%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG082+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 11:48:03 AM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 44
% Syntax : Number of formulae : 335 ( 76 unt; 39 def)
% Number of atoms : 1082 ( 681 equ)
% Maximal formula atoms : 110 ( 3 avg)
% Number of connectives : 1070 ( 323 ~; 435 |; 271 &)
% ( 39 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 41 ( 39 usr; 40 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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( op1(e14,e14) = e12
& op1(e14,e13) = e10
& op1(e14,e12) = e11
& op1(e14,e11) = e13
& op1(e14,e10) = e14
& op1(e13,e14) = e10
& op1(e13,e13) = e11
& op1(e13,e12) = e14
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e14) = e11
& op1(e12,e13) = e14
& op1(e12,e12) = e13
& op1(e12,e11) = e10
& op1(e12,e10) = e12
& op1(e11,e14) = e13
& op1(e11,e13) = e12
& op1(e11,e12) = e10
& op1(e11,e11) = e14
& 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/sandbox/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) = e21
& op2(e23,e23) = e24
& op2(e23,e22) = e20
& op2(e23,e21) = e22
& op2(e23,e20) = e23
& op2(e22,e24) = e23
& op2(e22,e23) = e21
& op2(e22,e22) = e24
& op2(e22,e21) = e20
& op2(e22,e20) = e22
& op2(e21,e24) = e22
& op2(e21,e23) = e20
& op2(e21,e22) = e23
& op2(e21,e21) = e24
& 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/sandbox/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/sandbox/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(f11,plain,
e10 != e14,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
e11 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
e11 != e14,
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(f18,plain,
e20 != e21,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
e20 != e22,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
e20 != e23,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
e20 != e24,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
e23 != e24,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f53,plain,
op1(e10,e10) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
op1(e11,e11) = e14,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f61,plain,
op1(e11,e13) = e12,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f62,plain,
op1(e11,e14) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f65,plain,
op1(e12,e12) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f66,plain,
op1(e12,e13) = e14,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f70,plain,
op1(e13,e12) = e14,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f71,plain,
op1(e13,e13) = e11,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f72,plain,
op1(e13,e14) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f77,plain,
op1(e14,e14) = e12,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f78,plain,
op2(e20,e20) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f84,plain,
op2(e21,e21) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f86,plain,
op2(e21,e23) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f87,plain,
op2(e21,e24) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f90,plain,
op2(e22,e22) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f94,plain,
op2(e23,e21) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f96,plain,
op2(e23,e23) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f97,plain,
op2(e23,e24) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f99,plain,
op2(e24,e21) = e23,
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(f107,plain,
( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f109,plain,
( j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 ),
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(f112,plain,
( j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f113,plain,
( j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = 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(f120,plain,
h(op1(e11,e11)) = op2(h(e11),h(e11)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f123,plain,
h(op1(e11,e14)) = op2(h(e11),h(e14)),
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(f133,plain,
h(op1(e13,e14)) = op2(h(e13),h(e14)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f138,plain,
h(op1(e14,e14)) = op2(h(e14),h(e14)),
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(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(f148,plain,
j(op2(e21,e24)) = op1(j(e21),j(e24)),
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(f155,plain,
j(op2(e23,e21)) = op1(j(e23),j(e21)),
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(f163,plain,
j(op2(e24,e24)) = op1(j(e24),j(e24)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f164,plain,
h(j(e20)) = e20,
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(f167,plain,
h(j(e23)) = e23,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f168,plain,
h(j(e24)) = e24,
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(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(f174,definition,
( sQ0_spl
<=> h(e10) = e20 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ0_spl
| h(e10) = e20 ),
inference(component_clause,[status(thm)],[f174]) ).
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(f183,definition,
( sQ3_spl
<=> h(e10) = e23 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ3_spl
| h(e10) = e23 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f185,plain,
( sQ3_spl
| h(e10) != e23 ),
inference(component_clause,[status(thm)],[f183]) ).
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(f192,plain,
( sQ5_spl
| h(e11) != e20 ),
inference(component_clause,[status(thm)],[f190]) ).
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(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(f208,plain,
( sQ10_spl
| h(e12) != e20 ),
inference(component_clause,[status(thm)],[f206]) ).
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(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(f228,definition,
( sQ17_spl
<=> h(e13) = e22 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( ~ sQ17_spl
| h(e13) = e22 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,definition,
( sQ18_spl
<=> h(e13) = e23 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f232,plain,
( ~ sQ18_spl
| h(e13) = e23 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,definition,
( sQ19_spl
<=> h(e13) = e24 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( ~ sQ19_spl
| h(e13) = e24 ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f107,f222,f225,f228,f231,f234]) ).
fof(f238,definition,
( sQ20_spl
<=> h(e14) = e20 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ20_spl
| h(e14) = e20 ),
inference(component_clause,[status(thm)],[f238]) ).
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(f244,definition,
( sQ22_spl
<=> h(e14) = e22 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ22_spl
| h(e14) = e22 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
( sQ23_spl
<=> h(e14) = e23 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( ~ sQ23_spl
| h(e14) = e23 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
( sQ24_spl
<=> h(e14) = e24 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( ~ sQ24_spl
| h(e14) = e24 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f252,plain,
( sQ24_spl
| h(e14) != e24 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f254,definition,
( sQ25_spl
<=> j(e20) = e10 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ25_spl
| j(e20) = e10 ),
inference(component_clause,[status(thm)],[f254]) ).
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(f263,definition,
( sQ28_spl
<=> j(e20) = e13 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ28_spl
| j(e20) = e13 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ29_spl
<=> j(e20) = e14 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ29_spl
| j(e20) = e14 ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
( sQ29_spl
| sQ28_spl
| sQ27_spl
| sQ26_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f109,f254,f257,f260,f263,f266]) ).
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(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(f280,plain,
( ~ sQ33_spl
| j(e21) = e13 ),
inference(component_clause,[status(thm)],[f279]) ).
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(f298,definition,
( sQ39_spl
<=> j(e22) = e14 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( ~ sQ39_spl
| j(e22) = e14 ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f302,definition,
( sQ40_spl
<=> j(e23) = e10 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( ~ sQ40_spl
| j(e23) = e10 ),
inference(component_clause,[status(thm)],[f302]) ).
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(f311,definition,
( sQ43_spl
<=> j(e23) = e13 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( ~ sQ43_spl
| j(e23) = e13 ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,definition,
( sQ44_spl
<=> j(e23) = e14 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ44_spl
| j(e23) = e14 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( sQ44_spl
| sQ43_spl
| sQ42_spl
| sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f112,f302,f305,f308,f311,f314]) ).
fof(f318,definition,
( sQ45_spl
<=> j(e24) = e10 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( ~ sQ45_spl
| j(e24) = e10 ),
inference(component_clause,[status(thm)],[f318]) ).
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(f327,definition,
( sQ48_spl
<=> j(e24) = e13 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( ~ sQ48_spl
| j(e24) = e13 ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f329,plain,
( sQ48_spl
| j(e24) != e13 ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f330,definition,
( sQ49_spl
<=> j(e24) = e14 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( ~ sQ49_spl
| j(e24) = e14 ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,plain,
( sQ49_spl
| sQ48_spl
| sQ47_spl
| sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f113,f318,f321,f324,f327,f330]) ).
fof(f347,plain,
h(e10) = op2(h(e10),h(e10)),
inference(backward_demodulation,[status(thm)],[f53,f114]) ).
fof(f433,plain,
( ~ sQ25_spl
| h(e10) = e20 ),
inference(forward_demodulation,[status(thm)],[f255,f164]) ).
fof(f434,plain,
( ~ sQ30_spl
| h(e10) = e21 ),
inference(forward_demodulation,[status(thm)],[f271,f165]) ).
fof(f435,plain,
( ~ sQ30_spl
| ~ sQ0_spl
| e20 = e21 ),
inference(forward_demodulation,[status(thm)],[f175,f434]) ).
fof(f436,plain,
( ~ sQ30_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f18]) ).
fof(f437,plain,
( ~ sQ30_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f436]) ).
fof(f438,plain,
( ~ sQ25_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f433,f174,f254]) ).
fof(f449,plain,
( ~ sQ35_spl
| h(e10) = e22 ),
inference(forward_demodulation,[status(thm)],[f287,f166]) ).
fof(f450,plain,
( ~ sQ35_spl
| ~ sQ0_spl
| e20 = e22 ),
inference(forward_demodulation,[status(thm)],[f175,f449]) ).
fof(f451,plain,
( ~ sQ35_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f19]) ).
fof(f452,plain,
( ~ sQ35_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f451]) ).
fof(f454,plain,
h(e14) = op2(h(e11),h(e11)),
inference(forward_demodulation,[status(thm)],[f59,f120]) ).
fof(f476,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| e20 = e21 ),
inference(forward_demodulation,[status(thm)],[f175,f178]) ).
fof(f477,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f476,f18]) ).
fof(f478,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f489,plain,
( ~ sQ40_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f303,f167]) ).
fof(f495,plain,
h(e13) = op2(h(e11),h(e14)),
inference(forward_demodulation,[status(thm)],[f62,f123]) ).
fof(f500,plain,
( ~ sQ0_spl
| ~ sQ40_spl
| e23 = e20 ),
inference(forward_demodulation,[status(thm)],[f489,f175]) ).
fof(f501,plain,
( ~ sQ0_spl
| ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f20]) ).
fof(f502,plain,
( ~ sQ0_spl
| ~ sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f520,plain,
h(e13) = op2(h(e12),h(e12)),
inference(forward_demodulation,[status(thm)],[f65,f126]) ).
fof(f529,plain,
( ~ sQ10_spl
| h(e13) = op2(h(e12),e20) ),
inference(backward_demodulation,[status(thm)],[f207,f520]) ).
fof(f530,plain,
( ~ sQ10_spl
| h(e13) = op2(e20,e20) ),
inference(forward_demodulation,[status(thm)],[f207,f529]) ).
fof(f531,plain,
( ~ sQ10_spl
| h(e13) = e20 ),
inference(forward_demodulation,[status(thm)],[f78,f530]) ).
fof(f567,plain,
h(e11) = op2(h(e13),h(e13)),
inference(forward_demodulation,[status(thm)],[f71,f132]) ).
fof(f568,plain,
h(e10) = op2(h(e13),h(e14)),
inference(forward_demodulation,[status(thm)],[f72,f133]) ).
fof(f569,plain,
( ~ sQ21_spl
| h(e10) = op2(h(e13),e21) ),
inference(forward_demodulation,[status(thm)],[f242,f568]) ).
fof(f610,plain,
h(e12) = op2(h(e14),h(e14)),
inference(forward_demodulation,[status(thm)],[f77,f138]) ).
fof(f611,plain,
( ~ sQ22_spl
| h(e12) = op2(h(e14),e22) ),
inference(backward_demodulation,[status(thm)],[f245,f610]) ).
fof(f617,plain,
( ~ sQ22_spl
| h(e12) = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f245,f611]) ).
fof(f618,plain,
( ~ sQ22_spl
| h(e12) = e24 ),
inference(forward_demodulation,[status(thm)],[f90,f617]) ).
fof(f620,plain,
j(e20) = op1(j(e20),j(e20)),
inference(forward_demodulation,[status(thm)],[f78,f139]) ).
fof(f621,plain,
( ~ sQ26_spl
| e11 = op1(j(e20),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f258,f620]) ).
fof(f622,plain,
( ~ sQ26_spl
| e11 = op1(e11,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f258,f621]) ).
fof(f623,plain,
( ~ sQ26_spl
| e11 = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f258,f622]) ).
fof(f624,plain,
( ~ sQ26_spl
| e11 = e14 ),
inference(forward_demodulation,[status(thm)],[f59,f623]) ).
fof(f625,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f624,f14]) ).
fof(f626,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f678,plain,
j(e24) = op1(j(e21),j(e21)),
inference(forward_demodulation,[status(thm)],[f84,f145]) ).
fof(f679,plain,
( ~ sQ48_spl
| e13 = op1(j(e21),j(e21)) ),
inference(forward_demodulation,[status(thm)],[f328,f678]) ).
fof(f692,plain,
j(e20) = op1(j(e21),j(e23)),
inference(forward_demodulation,[status(thm)],[f86,f147]) ).
fof(f709,plain,
j(e22) = op1(j(e21),j(e24)),
inference(forward_demodulation,[status(thm)],[f87,f148]) ).
fof(f710,plain,
( ~ sQ48_spl
| j(e22) = op1(j(e21),e13) ),
inference(forward_demodulation,[status(thm)],[f328,f709]) ).
fof(f720,plain,
( ~ sQ48_spl
| ~ sQ32_spl
| j(e22) = op1(e12,e13) ),
inference(backward_demodulation,[status(thm)],[f277,f710]) ).
fof(f724,plain,
( ~ sQ48_spl
| ~ sQ32_spl
| j(e22) = e14 ),
inference(forward_demodulation,[status(thm)],[f66,f720]) ).
fof(f726,plain,
j(e24) = op1(j(e22),j(e22)),
inference(forward_demodulation,[status(thm)],[f90,f151]) ).
fof(f749,plain,
( ~ sQ10_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f531,f222,f206]) ).
fof(f754,plain,
( ~ sQ22_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f618,f218,f244]) ).
fof(f771,plain,
j(e22) = op1(j(e23),j(e21)),
inference(forward_demodulation,[status(thm)],[f94,f155]) ).
fof(f787,plain,
j(e24) = op1(j(e23),j(e23)),
inference(forward_demodulation,[status(thm)],[f96,f157]) ).
fof(f819,plain,
j(e20) = op1(j(e24),j(e24)),
inference(forward_demodulation,[status(thm)],[f102,f163]) ).
fof(f824,plain,
( ~ sQ42_spl
| j(e24) = op1(j(e23),e12) ),
inference(backward_demodulation,[status(thm)],[f309,f787]) ).
fof(f825,plain,
( ~ sQ42_spl
| j(e24) = op1(e12,e12) ),
inference(forward_demodulation,[status(thm)],[f309,f824]) ).
fof(f826,plain,
( ~ sQ42_spl
| j(e24) = e13 ),
inference(forward_demodulation,[status(thm)],[f65,f825]) ).
fof(f827,plain,
( ~ sQ42_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f826,f329]) ).
fof(f828,plain,
( ~ sQ42_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f827]) ).
fof(f864,plain,
( ~ sQ47_spl
| h(e12) = e24 ),
inference(backward_demodulation,[status(thm)],[f325,f168]) ).
fof(f867,plain,
( ~ sQ47_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f864,f218,f324]) ).
fof(f885,plain,
( ~ sQ3_spl
| h(e10) = op2(h(e10),e23) ),
inference(backward_demodulation,[status(thm)],[f184,f347]) ).
fof(f889,plain,
( ~ sQ3_spl
| e23 = op2(h(e10),e23) ),
inference(forward_demodulation,[status(thm)],[f184,f885]) ).
fof(f890,plain,
( ~ sQ3_spl
| e23 = op2(e23,e23) ),
inference(forward_demodulation,[status(thm)],[f184,f889]) ).
fof(f891,plain,
( ~ sQ3_spl
| e23 = e24 ),
inference(forward_demodulation,[status(thm)],[f96,f890]) ).
fof(f892,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f891,f27]) ).
fof(f893,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f892]) ).
fof(f897,plain,
( ~ sQ27_spl
| h(e12) = e20 ),
inference(forward_demodulation,[status(thm)],[f261,f164]) ).
fof(f898,plain,
( ~ sQ27_spl
| sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f897,f208]) ).
fof(f899,plain,
( ~ sQ27_spl
| sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f898]) ).
fof(f906,plain,
( ~ sQ48_spl
| ~ sQ32_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f724,f298,f276,f327]) ).
fof(f920,plain,
( ~ sQ16_spl
| j(e21) = e13 ),
inference(backward_demodulation,[status(thm)],[f226,f172]) ).
fof(f933,plain,
( ~ sQ20_spl
| j(e20) = e14 ),
inference(backward_demodulation,[status(thm)],[f239,f173]) ).
fof(f939,plain,
( ~ sQ41_spl
| h(e11) = e23 ),
inference(forward_demodulation,[status(thm)],[f306,f167]) ).
fof(f961,plain,
( ~ sQ20_spl
| ~ sQ25_spl
| e10 = e14 ),
inference(forward_demodulation,[status(thm)],[f255,f933]) ).
fof(f962,plain,
( ~ sQ20_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f961,f11]) ).
fof(f963,plain,
( ~ sQ20_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f973,plain,
( ~ sQ39_spl
| h(e14) = e22 ),
inference(backward_demodulation,[status(thm)],[f299,f166]) ).
fof(f976,plain,
( ~ sQ39_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f973,f244,f298]) ).
fof(f979,plain,
( ~ sQ8_spl
| h(e13) = op2(e23,h(e14)) ),
inference(backward_demodulation,[status(thm)],[f200,f495]) ).
fof(f985,plain,
( ~ sQ8_spl
| h(e14) = op2(e23,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f200,f454]) ).
fof(f986,plain,
( ~ sQ8_spl
| h(e14) = op2(e23,e23) ),
inference(forward_demodulation,[status(thm)],[f200,f985]) ).
fof(f987,plain,
( ~ sQ8_spl
| h(e14) = e24 ),
inference(forward_demodulation,[status(thm)],[f96,f986]) ).
fof(f998,plain,
( sQ24_spl
| ~ sQ8_spl
| e24 != e24 ),
inference(forward_demodulation,[status(thm)],[f987,f252]) ).
fof(f999,plain,
( sQ24_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f998]) ).
fof(f1000,plain,
( sQ24_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f999]) ).
fof(f1009,plain,
( ~ sQ48_spl
| ~ sQ31_spl
| e13 = op1(e11,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f274,f679]) ).
fof(f1010,plain,
( ~ sQ48_spl
| ~ sQ31_spl
| e13 = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f274,f1009]) ).
fof(f1011,plain,
( ~ sQ48_spl
| ~ sQ31_spl
| e13 = e14 ),
inference(forward_demodulation,[status(thm)],[f59,f1010]) ).
fof(f1012,plain,
( ~ sQ48_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1011,f17]) ).
fof(f1013,plain,
( ~ sQ48_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1012]) ).
fof(f1014,plain,
( ~ sQ41_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f939,f199,f305]) ).
fof(f1038,plain,
( ~ sQ28_spl
| e13 = op1(j(e20),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f264,f620]) ).
fof(f1039,plain,
( ~ sQ28_spl
| e13 = op1(e13,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f264,f1038]) ).
fof(f1040,plain,
( ~ sQ28_spl
| e13 = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f264,f1039]) ).
fof(f1041,plain,
( ~ sQ28_spl
| e13 = e11 ),
inference(forward_demodulation,[status(thm)],[f71,f1040]) ).
fof(f1042,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1041,f13]) ).
fof(f1043,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f1042]) ).
fof(f1103,plain,
( ~ sQ0_spl
| j(e20) = e10 ),
inference(forward_demodulation,[status(thm)],[f175,f169]) ).
fof(f1107,plain,
( ~ sQ25_spl
| e10 = op1(j(e21),j(e23)) ),
inference(forward_demodulation,[status(thm)],[f255,f692]) ).
fof(f1108,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| e10 = op1(e13,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f280,f1107]) ).
fof(f1109,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| ~ sQ43_spl
| e10 = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f312,f1108]) ).
fof(f1110,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| ~ sQ43_spl
| e10 = e11 ),
inference(forward_demodulation,[status(thm)],[f71,f1109]) ).
fof(f1111,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1110,f8]) ).
fof(f1112,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f1111]) ).
fof(f1114,plain,
( ~ sQ48_spl
| ~ sQ33_spl
| e13 = op1(e13,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f280,f679]) ).
fof(f1115,plain,
( ~ sQ48_spl
| ~ sQ33_spl
| e13 = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f280,f1114]) ).
fof(f1116,plain,
( ~ sQ48_spl
| ~ sQ33_spl
| e13 = e11 ),
inference(forward_demodulation,[status(thm)],[f71,f1115]) ).
fof(f1117,plain,
( ~ sQ48_spl
| ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1116,f13]) ).
fof(f1118,plain,
( ~ sQ48_spl
| ~ sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f1117]) ).
fof(f1152,plain,
( ~ sQ16_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f920,f279,f225]) ).
fof(f1174,plain,
( ~ sQ32_spl
| j(e22) = op1(j(e23),e12) ),
inference(backward_demodulation,[status(thm)],[f277,f771]) ).
fof(f1193,plain,
( ~ sQ8_spl
| ~ sQ24_spl
| h(e13) = op2(e23,e24) ),
inference(forward_demodulation,[status(thm)],[f251,f979]) ).
fof(f1194,plain,
( ~ sQ8_spl
| ~ sQ24_spl
| h(e13) = e21 ),
inference(forward_demodulation,[status(thm)],[f97,f1193]) ).
fof(f1229,plain,
( ~ sQ48_spl
| h(e13) = e24 ),
inference(backward_demodulation,[status(thm)],[f328,f168]) ).
fof(f1253,plain,
( ~ sQ34_spl
| h(e14) = e21 ),
inference(backward_demodulation,[status(thm)],[f283,f165]) ).
fof(f1285,plain,
( ~ sQ21_spl
| ~ sQ0_spl
| e20 = op2(h(e13),e21) ),
inference(forward_demodulation,[status(thm)],[f175,f569]) ).
fof(f1314,plain,
( ~ sQ17_spl
| j(e22) = e13 ),
inference(backward_demodulation,[status(thm)],[f229,f172]) ).
fof(f1360,plain,
( ~ sQ8_spl
| e23 = op2(h(e13),h(e13)) ),
inference(forward_demodulation,[status(thm)],[f200,f567]) ).
fof(f1361,plain,
( ~ sQ8_spl
| ~ sQ24_spl
| e23 = op2(e21,h(e13)) ),
inference(forward_demodulation,[status(thm)],[f1194,f1360]) ).
fof(f1362,plain,
( ~ sQ8_spl
| ~ sQ24_spl
| e23 = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f1194,f1361]) ).
fof(f1363,plain,
( ~ sQ8_spl
| ~ sQ24_spl
| e23 = e24 ),
inference(forward_demodulation,[status(thm)],[f84,f1362]) ).
fof(f1364,plain,
( ~ sQ8_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1363,f27]) ).
fof(f1365,plain,
( ~ sQ8_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f1364]) ).
fof(f1383,plain,
( ~ sQ14_spl
| h(e13) = op2(e24,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f219,f520]) ).
fof(f1384,plain,
( ~ sQ14_spl
| h(e13) = op2(e24,e24) ),
inference(forward_demodulation,[status(thm)],[f219,f1383]) ).
fof(f1386,plain,
( ~ sQ14_spl
| h(e13) = e20 ),
inference(forward_demodulation,[status(thm)],[f102,f1384]) ).
fof(f1388,plain,
( ~ sQ29_spl
| e14 = op1(j(e20),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f267,f620]) ).
fof(f1389,plain,
( ~ sQ29_spl
| e14 = op1(e14,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f267,f1388]) ).
fof(f1390,plain,
( ~ sQ29_spl
| e14 = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f267,f1389]) ).
fof(f1391,plain,
( ~ sQ29_spl
| e14 = e12 ),
inference(forward_demodulation,[status(thm)],[f77,f1390]) ).
fof(f1392,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1391,f16]) ).
fof(f1393,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1392]) ).
fof(f1408,plain,
( ~ sQ19_spl
| h(e10) = op2(e24,h(e14)) ),
inference(forward_demodulation,[status(thm)],[f235,f568]) ).
fof(f1412,plain,
( ~ sQ19_spl
| ~ sQ21_spl
| h(e10) = op2(e24,e21) ),
inference(backward_demodulation,[status(thm)],[f242,f1408]) ).
fof(f1416,plain,
( ~ sQ19_spl
| ~ sQ21_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f99,f1412]) ).
fof(f1417,plain,
( ~ sQ19_spl
| ~ sQ21_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1416,f185]) ).
fof(f1418,plain,
( ~ sQ19_spl
| ~ sQ21_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1417]) ).
fof(f1466,plain,
( ~ sQ21_spl
| ~ sQ0_spl
| ~ sQ18_spl
| e20 = op2(e23,e21) ),
inference(forward_demodulation,[status(thm)],[f232,f1285]) ).
fof(f1467,plain,
( ~ sQ21_spl
| ~ sQ0_spl
| ~ sQ18_spl
| e20 = e22 ),
inference(forward_demodulation,[status(thm)],[f94,f1466]) ).
fof(f1468,plain,
( ~ sQ21_spl
| ~ sQ0_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1467,f19]) ).
fof(f1469,plain,
( ~ sQ21_spl
| ~ sQ0_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f1468]) ).
fof(f1477,plain,
( ~ sQ0_spl
| e10 = op1(j(e21),j(e23)) ),
inference(forward_demodulation,[status(thm)],[f1103,f692]) ).
fof(f1478,plain,
( ~ sQ0_spl
| ~ sQ31_spl
| e10 = op1(e11,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f274,f1477]) ).
fof(f1479,plain,
( ~ sQ0_spl
| ~ sQ31_spl
| ~ sQ43_spl
| e10 = op1(e11,e13) ),
inference(forward_demodulation,[status(thm)],[f312,f1478]) ).
fof(f1480,plain,
( ~ sQ0_spl
| ~ sQ31_spl
| ~ sQ43_spl
| e10 = e12 ),
inference(forward_demodulation,[status(thm)],[f61,f1479]) ).
fof(f1481,plain,
( ~ sQ0_spl
| ~ sQ31_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1480,f9]) ).
fof(f1482,plain,
( ~ sQ0_spl
| ~ sQ31_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f1481]) ).
fof(f1492,plain,
( ~ sQ32_spl
| ~ sQ43_spl
| j(e22) = op1(e13,e12) ),
inference(forward_demodulation,[status(thm)],[f312,f1174]) ).
fof(f1493,plain,
( ~ sQ32_spl
| ~ sQ43_spl
| j(e22) = e14 ),
inference(forward_demodulation,[status(thm)],[f70,f1492]) ).
fof(f1541,plain,
( ~ sQ34_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1253,f241,f282]) ).
fof(f1570,plain,
( ~ sQ17_spl
| j(e24) = op1(j(e22),e13) ),
inference(backward_demodulation,[status(thm)],[f1314,f726]) ).
fof(f1572,plain,
( ~ sQ17_spl
| j(e24) = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f1314,f1570]) ).
fof(f1573,plain,
( ~ sQ17_spl
| j(e24) = e11 ),
inference(forward_demodulation,[status(thm)],[f71,f1572]) ).
fof(f1599,plain,
( ~ sQ0_spl
| e10 = op1(j(e24),j(e24)) ),
inference(forward_demodulation,[status(thm)],[f1103,f819]) ).
fof(f1600,plain,
( ~ sQ0_spl
| ~ sQ46_spl
| e10 = op1(e11,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f322,f1599]) ).
fof(f1601,plain,
( ~ sQ0_spl
| ~ sQ46_spl
| e10 = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f322,f1600]) ).
fof(f1602,plain,
( ~ sQ0_spl
| ~ sQ46_spl
| e10 = e14 ),
inference(forward_demodulation,[status(thm)],[f59,f1601]) ).
fof(f1603,plain,
( ~ sQ0_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1602,f11]) ).
fof(f1604,plain,
( ~ sQ0_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f1603]) ).
fof(f1614,plain,
( ~ sQ32_spl
| ~ sQ43_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f1493,f298,f311,f276]) ).
fof(f1644,plain,
( ~ sQ45_spl
| h(e10) = e24 ),
inference(forward_demodulation,[status(thm)],[f319,f168]) ).
fof(f1645,plain,
( ~ sQ45_spl
| ~ sQ0_spl
| e20 = e24 ),
inference(forward_demodulation,[status(thm)],[f175,f1644]) ).
fof(f1646,plain,
( ~ sQ45_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1645,f21]) ).
fof(f1647,plain,
( ~ sQ45_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1646]) ).
fof(f1648,plain,
( ~ sQ17_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f1573,f321,f228]) ).
fof(f1658,plain,
( ~ sQ5_spl
| j(e20) = e11 ),
inference(backward_demodulation,[status(thm)],[f191,f170]) ).
fof(f1662,plain,
( ~ sQ5_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1658,f257,f190]) ).
fof(f1737,plain,
( ~ sQ44_spl
| h(e14) = e23 ),
inference(forward_demodulation,[status(thm)],[f315,f167]) ).
fof(f1738,plain,
( ~ sQ49_spl
| h(e14) = e24 ),
inference(forward_demodulation,[status(thm)],[f331,f168]) ).
fof(f1739,plain,
( ~ sQ49_spl
| ~ sQ23_spl
| e23 = e24 ),
inference(forward_demodulation,[status(thm)],[f248,f1738]) ).
fof(f1740,plain,
( ~ sQ49_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1739,f27]) ).
fof(f1741,plain,
( ~ sQ49_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f1740]) ).
fof(f1753,plain,
( ~ sQ44_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1737,f247,f314]) ).
fof(f1764,plain,
( ~ sQ14_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f1386,f222,f218]) ).
fof(f1770,plain,
( ~ sQ48_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f1229,f234,f327]) ).
fof(f1785,plain,
( ~ sQ15_spl
| h(e11) = op2(e20,h(e13)) ),
inference(forward_demodulation,[status(thm)],[f223,f567]) ).
fof(f1786,plain,
( ~ sQ15_spl
| h(e11) = op2(e20,e20) ),
inference(forward_demodulation,[status(thm)],[f223,f1785]) ).
fof(f1787,plain,
( ~ sQ15_spl
| h(e11) = e20 ),
inference(forward_demodulation,[status(thm)],[f78,f1786]) ).
fof(f1788,plain,
( ~ sQ15_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1787,f192]) ).
fof(f1789,plain,
( ~ sQ15_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1788]) ).
fof(f1790,plain,
$false,
inference(sat_refutation,[status(thm)],[f237,f269,f285,f317,f333,f437,f438,f452,f478,f502,f626,f749,f754,f828,f867,f893,f899,f906,f963,f976,f1000,f1013,f1014,f1043,f1112,f1118,f1152,f1365,f1393,f1418,f1469,f1482,f1541,f1604,f1614,f1647,f1648,f1662,f1741,f1753,f1764,f1770,f1789]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG082+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 12:55:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.088991 seconds
% 0.14/0.46 % CPU time: 0.362538 seconds
% 0.14/0.46 % Total memory used: 115.213 MB
% 0.14/0.46 % Net memory used: 114.968 MB
%------------------------------------------------------------------------------