ10_spl
| sQ45_spl
| ~ big_r(c4,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f537,f278]) ).
fof(f553,plain,
( ~ sQ1_spl
| sQ45_spl
| big_p(c4) ),
inference(resolution,[status(thm)],[f537,f233]) ).
fof(f554,plain,
( ~ sQ1_spl
| sQ45_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f553,f317,f535,f232]) ).
fof(f567,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ34_spl
| ~ big_r(c4,X0)
| ~ big_p(X0)
| ~ big_p(f6(c4)) ),
inference(resolution,[status(thm)],[f453,f256]) ).
fof(f571,definition,
( sQ49_spl
<=> big_p(f6(c4)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ49_spl
| ~ big_p(f6(c4)) ),
inference(component_clause,[status(thm)],[f571]) ).
fof(f574,plain,
( ~ sQ7_spl
| ~ sQ34_spl
| sQ26_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f567,f571,f406,f452,f255]) ).
fof(f587,plain,
! [X0] :
( ~ sQ5_spl
| sQ49_spl
| ~ big_r(c4,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f573,f248]) ).
fof(f588,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| big_p(c4)
| ~ big_p(f4(c4)) ),
inference(resolution,[status(thm)],[f389,f244]) ).
fof(f592,definition,
( sQ53_spl
<=> big_p(f4(c4)) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( sQ53_spl
| ~ big_p(f4(c4)) ),
inference(component_clause,[status(thm)],[f592]) ).
fof(f595,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| sQ16_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f588,f592,f317,f388,f243]) ).
fof(f608,plain,
( ~ sQ5_spl
| sQ49_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f587,f406,f571,f247]) ).
fof(f609,plain,
( ~ sQ10_spl
| sQ45_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f552,f406,f535,f277]) ).
fof(f610,plain,
( ~ sQ10_spl
| sQ29_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f440,f402,f428,f277]) ).
fof(f612,plain,
( ~ sQ2_spl
| sQ53_spl
| big_p(c4) ),
inference(resolution,[status(thm)],[f594,f236]) ).
fof(f613,plain,
( ~ sQ2_spl
| sQ53_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f612,f317,f592,f235]) ).
fof(f618,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ44_spl
| ~ big_r(c2,X0)
| ~ big_p(X0)
| ~ big_p(f6(c2)) ),
inference(resolution,[status(thm)],[f526,f256]) ).
fof(f621,definition,
( sQ57_spl
<=> big_p(f6(c2)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( sQ57_spl
| ~ big_p(f6(c2)) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,plain,
( ~ sQ7_spl
| ~ sQ44_spl
| sQ25_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f618,f621,f402,f525,f255]) ).
fof(f633,plain,
( ~ sQ4_spl
| ~ sQ43_spl
| big_p(c2)
| ~ big_p(f4(c2)) ),
inference(resolution,[status(thm)],[f522,f244]) ).
fof(f636,definition,
( sQ60_spl
<=> big_p(f4(c2)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( sQ60_spl
| ~ big_p(f4(c2)) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,plain,
( ~ sQ4_spl
| ~ sQ43_spl
| sQ17_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f633,f636,f328,f521,f243]) ).
fof(f648,plain,
! [X0] :
( ~ sQ5_spl
| sQ57_spl
| ~ big_r(c2,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f623,f248]) ).
fof(f649,plain,
( ~ sQ2_spl
| sQ60_spl
| big_p(c2) ),
inference(resolution,[status(thm)],[f638,f236]) ).
fof(f650,plain,
( ~ sQ2_spl
| sQ60_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f649,f328,f636,f235]) ).
fof(f651,plain,
( ~ sQ5_spl
| sQ57_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f648,f402,f621,f247]) ).
fof(f652,plain,
$false,
inference(sat_refutation,[status(thm)],[f238,f242,f246,f250,f254,f258,f262,f263,f264,f265,f266,f267,f271,f272,f273,f274,f275,f276,f280,f281,f282,f283,f284,f285,f289,f290,f291,f292,f293,f294,f298,f299,f300,f301,f302,f303,f304,f339,f340,f345,f354,f355,f360,f369,f370,f375,f380,f391,f398,f405,f409,f431,f432,f442,f455,f458,f461,f505,f524,f528,f538,f539,f554,f574,f595,f608,f609,f610,f613,f624,f639,f650,f651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN067-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.58 % Computer : n014.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Mon Sep 21 10:41:51 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.59 % Drodi V4.1.1
% 0.12/0.60 % Refutation found
% 0.12/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.62 % Elapsed time: 0.031369 seconds
% 0.12/0.62 % CPU time: 0.071514 seconds
% 0.12/0.62 % Total memory used: 4.562 MB
% 0.12/0.62 % Net memory used: 4.521 MB
%------------------------------------------------------------------------------