%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG089+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 11:48:04 AM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 33
% Syntax : Number of formulae : 295 ( 87 unt; 28 def)
% Number of atoms : 936 ( 653 equ)
% Maximal formula atoms : 110 ( 3 avg)
% Number of connectives : 879 ( 238 ~; 340 |; 271 &)
% ( 28 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( e13 != e14
& e12 != e14
& e12 != e13
& e11 != e14
& e11 != e13
& e11 != e12
& e10 != e14
& e10 != e13
& e10 != e12
& e10 != e11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( e23 != e24
& e22 != e24
& e22 != e23
& e21 != e24
& e21 != e23
& e21 != e22
& e20 != e24
& e20 != e23
& e20 != e22
& e20 != e21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( op1(e14,e14) = e10
& op1(e14,e13) = e12
& op1(e14,e12) = e11
& op1(e14,e11) = e13
& op1(e14,e10) = e14
& op1(e13,e14) = e11
& op1(e13,e13) = e10
& op1(e13,e12) = e14
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e14) = e13
& op1(e12,e13) = e11
& op1(e12,e12) = e10
& op1(e12,e11) = e14
& op1(e12,e10) = e12
& op1(e11,e14) = e12
& op1(e11,e13) = e14
& op1(e11,e12) = e13
& op1(e11,e11) = e10
& op1(e11,e10) = e11
& op1(e10,e14) = e14
& op1(e10,e13) = e13
& op1(e10,e12) = e12
& op1(e10,e11) = e11
& op1(e10,e10) = e10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( op2(e24,e24) = e20
& op2(e24,e23) = e22
& op2(e24,e22) = e21
& op2(e24,e21) = e23
& op2(e24,e20) = e24
& op2(e23,e24) = e22
& op2(e23,e23) = e21
& op2(e23,e22) = e20
& op2(e23,e21) = e24
& op2(e23,e20) = e23
& op2(e22,e24) = e21
& op2(e22,e23) = e24
& op2(e22,e22) = e23
& op2(e22,e21) = e20
& op2(e22,e20) = e22
& op2(e21,e24) = e23
& op2(e21,e23) = e20
& op2(e21,e22) = e24
& op2(e21,e21) = e22
& op2(e21,e20) = e21
& op2(e20,e24) = e24
& op2(e20,e23) = e23
& op2(e20,e22) = e22
& op2(e20,e21) = e21
& op2(e20,e20) = e20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
( ( ( j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e14)) = e14
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e24)) = e24
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e24,e24)) = op1(j(e24),j(e24))
& j(op2(e24,e23)) = op1(j(e24),j(e23))
& j(op2(e24,e22)) = op1(j(e24),j(e22))
& j(op2(e24,e21)) = op1(j(e24),j(e21))
& j(op2(e24,e20)) = op1(j(e24),j(e20))
& j(op2(e23,e24)) = op1(j(e23),j(e24))
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e24)) = op1(j(e22),j(e24))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e24)) = op1(j(e21),j(e24))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e24)) = op1(j(e20),j(e24))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e14,e14)) = op2(h(e14),h(e14))
& h(op1(e14,e13)) = op2(h(e14),h(e13))
& h(op1(e14,e12)) = op2(h(e14),h(e12))
& h(op1(e14,e11)) = op2(h(e14),h(e11))
& h(op1(e14,e10)) = op2(h(e14),h(e10))
& h(op1(e13,e14)) = op2(h(e13),h(e14))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e14)) = op2(h(e12),h(e14))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e14)) = op2(h(e11),h(e14))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e14)) = op2(h(e10),h(e14))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ( ( ( j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e14)) = e14
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e24)) = e24
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e24,e24)) = op1(j(e24),j(e24))
& j(op2(e24,e23)) = op1(j(e24),j(e23))
& j(op2(e24,e22)) = op1(j(e24),j(e22))
& j(op2(e24,e21)) = op1(j(e24),j(e21))
& j(op2(e24,e20)) = op1(j(e24),j(e20))
& j(op2(e23,e24)) = op1(j(e23),j(e24))
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e24)) = op1(j(e22),j(e24))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e24)) = op1(j(e21),j(e24))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e24)) = op1(j(e20),j(e24))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e14,e14)) = op2(h(e14),h(e14))
& h(op1(e14,e13)) = op2(h(e14),h(e13))
& h(op1(e14,e12)) = op2(h(e14),h(e12))
& h(op1(e14,e11)) = op2(h(e14),h(e11))
& h(op1(e14,e10)) = op2(h(e14),h(e10))
& h(op1(e13,e14)) = op2(h(e13),h(e14))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e14)) = op2(h(e12),h(e14))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e14)) = op2(h(e11),h(e14))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e14)) = op2(h(e10),h(e14))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10)) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
e10 != e11,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
e10 != e12,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
e10 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
e11 != e12,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
e12 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
e12 != e14,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
e13 != e14,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
e20 != e23,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
e22 != e23,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
e22 != e24,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f53,plain,
op1(e10,e10) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f54,plain,
op1(e10,e11) = e11,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f55,plain,
op1(e10,e12) = e12,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f58,plain,
op1(e11,e10) = e11,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
op1(e11,e11) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f60,plain,
op1(e11,e12) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f64,plain,
op1(e12,e11) = e14,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f65,plain,
op1(e12,e12) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f71,plain,
op1(e13,e13) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f77,plain,
op1(e14,e14) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f78,plain,
op2(e20,e20) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f79,plain,
op2(e20,e21) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f81,plain,
op2(e20,e23) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f82,plain,
op2(e20,e24) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f83,plain,
op2(e21,e20) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f84,plain,
op2(e21,e21) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f86,plain,
op2(e21,e23) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f88,plain,
op2(e22,e20) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f90,plain,
op2(e22,e22) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f91,plain,
op2(e22,e23) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f92,plain,
op2(e22,e24) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f96,plain,
op2(e23,e23) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f100,plain,
op2(e24,e22) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f102,plain,
op2(e24,e24) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f103,plain,
( j(h(e14)) = e14
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e24)) = e24
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e24,e24)) = op1(j(e24),j(e24))
& j(op2(e24,e23)) = op1(j(e24),j(e23))
& j(op2(e24,e22)) = op1(j(e24),j(e22))
& j(op2(e24,e21)) = op1(j(e24),j(e21))
& j(op2(e24,e20)) = op1(j(e24),j(e20))
& j(op2(e23,e24)) = op1(j(e23),j(e24))
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e24)) = op1(j(e22),j(e24))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e24)) = op1(j(e21),j(e24))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e24)) = op1(j(e20),j(e24))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e14,e14)) = op2(h(e14),h(e14))
& h(op1(e14,e13)) = op2(h(e14),h(e13))
& h(op1(e14,e12)) = op2(h(e14),h(e12))
& h(op1(e14,e11)) = op2(h(e14),h(e11))
& h(op1(e14,e10)) = op2(h(e14),h(e10))
& h(op1(e13,e14)) = op2(h(e13),h(e14))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e14)) = op2(h(e12),h(e14))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e14)) = op2(h(e11),h(e14))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e14)) = op2(h(e10),h(e14))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10))
& ( j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f105,plain,
( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f106,plain,
( h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f110,plain,
( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f114,plain,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f115,plain,
h(op1(e10,e11)) = op2(h(e10),h(e11)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f119,plain,
h(op1(e11,e10)) = op2(h(e11),h(e10)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f120,plain,
h(op1(e11,e11)) = op2(h(e11),h(e11)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f126,plain,
h(op1(e12,e12)) = op2(h(e12),h(e12)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f132,plain,
h(op1(e13,e13)) = op2(h(e13),h(e13)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f139,plain,
j(op2(e20,e20)) = op1(j(e20),j(e20)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f140,plain,
j(op2(e20,e21)) = op1(j(e20),j(e21)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f142,plain,
j(op2(e20,e23)) = op1(j(e20),j(e23)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f143,plain,
j(op2(e20,e24)) = op1(j(e20),j(e24)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f144,plain,
j(op2(e21,e20)) = op1(j(e21),j(e20)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f145,plain,
j(op2(e21,e21)) = op1(j(e21),j(e21)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f147,plain,
j(op2(e21,e23)) = op1(j(e21),j(e23)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f149,plain,
j(op2(e22,e20)) = op1(j(e22),j(e20)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f151,plain,
j(op2(e22,e22)) = op1(j(e22),j(e22)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f152,plain,
j(op2(e22,e23)) = op1(j(e22),j(e23)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f153,plain,
j(op2(e22,e24)) = op1(j(e22),j(e24)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f157,plain,
j(op2(e23,e23)) = op1(j(e23),j(e23)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f161,plain,
j(op2(e24,e22)) = op1(j(e24),j(e22)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f163,plain,
j(op2(e24,e24)) = op1(j(e24),j(e24)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f165,plain,
h(j(e21)) = e21,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f166,plain,
h(j(e22)) = e22,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f169,plain,
j(h(e10)) = e10,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f170,plain,
j(h(e11)) = e11,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f171,plain,
j(h(e12)) = e12,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f172,plain,
j(h(e13)) = e13,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f173,plain,
j(h(e14)) = e14,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f177,definition,
( sQ1_spl
<=> h(e10) = e21 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ1_spl
| h(e10) = e21 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
( sQ2_spl
<=> h(e10) = e22 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ2_spl
| h(e10) = e22 ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f182,plain,
( sQ2_spl
| h(e10) != e22 ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f190,definition,
( sQ5_spl
<=> h(e11) = e20 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( ~ sQ5_spl
| h(e11) = e20 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ6_spl
<=> h(e11) = e21 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ6_spl
| h(e11) = e21 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ7_spl
<=> h(e11) = e22 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ7_spl
| h(e11) = e22 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ8_spl
<=> h(e11) = e23 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ8_spl
| h(e11) = e23 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ9_spl
<=> h(e11) = e24 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ9_spl
| h(e11) = e24 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( sQ9_spl
| sQ8_spl
| sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f105,f190,f193,f196,f199,f202]) ).
fof(f206,definition,
( sQ10_spl
<=> h(e12) = e20 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ10_spl
| h(e12) = e20 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,definition,
( sQ11_spl
<=> h(e12) = e21 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( ~ sQ11_spl
| h(e12) = e21 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,definition,
( sQ12_spl
<=> h(e12) = e22 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ12_spl
| h(e12) = e22 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,definition,
( sQ13_spl
<=> h(e12) = e23 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ13_spl
| h(e12) = e23 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,definition,
( sQ14_spl
<=> h(e12) = e24 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ14_spl
| h(e12) = e24 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f106,f206,f209,f212,f215,f218]) ).
fof(f222,definition,
( sQ15_spl
<=> h(e13) = e20 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( ~ sQ15_spl
| h(e13) = e20 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,definition,
( sQ16_spl
<=> h(e13) = e21 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( ~ sQ16_spl
| h(e13) = e21 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f241,definition,
( sQ21_spl
<=> h(e14) = e21 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( ~ sQ21_spl
| h(e14) = e21 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f257,definition,
( sQ26_spl
<=> j(e20) = e11 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ26_spl
| j(e20) = e11 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ27_spl
<=> j(e20) = e12 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( ~ sQ27_spl
| j(e20) = e12 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f270,definition,
( sQ30_spl
<=> j(e21) = e10 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( ~ sQ30_spl
| j(e21) = e10 ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f272,plain,
( sQ30_spl
| j(e21) != e10 ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,definition,
( sQ31_spl
<=> j(e21) = e11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( ~ sQ31_spl
| j(e21) = e11 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,definition,
( sQ32_spl
<=> j(e21) = e12 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( ~ sQ32_spl
| j(e21) = e12 ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,definition,
( sQ33_spl
<=> j(e21) = e13 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f282,definition,
( sQ34_spl
<=> j(e21) = e14 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( ~ sQ34_spl
| j(e21) = e14 ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,plain,
( sQ34_spl
| sQ33_spl
| sQ32_spl
| sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f110,f270,f273,f276,f279,f282]) ).
fof(f286,definition,
( sQ35_spl
<=> j(e22) = e10 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ35_spl
| j(e22) = e10 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f288,plain,
( sQ35_spl
| j(e22) != e10 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f292,definition,
( sQ37_spl
<=> j(e22) = e12 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( ~ sQ37_spl
| j(e22) = e12 ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f305,definition,
( sQ41_spl
<=> j(e23) = e11 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ41_spl
| j(e23) = e11 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,definition,
( sQ42_spl
<=> j(e23) = e12 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( ~ sQ42_spl
| j(e23) = e12 ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f321,definition,
( sQ46_spl
<=> j(e24) = e11 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( ~ sQ46_spl
| j(e24) = e11 ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,definition,
( sQ47_spl
<=> j(e24) = e12 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( ~ sQ47_spl
| j(e24) = e12 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f334,plain,
h(e10) = op2(h(e10),h(e10)),
inference(forward_demodulation,[status(thm)],[f53,f114]) ).
fof(f335,plain,
h(e11) = op2(h(e10),h(e11)),
inference(forward_demodulation,[status(thm)],[f54,f115]) ).
fof(f339,plain,
h(e11) = op2(h(e11),h(e10)),
inference(forward_demodulation,[status(thm)],[f58,f119]) ).
fof(f340,plain,
h(e10) = op2(h(e11),h(e11)),
inference(forward_demodulation,[status(thm)],[f59,f120]) ).
fof(f346,plain,
h(e10) = op2(h(e12),h(e12)),
inference(forward_demodulation,[status(thm)],[f65,f126]) ).
fof(f352,plain,
h(e10) = op2(h(e13),h(e13)),
inference(forward_demodulation,[status(thm)],[f71,f132]) ).
fof(f359,plain,
j(e20) = op1(j(e20),j(e20)),
inference(forward_demodulation,[status(thm)],[f78,f139]) ).
fof(f360,plain,
j(e21) = op1(j(e20),j(e21)),
inference(forward_demodulation,[status(thm)],[f79,f140]) ).
fof(f362,plain,
j(e23) = op1(j(e20),j(e23)),
inference(forward_demodulation,[status(thm)],[f81,f142]) ).
fof(f363,plain,
j(e24) = op1(j(e20),j(e24)),
inference(forward_demodulation,[status(thm)],[f82,f143]) ).
fof(f364,plain,
j(e21) = op1(j(e21),j(e20)),
inference(forward_demodulation,[status(thm)],[f83,f144]) ).
fof(f365,plain,
j(e22) = op1(j(e21),j(e21)),
inference(forward_demodulation,[status(thm)],[f84,f145]) ).
fof(f367,plain,
j(e20) = op1(j(e21),j(e23)),
inference(forward_demodulation,[status(thm)],[f86,f147]) ).
fof(f369,plain,
j(e22) = op1(j(e22),j(e20)),
inference(forward_demodulation,[status(thm)],[f88,f149]) ).
fof(f371,plain,
j(e23) = op1(j(e22),j(e22)),
inference(forward_demodulation,[status(thm)],[f90,f151]) ).
fof(f372,plain,
j(e24) = op1(j(e22),j(e23)),
inference(forward_demodulation,[status(thm)],[f91,f152]) ).
fof(f373,plain,
j(e21) = op1(j(e22),j(e24)),
inference(forward_demodulation,[status(thm)],[f92,f153]) ).
fof(f377,plain,
j(e21) = op1(j(e23),j(e23)),
inference(forward_demodulation,[status(thm)],[f96,f157]) ).
fof(f381,plain,
j(e21) = op1(j(e24),j(e22)),
inference(forward_demodulation,[status(thm)],[f100,f161]) ).
fof(f383,plain,
j(e20) = op1(j(e24),j(e24)),
inference(forward_demodulation,[status(thm)],[f102,f163]) ).
fof(f400,plain,
( ~ sQ46_spl
| ~ sQ47_spl
| e12 = e11 ),
inference(forward_demodulation,[status(thm)],[f325,f322]) ).
fof(f401,plain,
( ~ sQ46_spl
| ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f400,f12]) ).
fof(f402,plain,
( ~ sQ46_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f429,plain,
( ~ sQ34_spl
| j(e21) = op1(j(e20),e14) ),
inference(backward_demodulation,[status(thm)],[f283,f360]) ).
fof(f476,plain,
( ~ sQ14_spl
| j(e24) = e12 ),
inference(backward_demodulation,[status(thm)],[f219,f171]) ).
fof(f486,plain,
( ~ sQ9_spl
| j(e24) = e11 ),
inference(backward_demodulation,[status(thm)],[f203,f170]) ).
fof(f561,plain,
( ~ sQ35_spl
| h(e10) = e22 ),
inference(forward_demodulation,[status(thm)],[f287,f166]) ).
fof(f580,plain,
( ~ sQ30_spl
| e10 = op1(j(e21),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f271,f364]) ).
fof(f581,plain,
( ~ sQ30_spl
| e10 = op1(e10,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f271,f580]) ).
fof(f636,plain,
( ~ sQ15_spl
| j(e20) = e13 ),
inference(forward_demodulation,[status(thm)],[f223,f172]) ).
fof(f657,plain,
( ~ sQ10_spl
| j(e20) = e12 ),
inference(forward_demodulation,[status(thm)],[f207,f171]) ).
fof(f672,plain,
( ~ sQ5_spl
| j(e20) = e11 ),
inference(forward_demodulation,[status(thm)],[f191,f170]) ).
fof(f750,plain,
( ~ sQ16_spl
| h(e10) = op2(e21,h(e13)) ),
inference(forward_demodulation,[status(thm)],[f226,f352]) ).
fof(f751,plain,
( ~ sQ16_spl
| h(e10) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f226,f750]) ).
fof(f752,plain,
( ~ sQ16_spl
| e22 = op2(h(e12),h(e12)) ),
inference(backward_demodulation,[status(thm)],[f753,f346]) ).
fof(f753,plain,
( ~ sQ16_spl
| h(e10) = e22 ),
inference(forward_demodulation,[status(thm)],[f84,f751]) ).
fof(f760,plain,
( ~ sQ21_spl
| j(e21) = e14 ),
inference(backward_demodulation,[status(thm)],[f242,f173]) ).
fof(f801,plain,
( ~ sQ5_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f672,f257,f190]) ).
fof(f805,plain,
( ~ sQ41_spl
| j(e21) = op1(e11,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f306,f377]) ).
fof(f806,plain,
( ~ sQ41_spl
| j(e21) = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f306,f805]) ).
fof(f813,plain,
( ~ sQ41_spl
| j(e21) = e10 ),
inference(forward_demodulation,[status(thm)],[f59,f806]) ).
fof(f816,plain,
( sQ30_spl
| ~ sQ41_spl
| e10 != e10 ),
inference(forward_demodulation,[status(thm)],[f813,f272]) ).
fof(f817,plain,
( sQ30_spl
| ~ sQ41_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f816]) ).
fof(f818,plain,
( sQ30_spl
| ~ sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f817]) ).
fof(f848,plain,
( ~ sQ21_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f760,f282,f241]) ).
fof(f850,plain,
( ~ sQ11_spl
| h(e10) = op2(e21,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f210,f346]) ).
fof(f851,plain,
( ~ sQ11_spl
| h(e10) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f210,f850]) ).
fof(f854,plain,
( ~ sQ11_spl
| h(e10) = e22 ),
inference(forward_demodulation,[status(thm)],[f84,f851]) ).
fof(f877,plain,
( ~ sQ2_spl
| e22 = op2(h(e10),h(e10)) ),
inference(forward_demodulation,[status(thm)],[f181,f334]) ).
fof(f878,plain,
( ~ sQ2_spl
| e22 = op2(e22,h(e10)) ),
inference(forward_demodulation,[status(thm)],[f181,f877]) ).
fof(f879,plain,
( ~ sQ2_spl
| e22 = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f181,f878]) ).
fof(f880,plain,
( ~ sQ2_spl
| e22 = e23 ),
inference(forward_demodulation,[status(thm)],[f90,f879]) ).
fof(f881,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f880,f25]) ).
fof(f882,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f881]) ).
fof(f898,plain,
( ~ sQ31_spl
| j(e22) = op1(e11,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f274,f365]) ).
fof(f899,plain,
( ~ sQ31_spl
| j(e22) = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f274,f898]) ).
fof(f903,plain,
( ~ sQ31_spl
| j(e22) = e10 ),
inference(forward_demodulation,[status(thm)],[f59,f899]) ).
fof(f944,plain,
( ~ sQ6_spl
| j(e21) = e11 ),
inference(backward_demodulation,[status(thm)],[f194,f170]) ).
fof(f984,plain,
( ~ sQ12_spl
| j(e22) = e12 ),
inference(backward_demodulation,[status(thm)],[f213,f171]) ).
fof(f1000,plain,
( ~ sQ26_spl
| j(e23) = op1(e11,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f258,f362]) ).
fof(f1001,plain,
( ~ sQ37_spl
| e12 = op1(j(e22),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f293,f369]) ).
fof(f1002,plain,
( ~ sQ37_spl
| e12 = op1(e12,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f293,f1001]) ).
fof(f1003,plain,
( ~ sQ37_spl
| ~ sQ26_spl
| e12 = op1(e12,e11) ),
inference(forward_demodulation,[status(thm)],[f258,f1002]) ).
fof(f1004,plain,
( ~ sQ37_spl
| ~ sQ26_spl
| e12 = e14 ),
inference(forward_demodulation,[status(thm)],[f64,f1003]) ).
fof(f1005,plain,
( ~ sQ37_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1004,f16]) ).
fof(f1006,plain,
( ~ sQ37_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f1005]) ).
fof(f1012,plain,
( ~ sQ47_spl
| j(e24) = op1(j(e20),e12) ),
inference(backward_demodulation,[status(thm)],[f325,f363]) ).
fof(f1013,plain,
( ~ sQ47_spl
| e12 = op1(j(e22),j(e23)) ),
inference(backward_demodulation,[status(thm)],[f325,f372]) ).
fof(f1030,plain,
( ~ sQ32_spl
| h(e12) = e21 ),
inference(forward_demodulation,[status(thm)],[f277,f165]) ).
fof(f1059,plain,
( ~ sQ1_spl
| j(e21) = e10 ),
inference(backward_demodulation,[status(thm)],[f178,f169]) ).
fof(f1077,plain,
( ~ sQ7_spl
| h(e10) = op2(e22,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f197,f340]) ).
fof(f1078,plain,
( ~ sQ7_spl
| h(e10) = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f197,f1077]) ).
fof(f1084,plain,
( ~ sQ7_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f90,f1078]) ).
fof(f1091,plain,
( ~ sQ35_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f561,f180,f286]) ).
fof(f1123,plain,
( ~ sQ7_spl
| e22 = op2(h(e11),h(e10)) ),
inference(forward_demodulation,[status(thm)],[f197,f339]) ).
fof(f1124,plain,
( ~ sQ7_spl
| e22 = op2(e22,h(e10)) ),
inference(forward_demodulation,[status(thm)],[f197,f1123]) ).
fof(f1125,plain,
( ~ sQ7_spl
| e22 = op2(e22,e23) ),
inference(forward_demodulation,[status(thm)],[f1084,f1124]) ).
fof(f1126,plain,
( ~ sQ7_spl
| e22 = e24 ),
inference(forward_demodulation,[status(thm)],[f91,f1125]) ).
fof(f1127,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1126,f26]) ).
fof(f1128,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1127]) ).
fof(f1138,plain,
( ~ sQ12_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f984,f292,f212]) ).
fof(f1173,plain,
( ~ sQ15_spl
| e13 = op1(j(e20),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f636,f359]) ).
fof(f1174,plain,
( ~ sQ15_spl
| e13 = op1(e13,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f636,f1173]) ).
fof(f1175,plain,
( ~ sQ15_spl
| e13 = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f636,f1174]) ).
fof(f1176,plain,
( ~ sQ15_spl
| e13 = e10 ),
inference(forward_demodulation,[status(thm)],[f71,f1175]) ).
fof(f1177,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1176,f10]) ).
fof(f1178,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1177]) ).
fof(f1191,plain,
( ~ sQ30_spl
| ~ sQ26_spl
| e10 = op1(e10,e11) ),
inference(forward_demodulation,[status(thm)],[f258,f581]) ).
fof(f1192,plain,
( ~ sQ30_spl
| ~ sQ26_spl
| e10 = e11 ),
inference(forward_demodulation,[status(thm)],[f54,f1191]) ).
fof(f1193,plain,
( ~ sQ30_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1192,f8]) ).
fof(f1194,plain,
( ~ sQ30_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f1193]) ).
fof(f1248,plain,
( ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f854,f180,f209]) ).
fof(f1249,plain,
( ~ sQ42_spl
| j(e21) = op1(j(e23),e12) ),
inference(backward_demodulation,[status(thm)],[f309,f377]) ).
fof(f1255,plain,
( ~ sQ42_spl
| e12 = op1(j(e22),j(e22)) ),
inference(backward_demodulation,[status(thm)],[f309,f371]) ).
fof(f1260,plain,
( ~ sQ37_spl
| j(e21) = op1(j(e24),e12) ),
inference(backward_demodulation,[status(thm)],[f293,f381]) ).
fof(f1261,plain,
( ~ sQ37_spl
| j(e21) = op1(e12,j(e24)) ),
inference(backward_demodulation,[status(thm)],[f293,f373]) ).
fof(f1364,plain,
( ~ sQ9_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f486,f321,f202]) ).
fof(f1380,plain,
( ~ sQ9_spl
| j(e24) = e11 ),
inference(backward_demodulation,[status(thm)],[f203,f170]) ).
fof(f1381,plain,
( ~ sQ34_spl
| e14 = op1(j(e20),e14) ),
inference(backward_demodulation,[status(thm)],[f283,f429]) ).
fof(f1390,plain,
( ~ sQ34_spl
| j(e21) = op1(j(e20),e14) ),
inference(backward_demodulation,[status(thm)],[f283,f360]) ).
fof(f1420,plain,
( ~ sQ13_spl
| j(e23) = e12 ),
inference(backward_demodulation,[status(thm)],[f216,f171]) ).
fof(f1457,plain,
( ~ sQ9_spl
| j(e20) = op1(j(e24),e11) ),
inference(backward_demodulation,[status(thm)],[f1380,f383]) ).
fof(f1461,plain,
( ~ sQ37_spl
| ~ sQ9_spl
| j(e21) = op1(e11,e12) ),
inference(forward_demodulation,[status(thm)],[f1380,f1260]) ).
fof(f1464,plain,
( ~ sQ37_spl
| ~ sQ9_spl
| j(e21) = e13 ),
inference(forward_demodulation,[status(thm)],[f60,f1461]) ).
fof(f1465,plain,
( ~ sQ37_spl
| ~ sQ9_spl
| e13 = op1(e12,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f1464,f1261]) ).
fof(f1466,plain,
( ~ sQ37_spl
| ~ sQ9_spl
| e13 = op1(e12,e11) ),
inference(forward_demodulation,[status(thm)],[f1380,f1465]) ).
fof(f1467,plain,
( ~ sQ37_spl
| ~ sQ9_spl
| e13 = e14 ),
inference(forward_demodulation,[status(thm)],[f64,f1466]) ).
fof(f1468,plain,
( ~ sQ37_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1467,f17]) ).
fof(f1469,plain,
( ~ sQ37_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1468]) ).
fof(f1497,plain,
( ~ sQ27_spl
| e12 = op1(j(e20),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f261,f359]) ).
fof(f1498,plain,
( ~ sQ27_spl
| e12 = op1(e12,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f261,f1497]) ).
fof(f1499,plain,
( ~ sQ27_spl
| e12 = op1(e12,e12) ),
inference(forward_demodulation,[status(thm)],[f261,f1498]) ).
fof(f1500,plain,
( ~ sQ27_spl
| e12 = e10 ),
inference(forward_demodulation,[status(thm)],[f65,f1499]) ).
fof(f1501,plain,
( ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1500,f9]) ).
fof(f1502,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1501]) ).
fof(f1531,plain,
( ~ sQ42_spl
| j(e21) = op1(e12,e12) ),
inference(backward_demodulation,[status(thm)],[f1548,f1249]) ).
fof(f1533,plain,
( ~ sQ42_spl
| j(e20) = op1(j(e21),e12) ),
inference(backward_demodulation,[status(thm)],[f1548,f367]) ).
fof(f1548,plain,
( ~ sQ42_spl
| e12 = j(e23) ),
inference(forward_demodulation,[status(thm)],[f371,f1255]) ).
fof(f1560,plain,
( ~ sQ6_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f944,f273,f193]) ).
fof(f1633,plain,
( ~ sQ26_spl
| ~ sQ42_spl
| e12 = op1(e11,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f1548,f1000]) ).
fof(f1634,plain,
( ~ sQ26_spl
| ~ sQ42_spl
| e12 = op1(e11,e12) ),
inference(forward_demodulation,[status(thm)],[f1548,f1633]) ).
fof(f1635,plain,
( ~ sQ26_spl
| ~ sQ42_spl
| e12 = e13 ),
inference(forward_demodulation,[status(thm)],[f60,f1634]) ).
fof(f1636,plain,
( ~ sQ26_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1635,f15]) ).
fof(f1637,plain,
( ~ sQ26_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f1636]) ).
fof(f1647,plain,
( ~ sQ1_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f1059,f270,f177]) ).
fof(f1662,plain,
( ~ sQ9_spl
| j(e20) = op1(e11,e11) ),
inference(backward_demodulation,[status(thm)],[f1380,f1457]) ).
fof(f1683,plain,
( ~ sQ13_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1420,f308,f215]) ).
fof(f1758,plain,
( ~ sQ31_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f903,f286,f273]) ).
fof(f1761,plain,
( ~ sQ47_spl
| e12 = op1(j(e20),e12) ),
inference(backward_demodulation,[status(thm)],[f1771,f1012]) ).
fof(f1771,plain,
( ~ sQ47_spl
| e12 = j(e24) ),
inference(forward_demodulation,[status(thm)],[f372,f1013]) ).
fof(f1845,plain,
( ~ sQ16_spl
| e22 = h(e10) ),
inference(forward_demodulation,[status(thm)],[f346,f752]) ).
fof(f1846,plain,
( ~ sQ16_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1845,f182]) ).
fof(f1847,plain,
( ~ sQ16_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1846]) ).
fof(f1848,plain,
( ~ sQ10_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f657,f260,f206]) ).
fof(f1896,plain,
( ~ sQ9_spl
| j(e20) = e10 ),
inference(forward_demodulation,[status(thm)],[f59,f1662]) ).
fof(f1901,plain,
( ~ sQ42_spl
| j(e21) = e10 ),
inference(forward_demodulation,[status(thm)],[f65,f1531]) ).
fof(f1903,plain,
( ~ sQ42_spl
| ~ sQ9_spl
| e10 = op1(j(e21),e12) ),
inference(forward_demodulation,[status(thm)],[f1896,f1533]) ).
fof(f1904,plain,
( ~ sQ42_spl
| ~ sQ9_spl
| e10 = op1(e10,e12) ),
inference(forward_demodulation,[status(thm)],[f1901,f1903]) ).
fof(f1905,plain,
( ~ sQ42_spl
| ~ sQ9_spl
| e10 = e12 ),
inference(forward_demodulation,[status(thm)],[f55,f1904]) ).
fof(f1906,plain,
( ~ sQ42_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1905,f9]) ).
fof(f1907,plain,
( ~ sQ42_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1906]) ).
fof(f1927,plain,
( ~ sQ34_spl
| j(e21) = e14 ),
inference(forward_demodulation,[status(thm)],[f1381,f1390]) ).
fof(f1934,plain,
( ~ sQ34_spl
| j(e22) = op1(e14,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f1927,f365]) ).
fof(f1935,plain,
( ~ sQ34_spl
| j(e22) = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f1927,f1934]) ).
fof(f1936,plain,
( ~ sQ34_spl
| j(e22) = e10 ),
inference(forward_demodulation,[status(thm)],[f77,f1935]) ).
fof(f1937,plain,
( ~ sQ34_spl
| sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1936,f288]) ).
fof(f1938,plain,
( ~ sQ34_spl
| sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f1937]) ).
fof(f1968,plain,
( ~ sQ47_spl
| ~ sQ26_spl
| e12 = op1(e11,e12) ),
inference(forward_demodulation,[status(thm)],[f258,f1761]) ).
fof(f1969,plain,
( ~ sQ47_spl
| ~ sQ26_spl
| e12 = e13 ),
inference(forward_demodulation,[status(thm)],[f60,f1968]) ).
fof(f1970,plain,
( ~ sQ47_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1969,f15]) ).
fof(f1971,plain,
( ~ sQ47_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f1970]) ).
fof(f1983,plain,
( ~ sQ14_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f476,f324,f218]) ).
fof(f2163,plain,
( ~ sQ32_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1030,f209,f276]) ).
fof(f2186,plain,
( ~ sQ8_spl
| h(e10) = op2(e23,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f200,f340]) ).
fof(f2187,plain,
( ~ sQ8_spl
| h(e10) = op2(e23,e23) ),
inference(forward_demodulation,[status(thm)],[f200,f2186]) ).
fof(f2192,plain,
( ~ sQ8_spl
| h(e10) = e21 ),
inference(forward_demodulation,[status(thm)],[f96,f2187]) ).
fof(f2193,plain,
( ~ sQ8_spl
| e23 = op2(h(e10),h(e11)) ),
inference(forward_demodulation,[status(thm)],[f200,f335]) ).
fof(f2194,plain,
( ~ sQ8_spl
| e23 = op2(e21,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f2192,f2193]) ).
fof(f2195,plain,
( ~ sQ8_spl
| e23 = op2(e21,e23) ),
inference(forward_demodulation,[status(thm)],[f200,f2194]) ).
fof(f2196,plain,
( ~ sQ8_spl
| e23 = e20 ),
inference(forward_demodulation,[status(thm)],[f86,f2195]) ).
fof(f2197,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2196,f20]) ).
fof(f2198,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f2197]) ).
fof(f2199,plain,
$false,
inference(sat_refutation,[status(thm)],[f205,f221,f285,f402,f801,f818,f848,f882,f1006,f1091,f1128,f1138,f1178,f1194,f1248,f1364,f1469,f1502,f1560,f1637,f1647,f1683,f1758,f1847,f1848,f1907,f1938,f1971,f1983,f2163,f2198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG089+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 12:55:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.063855 seconds
% 0.11/0.45 % CPU time: 0.283040 seconds
% 0.11/0.45 % Total memory used: 73.887 MB
% 0.11/0.45 % Net memory used: 73.719 MB
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