%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG079+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 : n026.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 11:48:02 AM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 319 ( 63 unt; 36 def)
% Number of atoms : 1063 ( 665 equ)
% Maximal formula atoms : 110 ( 3 avg)
% Number of connectives : 1061 ( 317 ~; 435 |; 271 &)
% ( 36 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 38 ( 36 usr; 37 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) = e11
& op1(e14,e12) = e10
& op1(e14,e11) = e13
& op1(e14,e10) = e14
& op1(e13,e14) = e10
& op1(e13,e13) = e14
& op1(e13,e12) = e11
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e14) = e11
& op1(e12,e13) = e10
& op1(e12,e12) = e13
& op1(e12,e11) = e14
& op1(e12,e10) = e12
& op1(e11,e14) = e13
& op1(e11,e13) = e12
& op1(e11,e12) = e14
& 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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( op2(e24,e24) = e21
& op2(e24,e23) = e22
& op2(e24,e22) = e20
& op2(e24,e21) = e23
& op2(e24,e20) = e24
& op2(e23,e24) = e22
& op2(e23,e23) = e21
& op2(e23,e22) = e24
& op2(e23,e21) = e20
& op2(e23,e20) = e23
& op2(e22,e24) = e23
& op2(e22,e23) = e20
& op2(e22,e22) = e21
& op2(e22,e21) = e24
& op2(e22,e20) = e22
& op2(e21,e24) = e20
& op2(e21,e23) = e24
& op2(e21,e22) = e23
& 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/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(f12,plain,
e11 != e12,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
e11 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
e12 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
e20 != e21,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
e20 != e24,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
e21 != e22,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
e21 != e23,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
e21 != e24,
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(f59,plain,
op1(e11,e11) = e10,
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) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f71,plain,
op1(e13,e13) = e14,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f74,plain,
op1(e14,e11) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f75,plain,
op1(e14,e12) = 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) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f87,plain,
op2(e21,e24) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f90,plain,
op2(e22,e22) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f92,plain,
op2(e22,e24) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f95,plain,
op2(e23,e22) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f96,plain,
op2(e23,e23) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f102,plain,
op2(e24,e24) = e21,
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(f107,plain,
( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = 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(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(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(f135,plain,
h(op1(e14,e11)) = op2(h(e14),h(e11)),
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(f145,plain,
j(op2(e21,e21)) = op1(j(e21),j(e21)),
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(f153,plain,
j(op2(e22,e24)) = op1(j(e22),j(e24)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f156,plain,
j(op2(e23,e22)) = op1(j(e23),j(e22)),
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(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(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(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(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(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(f211,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(f214,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(f224,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(f230,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(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(f246,plain,
( sQ22_spl
| h(e14) != e22 ),
inference(component_clause,[status(thm)],[f244]) ).
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(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(f289,definition,
( sQ36_spl
<=> j(e22) = e11 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( ~ sQ36_spl
| j(e22) = e11 ),
inference(component_clause,[status(thm)],[f289]) ).
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(f294,plain,
( sQ37_spl
| j(e22) != e12 ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
( sQ38_spl
<=> j(e22) = e13 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( ~ sQ38_spl
| j(e22) = e13 ),
inference(component_clause,[status(thm)],[f295]) ).
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(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(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(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(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(f389,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| e22 = e21 ),
inference(forward_demodulation,[status(thm)],[f213,f210]) ).
fof(f390,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f22]) ).
fof(f391,plain,
( ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f432,plain,
( ~ sQ30_spl
| h(e10) = e21 ),
inference(forward_demodulation,[status(thm)],[f271,f165]) ).
fof(f482,plain,
h(e10) = op2(h(e11),h(e11)),
inference(forward_demodulation,[status(thm)],[f59,f120]) ).
fof(f554,plain,
h(e13) = op2(h(e12),h(e12)),
inference(forward_demodulation,[status(thm)],[f65,f126]) ).
fof(f577,plain,
( ~ sQ10_spl
| h(e13) = op2(e20,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f207,f554]) ).
fof(f578,plain,
( ~ sQ10_spl
| h(e13) = op2(e20,e20) ),
inference(forward_demodulation,[status(thm)],[f207,f577]) ).
fof(f607,plain,
h(e14) = op2(h(e13),h(e13)),
inference(forward_demodulation,[status(thm)],[f71,f132]) ).
fof(f623,plain,
h(e13) = op2(h(e14),h(e11)),
inference(forward_demodulation,[status(thm)],[f74,f135]) ).
fof(f666,plain,
h(e12) = op2(h(e14),h(e14)),
inference(forward_demodulation,[status(thm)],[f77,f138]) ).
fof(f680,plain,
( ~ sQ48_spl
| h(e13) = e24 ),
inference(forward_demodulation,[status(thm)],[f328,f168]) ).
fof(f681,plain,
( ~ sQ48_spl
| ~ sQ15_spl
| e20 = e24 ),
inference(forward_demodulation,[status(thm)],[f223,f680]) ).
fof(f682,plain,
( ~ sQ48_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f681,f21]) ).
fof(f683,plain,
( ~ sQ48_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f682]) ).
fof(f684,plain,
( ~ sQ48_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f680,f234,f327]) ).
fof(f696,plain,
( ~ sQ21_spl
| h(e12) = op2(e21,h(e14)) ),
inference(forward_demodulation,[status(thm)],[f242,f666]) ).
fof(f697,plain,
( ~ sQ21_spl
| h(e12) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f242,f696]) ).
fof(f698,plain,
( ~ sQ21_spl
| h(e12) = e22 ),
inference(forward_demodulation,[status(thm)],[f84,f697]) ).
fof(f711,plain,
( sQ12_spl
| ~ sQ21_spl
| e22 != e22 ),
inference(forward_demodulation,[status(thm)],[f698,f214]) ).
fof(f712,plain,
( sQ12_spl
| ~ sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f711]) ).
fof(f713,plain,
( sQ12_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f741,plain,
j(e22) = op1(j(e21),j(e21)),
inference(forward_demodulation,[status(thm)],[f84,f145]) ).
fof(f769,plain,
j(e20) = op1(j(e21),j(e24)),
inference(forward_demodulation,[status(thm)],[f87,f148]) ).
fof(f794,plain,
j(e21) = op1(j(e22),j(e22)),
inference(forward_demodulation,[status(thm)],[f90,f151]) ).
fof(f810,plain,
j(e23) = op1(j(e22),j(e24)),
inference(forward_demodulation,[status(thm)],[f92,f153]) ).
fof(f811,plain,
( ~ sQ46_spl
| j(e23) = op1(j(e22),e11) ),
inference(forward_demodulation,[status(thm)],[f322,f810]) ).
fof(f819,plain,
( ~ sQ46_spl
| ~ sQ37_spl
| j(e23) = op1(e12,e11) ),
inference(backward_demodulation,[status(thm)],[f293,f811]) ).
fof(f820,plain,
( ~ sQ46_spl
| ~ sQ37_spl
| j(e23) = e14 ),
inference(forward_demodulation,[status(thm)],[f64,f819]) ).
fof(f844,plain,
( ~ sQ46_spl
| ~ sQ37_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f820,f314,f292,f321]) ).
fof(f852,plain,
j(e24) = op1(j(e23),j(e22)),
inference(forward_demodulation,[status(thm)],[f95,f156]) ).
fof(f853,plain,
j(e21) = op1(j(e23),j(e23)),
inference(forward_demodulation,[status(thm)],[f96,f157]) ).
fof(f892,plain,
( ~ sQ42_spl
| j(e21) = op1(e12,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f309,f853]) ).
fof(f893,plain,
( ~ sQ42_spl
| j(e21) = op1(e12,e12) ),
inference(forward_demodulation,[status(thm)],[f309,f892]) ).
fof(f894,plain,
( ~ sQ42_spl
| j(e21) = e13 ),
inference(forward_demodulation,[status(thm)],[f65,f893]) ).
fof(f930,plain,
j(e21) = op1(j(e24),j(e24)),
inference(forward_demodulation,[status(thm)],[f102,f163]) ).
fof(f931,plain,
( ~ sQ31_spl
| e11 = op1(j(e24),j(e24)) ),
inference(forward_demodulation,[status(thm)],[f274,f930]) ).
fof(f933,plain,
( ~ sQ7_spl
| j(e22) = e11 ),
inference(backward_demodulation,[status(thm)],[f197,f170]) ).
fof(f936,plain,
( ~ sQ7_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f933,f289,f196]) ).
fof(f940,plain,
( ~ sQ0_spl
| j(e20) = e10 ),
inference(backward_demodulation,[status(thm)],[f175,f169]) ).
fof(f948,plain,
( ~ sQ13_spl
| j(e23) = e12 ),
inference(backward_demodulation,[status(thm)],[f216,f171]) ).
fof(f952,plain,
( ~ sQ13_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f948,f308,f215]) ).
fof(f955,plain,
( ~ sQ31_spl
| ~ sQ47_spl
| e11 = op1(e12,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f325,f931]) ).
fof(f956,plain,
( ~ sQ31_spl
| ~ sQ47_spl
| e11 = op1(e12,e12) ),
inference(forward_demodulation,[status(thm)],[f325,f955]) ).
fof(f957,plain,
( ~ sQ31_spl
| ~ sQ47_spl
| e11 = e13 ),
inference(forward_demodulation,[status(thm)],[f65,f956]) ).
fof(f958,plain,
( ~ sQ31_spl
| ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f957,f13]) ).
fof(f959,plain,
( ~ sQ31_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f958]) ).
fof(f978,plain,
h(e10) = op2(h(e10),h(e10)),
inference(forward_demodulation,[status(thm)],[f53,f114]) ).
fof(f991,plain,
( ~ sQ32_spl
| h(e12) = e21 ),
inference(forward_demodulation,[status(thm)],[f277,f165]) ).
fof(f997,plain,
( ~ sQ22_spl
| j(e22) = e14 ),
inference(backward_demodulation,[status(thm)],[f245,f173]) ).
fof(f1015,plain,
( sQ11_spl
| ~ sQ32_spl
| e21 != e21 ),
inference(forward_demodulation,[status(thm)],[f991,f211]) ).
fof(f1016,plain,
( sQ11_spl
| ~ sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1015]) ).
fof(f1017,plain,
( sQ11_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f1016]) ).
fof(f1018,plain,
( ~ sQ30_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f432,f177,f270]) ).
fof(f1120,plain,
( ~ sQ19_spl
| e24 = op2(h(e12),h(e12)) ),
inference(forward_demodulation,[status(thm)],[f235,f554]) ).
fof(f1121,plain,
( ~ sQ19_spl
| ~ sQ12_spl
| e24 = op2(e22,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f213,f1120]) ).
fof(f1122,plain,
( ~ sQ19_spl
| ~ sQ12_spl
| e24 = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f213,f1121]) ).
fof(f1123,plain,
( ~ sQ19_spl
| ~ sQ12_spl
| e24 = e21 ),
inference(forward_demodulation,[status(thm)],[f90,f1122]) ).
fof(f1124,plain,
( ~ sQ19_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1123,f24]) ).
fof(f1125,plain,
( ~ sQ19_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1124]) ).
fof(f1139,plain,
( ~ sQ22_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f997,f298,f244]) ).
fof(f1152,plain,
( ~ sQ10_spl
| h(e13) = e20 ),
inference(forward_demodulation,[status(thm)],[f78,f578]) ).
fof(f1180,plain,
( sQ15_spl
| ~ sQ10_spl
| e20 != e20 ),
inference(forward_demodulation,[status(thm)],[f1152,f224]) ).
fof(f1181,plain,
( sQ15_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1180]) ).
fof(f1182,plain,
( sQ15_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1181]) ).
fof(f1216,plain,
( ~ sQ47_spl
| h(e12) = e24 ),
inference(forward_demodulation,[status(thm)],[f325,f168]) ).
fof(f1239,plain,
( ~ sQ16_spl
| h(e14) = op2(h(e13),e21) ),
inference(backward_demodulation,[status(thm)],[f226,f607]) ).
fof(f1241,plain,
( ~ sQ16_spl
| h(e14) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f226,f1239]) ).
fof(f1242,plain,
( ~ sQ16_spl
| h(e14) = e22 ),
inference(forward_demodulation,[status(thm)],[f84,f1241]) ).
fof(f1243,plain,
( ~ sQ16_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1242,f246]) ).
fof(f1244,plain,
( ~ sQ16_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1243]) ).
fof(f1280,plain,
( ~ sQ36_spl
| e11 = op1(j(e21),j(e21)) ),
inference(forward_demodulation,[status(thm)],[f290,f741]) ).
fof(f1380,plain,
( ~ sQ38_spl
| j(e21) = op1(e13,j(e22)) ),
inference(forward_demodulation,[status(thm)],[f296,f794]) ).
fof(f1381,plain,
( ~ sQ38_spl
| j(e21) = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f296,f1380]) ).
fof(f1382,plain,
( ~ sQ38_spl
| j(e21) = e14 ),
inference(forward_demodulation,[status(thm)],[f71,f1381]) ).
fof(f1385,plain,
( ~ sQ42_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f894,f279,f308]) ).
fof(f1474,plain,
( ~ sQ41_spl
| j(e21) = op1(e11,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f306,f853]) ).
fof(f1475,plain,
( ~ sQ41_spl
| j(e21) = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f306,f1474]) ).
fof(f1476,plain,
( ~ sQ41_spl
| j(e21) = e10 ),
inference(forward_demodulation,[status(thm)],[f59,f1475]) ).
fof(f1498,plain,
( ~ sQ45_spl
| j(e21) = op1(j(e24),e10) ),
inference(backward_demodulation,[status(thm)],[f319,f930]) ).
fof(f1499,plain,
( ~ sQ45_spl
| j(e21) = op1(e10,e10) ),
inference(forward_demodulation,[status(thm)],[f319,f1498]) ).
fof(f1500,plain,
( ~ sQ45_spl
| j(e21) = e10 ),
inference(forward_demodulation,[status(thm)],[f53,f1499]) ).
fof(f1501,plain,
( ~ sQ45_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1500,f272]) ).
fof(f1502,plain,
( ~ sQ45_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f1501]) ).
fof(f1516,plain,
( ~ sQ41_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f1476,f270,f305]) ).
fof(f1523,plain,
( ~ sQ47_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f1216,f218,f324]) ).
fof(f1534,plain,
( ~ sQ6_spl
| j(e21) = e11 ),
inference(backward_demodulation,[status(thm)],[f194,f170]) ).
fof(f1548,plain,
( ~ sQ1_spl
| h(e10) = op2(h(e10),e21) ),
inference(backward_demodulation,[status(thm)],[f178,f978]) ).
fof(f1549,plain,
( ~ sQ1_spl
| e21 = op2(h(e10),e21) ),
inference(forward_demodulation,[status(thm)],[f178,f1548]) ).
fof(f1550,plain,
( ~ sQ1_spl
| e21 = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f178,f1549]) ).
fof(f1551,plain,
( ~ sQ1_spl
| e21 = e22 ),
inference(forward_demodulation,[status(thm)],[f84,f1550]) ).
fof(f1552,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1551,f22]) ).
fof(f1553,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1552]) ).
fof(f1562,plain,
( ~ sQ5_spl
| h(e10) = op2(h(e11),e20) ),
inference(backward_demodulation,[status(thm)],[f191,f482]) ).
fof(f1564,plain,
( ~ sQ5_spl
| h(e10) = op2(e20,e20) ),
inference(forward_demodulation,[status(thm)],[f191,f1562]) ).
fof(f1565,plain,
( ~ sQ5_spl
| h(e10) = e20 ),
inference(forward_demodulation,[status(thm)],[f78,f1564]) ).
fof(f1606,plain,
( ~ sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1565,f174,f190]) ).
fof(f1610,plain,
( ~ sQ31_spl
| ~ sQ46_spl
| e11 = op1(e11,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f322,f931]) ).
fof(f1611,plain,
( ~ sQ31_spl
| ~ sQ46_spl
| e11 = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f322,f1610]) ).
fof(f1612,plain,
( ~ sQ31_spl
| ~ sQ46_spl
| e11 = e10 ),
inference(forward_demodulation,[status(thm)],[f59,f1611]) ).
fof(f1613,plain,
( ~ sQ31_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1612,f8]) ).
fof(f1614,plain,
( ~ sQ31_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f1613]) ).
fof(f1616,plain,
( ~ sQ6_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f1534,f273,f193]) ).
fof(f1618,plain,
( ~ sQ19_spl
| j(e24) = e13 ),
inference(backward_demodulation,[status(thm)],[f235,f172]) ).
fof(f1656,plain,
( ~ sQ38_spl
| h(e14) = e21 ),
inference(backward_demodulation,[status(thm)],[f1382,f165]) ).
fof(f1657,plain,
( ~ sQ38_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1656,f241,f295]) ).
fof(f1684,plain,
( ~ sQ11_spl
| h(e13) = op2(e21,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f210,f554]) ).
fof(f1685,plain,
( ~ sQ11_spl
| h(e13) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f210,f1684]) ).
fof(f1686,plain,
( ~ sQ11_spl
| h(e13) = e22 ),
inference(forward_demodulation,[status(thm)],[f84,f1685]) ).
fof(f1705,plain,
( ~ sQ11_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1686,f230]) ).
fof(f1706,plain,
( ~ sQ11_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f1705]) ).
fof(f1785,plain,
( ~ sQ14_spl
| j(e24) = e12 ),
inference(forward_demodulation,[status(thm)],[f219,f171]) ).
fof(f1786,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| e13 = e12 ),
inference(forward_demodulation,[status(thm)],[f1618,f1785]) ).
fof(f1787,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1786,f15]) ).
fof(f1788,plain,
( ~ sQ14_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f1787]) ).
fof(f1798,plain,
( ~ sQ12_spl
| ~ sQ14_spl
| e24 = e22 ),
inference(forward_demodulation,[status(thm)],[f219,f213]) ).
fof(f1799,plain,
( ~ sQ12_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1798,f26]) ).
fof(f1800,plain,
( ~ sQ12_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1799]) ).
fof(f1871,plain,
( ~ sQ0_spl
| e10 = op1(j(e21),j(e24)) ),
inference(backward_demodulation,[status(thm)],[f940,f769]) ).
fof(f1885,plain,
( ~ sQ39_spl
| j(e21) = op1(j(e22),e14) ),
inference(backward_demodulation,[status(thm)],[f299,f794]) ).
fof(f1888,plain,
( ~ sQ39_spl
| j(e21) = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f299,f1885]) ).
fof(f1889,plain,
( ~ sQ39_spl
| j(e21) = e12 ),
inference(forward_demodulation,[status(thm)],[f77,f1888]) ).
fof(f1973,plain,
( ~ sQ46_spl
| e11 = op1(j(e23),j(e22)) ),
inference(forward_demodulation,[status(thm)],[f322,f852]) ).
fof(f1974,plain,
( ~ sQ46_spl
| ~ sQ44_spl
| e11 = op1(e14,j(e22)) ),
inference(forward_demodulation,[status(thm)],[f315,f1973]) ).
fof(f1975,plain,
( ~ sQ46_spl
| ~ sQ44_spl
| ~ sQ37_spl
| e11 = op1(e14,e12) ),
inference(forward_demodulation,[status(thm)],[f293,f1974]) ).
fof(f1976,plain,
( ~ sQ46_spl
| ~ sQ44_spl
| ~ sQ37_spl
| e11 = e10 ),
inference(forward_demodulation,[status(thm)],[f75,f1975]) ).
fof(f1977,plain,
( ~ sQ46_spl
| ~ sQ44_spl
| ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1976,f8]) ).
fof(f1978,plain,
( ~ sQ46_spl
| ~ sQ44_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f1977]) ).
fof(f2035,plain,
( ~ sQ8_spl
| j(e23) = e11 ),
inference(forward_demodulation,[status(thm)],[f200,f170]) ).
fof(f2049,plain,
( ~ sQ37_spl
| h(e12) = e22 ),
inference(forward_demodulation,[status(thm)],[f293,f166]) ).
fof(f2063,plain,
( ~ sQ39_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1889,f276,f298]) ).
fof(f2087,plain,
( ~ sQ33_spl
| h(e13) = e21 ),
inference(backward_demodulation,[status(thm)],[f280,f165]) ).
fof(f2091,plain,
( ~ sQ33_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f2087,f225,f279]) ).
fof(f2105,plain,
( ~ sQ17_spl
| j(e22) = e13 ),
inference(forward_demodulation,[status(thm)],[f229,f172]) ).
fof(f2109,plain,
( ~ sQ37_spl
| ~ sQ17_spl
| e13 = e12 ),
inference(forward_demodulation,[status(thm)],[f2105,f293]) ).
fof(f2110,plain,
( ~ sQ37_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2109,f15]) ).
fof(f2111,plain,
( ~ sQ37_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f2110]) ).
fof(f2161,plain,
( ~ sQ49_spl
| h(e14) = e24 ),
inference(backward_demodulation,[status(thm)],[f331,f168]) ).
fof(f2168,plain,
( ~ sQ15_spl
| e20 = op2(h(e12),h(e12)) ),
inference(forward_demodulation,[status(thm)],[f223,f554]) ).
fof(f2169,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| e20 = op2(e22,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f213,f2168]) ).
fof(f2170,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| e20 = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f213,f2169]) ).
fof(f2171,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| e20 = e21 ),
inference(forward_demodulation,[status(thm)],[f90,f2170]) ).
fof(f2172,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2171,f18]) ).
fof(f2173,plain,
( ~ sQ15_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f2172]) ).
fof(f2194,plain,
( ~ sQ31_spl
| ~ sQ49_spl
| e11 = op1(e14,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f331,f931]) ).
fof(f2195,plain,
( ~ sQ31_spl
| ~ sQ49_spl
| e11 = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f331,f2194]) ).
fof(f2196,plain,
( ~ sQ31_spl
| ~ sQ49_spl
| e11 = e12 ),
inference(forward_demodulation,[status(thm)],[f77,f2195]) ).
fof(f2197,plain,
( ~ sQ31_spl
| ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2196,f12]) ).
fof(f2198,plain,
( ~ sQ31_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f2197]) ).
fof(f2199,plain,
( ~ sQ8_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2035,f305,f199]) ).
fof(f2205,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| e10 = op1(j(e21),e14) ),
inference(forward_demodulation,[status(thm)],[f331,f1871]) ).
fof(f2217,plain,
( ~ sQ49_spl
| h(e13) = op2(e24,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f2161,f623]) ).
fof(f2233,plain,
( ~ sQ49_spl
| ~ sQ18_spl
| e23 = op2(e24,h(e11)) ),
inference(backward_demodulation,[status(thm)],[f232,f2217]) ).
fof(f2277,plain,
( ~ sQ36_spl
| ~ sQ34_spl
| e11 = op1(e14,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f283,f1280]) ).
fof(f2278,plain,
( ~ sQ36_spl
| ~ sQ34_spl
| e11 = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f283,f2277]) ).
fof(f2279,plain,
( ~ sQ36_spl
| ~ sQ34_spl
| e11 = e12 ),
inference(forward_demodulation,[status(thm)],[f77,f2278]) ).
fof(f2280,plain,
( ~ sQ36_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2279,f12]) ).
fof(f2281,plain,
( ~ sQ36_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f2280]) ).
fof(f2283,plain,
( ~ sQ37_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f2049,f212,f292]) ).
fof(f2299,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ34_spl
| e10 = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f283,f2205]) ).
fof(f2300,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ34_spl
| e10 = e12 ),
inference(forward_demodulation,[status(thm)],[f77,f2299]) ).
fof(f2301,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2300,f9]) ).
fof(f2302,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f2301]) ).
fof(f2304,plain,
( ~ sQ34_spl
| j(e22) = op1(e14,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f283,f741]) ).
fof(f2305,plain,
( ~ sQ34_spl
| j(e22) = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f283,f2304]) ).
fof(f2309,plain,
( ~ sQ34_spl
| j(e22) = e12 ),
inference(forward_demodulation,[status(thm)],[f77,f2305]) ).
fof(f2357,plain,
( ~ sQ17_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f2105,f295,f228]) ).
fof(f2379,plain,
( ~ sQ49_spl
| ~ sQ18_spl
| ~ sQ9_spl
| e23 = op2(e24,e24) ),
inference(forward_demodulation,[status(thm)],[f203,f2233]) ).
fof(f2380,plain,
( ~ sQ49_spl
| ~ sQ18_spl
| ~ sQ9_spl
| e23 = e21 ),
inference(forward_demodulation,[status(thm)],[f102,f2379]) ).
fof(f2381,plain,
( ~ sQ49_spl
| ~ sQ18_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2380,f23]) ).
fof(f2382,plain,
( ~ sQ49_spl
| ~ sQ18_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f2381]) ).
fof(f2410,plain,
( sQ37_spl
| ~ sQ34_spl
| e12 != e12 ),
inference(forward_demodulation,[status(thm)],[f2309,f294]) ).
fof(f2411,plain,
( sQ37_spl
| ~ sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2410]) ).
fof(f2412,plain,
( sQ37_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f2411]) ).
fof(f2413,plain,
$false,
inference(sat_refutation,[status(thm)],[f205,f221,f237,f285,f333,f391,f683,f684,f713,f844,f936,f952,f959,f1017,f1018,f1125,f1139,f1182,f1244,f1385,f1502,f1516,f1523,f1553,f1606,f1614,f1616,f1657,f1706,f1788,f1800,f1978,f2063,f2091,f2111,f2173,f2198,f2199,f2281,f2283,f2302,f2357,f2382,f2412]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG079+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n026.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 12:58:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.071925 seconds
% 0.12/0.43 % CPU time: 0.319432 seconds
% 0.12/0.43 % Total memory used: 114.056 MB
% 0.12/0.43 % Net memory used: 113.856 MB
%------------------------------------------------------------------------------