%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG076+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 : n016.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 0.15s 0.63s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 43
% Syntax : Number of formulae : 303 ( 68 unt; 38 def)
% Number of atoms : 984 ( 658 equ)
% Maximal formula atoms : 110 ( 3 avg)
% Number of connectives : 938 ( 257 ~; 370 |; 271 &)
% ( 38 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 40 ( 38 usr; 39 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) = e10
& op1(e14,e13) = e12
& op1(e14,e12) = e11
& op1(e14,e11) = e13
& op1(e14,e10) = e14
& op1(e13,e14) = e11
& op1(e13,e13) = e14
& op1(e13,e12) = e10
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e14) = e13
& op1(e12,e13) = e11
& op1(e12,e12) = e14
& op1(e12,e11) = e10
& op1(e12,e10) = e12
& op1(e11,e14) = e12
& op1(e11,e13) = e10
& op1(e11,e12) = e13
& 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) = e22
& op2(e24,e23) = e21
& op2(e24,e22) = e20
& op2(e24,e21) = e23
& op2(e24,e20) = e24
& op2(e23,e24) = e20
& op2(e23,e23) = e24
& op2(e23,e22) = e21
& op2(e23,e21) = e22
& op2(e23,e20) = e23
& op2(e22,e24) = e21
& op2(e22,e23) = e20
& op2(e22,e22) = e23
& op2(e22,e21) = e24
& op2(e22,e20) = e22
& op2(e21,e24) = e23
& op2(e21,e23) = e22
& op2(e21,e22) = e24
& op2(e21,e21) = e20
& 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(f11,plain,
e10 != e14,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
e11 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
e12 != e14,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
e13 != e14,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
e20 != e21,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
e20 != e23,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
e22 != e24,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f53,plain,
op1(e10,e10) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f58,plain,
op1(e11,e10) = e11,
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) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f62,plain,
op1(e11,e14) = e12,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f65,plain,
op1(e12,e12) = e14,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f67,plain,
op1(e12,e14) = 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(f77,plain,
op1(e14,e14) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f78,plain,
op2(e20,e20) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f83,plain,
op2(e21,e20) = e21,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f84,plain,
op2(e21,e21) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f87,plain,
op2(e21,e24) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f90,plain,
op2(e22,e22) = e23,
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) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f102,plain,
op2(e24,e24) = e22,
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(f107,plain,
( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f108,plain,
( h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = 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(f114,plain,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f119,plain,
h(op1(e11,e10)) = op2(h(e11),h(e10)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f120,plain,
h(op1(e11,e11)) = op2(h(e11),h(e11)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f122,plain,
h(op1(e11,e13)) = op2(h(e11),h(e13)),
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(f128,plain,
h(op1(e12,e14)) = op2(h(e12),h(e14)),
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(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(f151,plain,
j(op2(e22,e22)) = op1(j(e22),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(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(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(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(f186,definition,
( sQ4_spl
<=> h(e10) = e24 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ4_spl
| h(e10) = e24 ),
inference(component_clause,[status(thm)],[f186]) ).
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(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(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(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(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(f253,plain,
( sQ24_spl
| sQ23_spl
| sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f108,f238,f241,f244,f247,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(f268,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(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(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(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(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(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(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(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(f335,plain,
( ~ sQ48_spl
| ~ sQ49_spl
| e14 = e13 ),
inference(forward_demodulation,[status(thm)],[f331,f328]) ).
fof(f339,plain,
( ~ sQ48_spl
| ~ sQ49_spl
| e13 != e13 ),
inference(forward_demodulation,[status(thm)],[f335,f17]) ).
fof(f340,plain,
( ~ sQ48_spl
| ~ sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f339]) ).
fof(f341,plain,
( ~ sQ48_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f356,plain,
h(e10) = op2(h(e10),h(e10)),
inference(backward_demodulation,[status(thm)],[f53,f114]) ).
fof(f376,plain,
h(e11) = op2(h(e11),h(e10)),
inference(forward_demodulation,[status(thm)],[f58,f119]) ).
fof(f394,plain,
h(e14) = op2(h(e11),h(e11)),
inference(forward_demodulation,[status(thm)],[f59,f120]) ).
fof(f430,plain,
h(e10) = op2(h(e11),h(e13)),
inference(forward_demodulation,[status(thm)],[f61,f122]) ).
fof(f456,plain,
h(e12) = op2(h(e11),h(e14)),
inference(forward_demodulation,[status(thm)],[f62,f123]) ).
fof(f470,plain,
( ~ sQ15_spl
| h(e10) = op2(h(e11),e20) ),
inference(forward_demodulation,[status(thm)],[f223,f430]) ).
fof(f510,plain,
h(e14) = op2(h(e12),h(e12)),
inference(forward_demodulation,[status(thm)],[f65,f126]) ).
fof(f537,plain,
h(e13) = op2(h(e12),h(e14)),
inference(forward_demodulation,[status(thm)],[f67,f128]) ).
fof(f564,plain,
h(e14) = op2(h(e13),h(e13)),
inference(forward_demodulation,[status(thm)],[f71,f132]) ).
fof(f582,plain,
h(e13) = op2(h(e14),h(e11)),
inference(forward_demodulation,[status(thm)],[f74,f135]) ).
fof(f592,plain,
h(e10) = op2(h(e14),h(e14)),
inference(forward_demodulation,[status(thm)],[f77,f138]) ).
fof(f593,plain,
( ~ sQ0_spl
| e20 = op2(h(e14),h(e14)) ),
inference(forward_demodulation,[status(thm)],[f175,f592]) ).
fof(f594,plain,
j(e20) = op1(j(e20),j(e20)),
inference(forward_demodulation,[status(thm)],[f78,f139]) ).
fof(f611,plain,
( ~ sQ0_spl
| ~ sQ22_spl
| e20 = op2(h(e14),e22) ),
inference(backward_demodulation,[status(thm)],[f245,f593]) ).
fof(f612,plain,
( ~ sQ0_spl
| ~ sQ22_spl
| e20 = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f245,f611]) ).
fof(f613,plain,
( ~ sQ0_spl
| ~ sQ22_spl
| e20 = e23 ),
inference(forward_demodulation,[status(thm)],[f90,f612]) ).
fof(f614,plain,
( ~ sQ0_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f20]) ).
fof(f615,plain,
( ~ sQ0_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f614]) ).
fof(f649,plain,
j(e20) = op1(j(e21),j(e21)),
inference(forward_demodulation,[status(thm)],[f84,f145]) ).
fof(f650,plain,
( ~ sQ25_spl
| e10 = op1(j(e21),j(e21)) ),
inference(forward_demodulation,[status(thm)],[f255,f649]) ).
fof(f685,plain,
j(e23) = op1(j(e22),j(e22)),
inference(forward_demodulation,[status(thm)],[f90,f151]) ).
fof(f696,plain,
( ~ sQ25_spl
| h(e10) = e20 ),
inference(forward_demodulation,[status(thm)],[f255,f164]) ).
fof(f700,plain,
( ~ sQ25_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f696,f174,f254]) ).
fof(f742,plain,
j(e24) = op1(j(e23),j(e23)),
inference(forward_demodulation,[status(thm)],[f96,f157]) ).
fof(f768,plain,
( ~ sQ30_spl
| h(e10) = e21 ),
inference(forward_demodulation,[status(thm)],[f271,f165]) ).
fof(f769,plain,
( ~ sQ30_spl
| ~ sQ0_spl
| e20 = e21 ),
inference(forward_demodulation,[status(thm)],[f175,f768]) ).
fof(f770,plain,
( ~ sQ30_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f769,f18]) ).
fof(f771,plain,
( ~ sQ30_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f770]) ).
fof(f777,plain,
( ~ sQ40_spl
| j(e24) = op1(e10,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f303,f742]) ).
fof(f778,plain,
( ~ sQ40_spl
| j(e24) = op1(e10,e10) ),
inference(forward_demodulation,[status(thm)],[f303,f777]) ).
fof(f779,plain,
( ~ sQ40_spl
| j(e24) = e10 ),
inference(forward_demodulation,[status(thm)],[f53,f778]) ).
fof(f790,plain,
( ~ sQ35_spl
| j(e23) = op1(e10,j(e22)) ),
inference(forward_demodulation,[status(thm)],[f287,f685]) ).
fof(f791,plain,
( ~ sQ35_spl
| j(e23) = op1(e10,e10) ),
inference(forward_demodulation,[status(thm)],[f287,f790]) ).
fof(f792,plain,
( ~ sQ35_spl
| j(e23) = e10 ),
inference(forward_demodulation,[status(thm)],[f53,f791]) ).
fof(f812,plain,
( ~ sQ10_spl
| j(e20) = e12 ),
inference(forward_demodulation,[status(thm)],[f207,f171]) ).
fof(f834,plain,
( ~ sQ45_spl
| h(e10) = e24 ),
inference(backward_demodulation,[status(thm)],[f319,f168]) ).
fof(f836,plain,
( ~ sQ45_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f834,f186,f318]) ).
fof(f880,plain,
( ~ sQ16_spl
| j(e21) = e13 ),
inference(backward_demodulation,[status(thm)],[f226,f172]) ).
fof(f890,plain,
( ~ sQ7_spl
| h(e14) = op2(h(e11),e22) ),
inference(backward_demodulation,[status(thm)],[f197,f394]) ).
fof(f894,plain,
( ~ sQ7_spl
| h(e14) = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f197,f890]) ).
fof(f895,plain,
( ~ sQ7_spl
| h(e14) = e23 ),
inference(forward_demodulation,[status(thm)],[f90,f894]) ).
fof(f922,plain,
( ~ sQ21_spl
| h(e13) = op2(e21,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f242,f582]) ).
fof(f960,plain,
( ~ sQ7_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f895,f247,f196]) ).
fof(f997,plain,
( ~ sQ26_spl
| h(e11) = e20 ),
inference(backward_demodulation,[status(thm)],[f258,f164]) ).
fof(f1007,plain,
( ~ sQ41_spl
| j(e24) = op1(e11,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f306,f742]) ).
fof(f1008,plain,
( ~ sQ41_spl
| j(e24) = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f306,f1007]) ).
fof(f1009,plain,
( ~ sQ41_spl
| j(e24) = e14 ),
inference(forward_demodulation,[status(thm)],[f59,f1008]) ).
fof(f1037,plain,
( ~ sQ36_spl
| h(e11) = e22 ),
inference(forward_demodulation,[status(thm)],[f290,f166]) ).
fof(f1048,plain,
( ~ sQ26_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f997,f190,f257]) ).
fof(f1097,plain,
( ~ sQ41_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f1009,f330,f305]) ).
fof(f1128,plain,
( ~ sQ35_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f792,f302,f286]) ).
fof(f1132,plain,
( ~ sQ10_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f812,f260,f206]) ).
fof(f1133,plain,
( ~ sQ40_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f779,f318,f302]) ).
fof(f1144,plain,
( ~ sQ8_spl
| j(e23) = e11 ),
inference(backward_demodulation,[status(thm)],[f200,f170]) ).
fof(f1145,plain,
( ~ sQ8_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1144,f305,f199]) ).
fof(f1181,plain,
( ~ sQ0_spl
| e20 = h(e10) ),
inference(forward_demodulation,[status(thm)],[f592,f593]) ).
fof(f1190,plain,
( ~ sQ4_spl
| h(e10) = op2(h(e10),e24) ),
inference(backward_demodulation,[status(thm)],[f187,f356]) ).
fof(f1198,plain,
( ~ sQ4_spl
| e24 = op2(h(e10),e24) ),
inference(forward_demodulation,[status(thm)],[f187,f1190]) ).
fof(f1199,plain,
( ~ sQ4_spl
| e24 = op2(e24,e24) ),
inference(forward_demodulation,[status(thm)],[f187,f1198]) ).
fof(f1200,plain,
( ~ sQ4_spl
| e24 = e22 ),
inference(forward_demodulation,[status(thm)],[f102,f1199]) ).
fof(f1201,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1200,f26]) ).
fof(f1202,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f1201]) ).
fof(f1205,plain,
( ~ sQ5_spl
| h(e14) = op2(e20,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f191,f394]) ).
fof(f1206,plain,
( ~ sQ5_spl
| h(e14) = op2(e20,e20) ),
inference(forward_demodulation,[status(thm)],[f191,f1205]) ).
fof(f1207,plain,
( ~ sQ5_spl
| j(e20) = e14 ),
inference(backward_demodulation,[status(thm)],[f1208,f173]) ).
fof(f1208,plain,
( ~ sQ5_spl
| h(e14) = e20 ),
inference(forward_demodulation,[status(thm)],[f78,f1206]) ).
fof(f1209,plain,
( ~ sQ5_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f1207,f266,f190]) ).
fof(f1217,plain,
( ~ sQ16_spl
| j(e20) = op1(j(e21),e13) ),
inference(backward_demodulation,[status(thm)],[f880,f649]) ).
fof(f1221,plain,
( ~ sQ16_spl
| j(e20) = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f880,f1217]) ).
fof(f1222,plain,
( ~ sQ16_spl
| j(e20) = e14 ),
inference(forward_demodulation,[status(thm)],[f71,f1221]) ).
fof(f1223,plain,
( ~ sQ16_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1222,f268]) ).
fof(f1224,plain,
( ~ sQ16_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1223]) ).
fof(f1234,plain,
( ~ sQ3_spl
| j(e23) = e10 ),
inference(backward_demodulation,[status(thm)],[f184,f169]) ).
fof(f1235,plain,
( ~ sQ3_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1234,f302,f183]) ).
fof(f1264,plain,
( ~ sQ27_spl
| j(e20) = op1(j(e20),e12) ),
inference(backward_demodulation,[status(thm)],[f261,f594]) ).
fof(f1266,plain,
( ~ sQ27_spl
| e12 = op1(j(e20),e12) ),
inference(forward_demodulation,[status(thm)],[f261,f1264]) ).
fof(f1267,plain,
( ~ sQ27_spl
| e12 = op1(e12,e12) ),
inference(forward_demodulation,[status(thm)],[f261,f1266]) ).
fof(f1268,plain,
( ~ sQ27_spl
| e12 = e14 ),
inference(forward_demodulation,[status(thm)],[f65,f1267]) ).
fof(f1269,plain,
( ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1268,f16]) ).
fof(f1270,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1269]) ).
fof(f1291,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| e10 = op1(e13,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f280,f650]) ).
fof(f1292,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| e10 = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f280,f1291]) ).
fof(f1293,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| e10 = e14 ),
inference(forward_demodulation,[status(thm)],[f71,f1292]) ).
fof(f1294,plain,
( ~ sQ25_spl
| ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1293,f11]) ).
fof(f1295,plain,
( ~ sQ25_spl
| ~ sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f1294]) ).
fof(f1303,plain,
( ~ sQ38_spl
| h(e13) = e22 ),
inference(backward_demodulation,[status(thm)],[f296,f166]) ).
fof(f1308,plain,
( ~ sQ38_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f1303,f228,f295]) ).
fof(f1309,plain,
( ~ sQ36_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1037,f196,f289]) ).
fof(f1324,plain,
( ~ sQ20_spl
| h(e12) = op2(h(e11),e20) ),
inference(forward_demodulation,[status(thm)],[f239,f456]) ).
fof(f1325,plain,
( ~ sQ20_spl
| ~ sQ6_spl
| h(e12) = op2(e21,e20) ),
inference(backward_demodulation,[status(thm)],[f194,f1324]) ).
fof(f1329,plain,
( ~ sQ20_spl
| ~ sQ6_spl
| h(e12) = e21 ),
inference(forward_demodulation,[status(thm)],[f83,f1325]) ).
fof(f1331,plain,
( ~ sQ11_spl
| j(e21) = e12 ),
inference(backward_demodulation,[status(thm)],[f210,f171]) ).
fof(f1336,plain,
( ~ sQ11_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1331,f276,f209]) ).
fof(f1337,plain,
( ~ sQ21_spl
| ~ sQ6_spl
| h(e13) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f194,f922]) ).
fof(f1338,plain,
( ~ sQ21_spl
| ~ sQ6_spl
| h(e13) = e20 ),
inference(forward_demodulation,[status(thm)],[f84,f1337]) ).
fof(f1339,plain,
( ~ sQ21_spl
| ~ sQ6_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1338,f224]) ).
fof(f1340,plain,
( ~ sQ21_spl
| ~ sQ6_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f1339]) ).
fof(f1409,plain,
( ~ sQ13_spl
| h(e14) = op2(h(e12),e23) ),
inference(backward_demodulation,[status(thm)],[f216,f510]) ).
fof(f1410,plain,
( ~ sQ13_spl
| h(e14) = op2(e23,e23) ),
inference(forward_demodulation,[status(thm)],[f216,f1409]) ).
fof(f1411,plain,
( ~ sQ13_spl
| h(e14) = e24 ),
inference(forward_demodulation,[status(thm)],[f96,f1410]) ).
fof(f1421,plain,
( ~ sQ0_spl
| h(e11) = op2(h(e11),e20) ),
inference(forward_demodulation,[status(thm)],[f1181,f376]) ).
fof(f1426,plain,
( ~ sQ18_spl
| j(e23) = e13 ),
inference(backward_demodulation,[status(thm)],[f232,f172]) ).
fof(f1432,plain,
( ~ sQ18_spl
| ~ sQ41_spl
| e11 = e13 ),
inference(forward_demodulation,[status(thm)],[f306,f1426]) ).
fof(f1433,plain,
( ~ sQ18_spl
| ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1432,f13]) ).
fof(f1434,plain,
( ~ sQ18_spl
| ~ sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f1433]) ).
fof(f1435,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| e20 = op2(h(e11),e20) ),
inference(forward_demodulation,[status(thm)],[f1181,f470]) ).
fof(f1436,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| e20 = h(e11) ),
inference(forward_demodulation,[status(thm)],[f1421,f1435]) ).
fof(f1437,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1436,f192]) ).
fof(f1438,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1437]) ).
fof(f1456,plain,
( ~ sQ25_spl
| e10 = op1(j(e21),j(e21)) ),
inference(forward_demodulation,[status(thm)],[f255,f649]) ).
fof(f1457,plain,
( ~ sQ25_spl
| ~ sQ32_spl
| e10 = op1(e12,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f277,f1456]) ).
fof(f1458,plain,
( ~ sQ25_spl
| ~ sQ32_spl
| e10 = op1(e12,e12) ),
inference(forward_demodulation,[status(thm)],[f277,f1457]) ).
fof(f1459,plain,
( ~ sQ25_spl
| ~ sQ32_spl
| e10 = e14 ),
inference(forward_demodulation,[status(thm)],[f65,f1458]) ).
fof(f1460,plain,
( ~ sQ25_spl
| ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1459,f11]) ).
fof(f1461,plain,
( ~ sQ25_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f1460]) ).
fof(f1479,plain,
( ~ sQ17_spl
| h(e14) = op2(h(e13),e22) ),
inference(backward_demodulation,[status(thm)],[f229,f564]) ).
fof(f1480,plain,
( ~ sQ17_spl
| h(e14) = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f229,f1479]) ).
fof(f1481,plain,
( ~ sQ17_spl
| h(e14) = e23 ),
inference(forward_demodulation,[status(thm)],[f90,f1480]) ).
fof(f1496,plain,
( ~ sQ23_spl
| h(e10) = op2(e23,h(e14)) ),
inference(forward_demodulation,[status(thm)],[f248,f592]) ).
fof(f1497,plain,
( ~ sQ23_spl
| h(e10) = op2(e23,e23) ),
inference(forward_demodulation,[status(thm)],[f248,f1496]) ).
fof(f1498,plain,
( ~ sQ23_spl
| h(e10) = e24 ),
inference(forward_demodulation,[status(thm)],[f96,f1497]) ).
fof(f1540,plain,
( ~ sQ23_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1498,f186,f247]) ).
fof(f1558,plain,
( ~ sQ29_spl
| j(e20) = op1(j(e20),e14) ),
inference(backward_demodulation,[status(thm)],[f267,f594]) ).
fof(f1560,plain,
( ~ sQ29_spl
| e14 = op1(j(e20),e14) ),
inference(forward_demodulation,[status(thm)],[f267,f1558]) ).
fof(f1561,plain,
( ~ sQ29_spl
| e14 = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f267,f1560]) ).
fof(f1562,plain,
( ~ sQ29_spl
| e14 = e10 ),
inference(forward_demodulation,[status(thm)],[f77,f1561]) ).
fof(f1563,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1562,f11]) ).
fof(f1564,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1563]) ).
fof(f1596,plain,
( ~ sQ13_spl
| h(e13) = op2(e23,h(e14)) ),
inference(forward_demodulation,[status(thm)],[f216,f537]) ).
fof(f1597,plain,
( ~ sQ13_spl
| h(e13) = op2(e23,e24) ),
inference(forward_demodulation,[status(thm)],[f1411,f1596]) ).
fof(f1598,plain,
( ~ sQ13_spl
| h(e13) = e20 ),
inference(forward_demodulation,[status(thm)],[f97,f1597]) ).
fof(f1626,plain,
( ~ sQ6_spl
| h(e12) = op2(e21,h(e14)) ),
inference(forward_demodulation,[status(thm)],[f194,f456]) ).
fof(f1627,plain,
( ~ sQ6_spl
| ~ sQ24_spl
| h(e12) = op2(e21,e24) ),
inference(forward_demodulation,[status(thm)],[f251,f1626]) ).
fof(f1629,plain,
( ~ sQ6_spl
| ~ sQ24_spl
| h(e12) = e23 ),
inference(forward_demodulation,[status(thm)],[f87,f1627]) ).
fof(f1656,plain,
( ~ sQ20_spl
| ~ sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1329,f209,f193,f238]) ).
fof(f1662,plain,
( ~ sQ13_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f1598,f222,f215]) ).
fof(f1664,plain,
( ~ sQ17_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1481,f247,f228]) ).
fof(f1710,plain,
( ~ sQ19_spl
| j(e24) = e13 ),
inference(backward_demodulation,[status(thm)],[f235,f172]) ).
fof(f1716,plain,
( ~ sQ19_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f1710,f327,f234]) ).
fof(f1723,plain,
( ~ sQ1_spl
| h(e10) = op2(h(e10),e21) ),
inference(backward_demodulation,[status(thm)],[f178,f356]) ).
fof(f1725,plain,
( ~ sQ1_spl
| e21 = op2(h(e10),e21) ),
inference(forward_demodulation,[status(thm)],[f178,f1723]) ).
fof(f1726,plain,
( ~ sQ1_spl
| e21 = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f178,f1725]) ).
fof(f1727,plain,
( ~ sQ1_spl
| e21 = e20 ),
inference(forward_demodulation,[status(thm)],[f84,f1726]) ).
fof(f1728,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1727,f18]) ).
fof(f1729,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1728]) ).
fof(f1745,plain,
( ~ sQ9_spl
| h(e14) = op2(h(e11),e24) ),
inference(backward_demodulation,[status(thm)],[f203,f394]) ).
fof(f1750,plain,
( ~ sQ9_spl
| h(e14) = op2(e24,e24) ),
inference(forward_demodulation,[status(thm)],[f203,f1745]) ).
fof(f1751,plain,
( ~ sQ9_spl
| h(e14) = e22 ),
inference(forward_demodulation,[status(thm)],[f102,f1750]) ).
fof(f1804,plain,
( ~ sQ28_spl
| e13 = op1(j(e20),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f264,f594]) ).
fof(f1805,plain,
( ~ sQ28_spl
| e13 = op1(e13,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f264,f1804]) ).
fof(f1806,plain,
( ~ sQ28_spl
| e13 = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f264,f1805]) ).
fof(f1807,plain,
( ~ sQ28_spl
| e13 = e14 ),
inference(forward_demodulation,[status(thm)],[f71,f1806]) ).
fof(f1808,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1807,f17]) ).
fof(f1809,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f1808]) ).
fof(f1813,plain,
( ~ sQ6_spl
| ~ sQ24_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1629,f215,f250,f193]) ).
fof(f1823,plain,
( ~ sQ9_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f1751,f244,f202]) ).
fof(f1824,plain,
$false,
inference(sat_refutation,[status(thm)],[f205,f237,f253,f269,f341,f615,f700,f771,f836,f960,f1048,f1097,f1128,f1132,f1133,f1145,f1202,f1209,f1224,f1235,f1270,f1295,f1308,f1309,f1336,f1340,f1434,f1438,f1461,f1540,f1564,f1656,f1662,f1664,f1716,f1729,f1809,f1813,f1823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG076+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n016.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Mon Sep 21 13:00:09 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.15/0.58 % Drodi V4.1.1
% 0.15/0.63 % Refutation found
% 0.15/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.67 % Elapsed time: 0.083865 seconds
% 0.15/0.67 % CPU time: 0.358140 seconds
% 0.15/0.67 % Total memory used: 115.266 MB
% 0.15/0.67 % Net memory used: 115.044 MB
%------------------------------------------------------------------------------