%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG088+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 11:48:04 AM UTC 2026
% Result : Theorem 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 112 ( 32 unt; 11 def)
% Number of atoms : 586 ( 490 equ)
% Maximal formula atoms : 110 ( 5 avg)
% Number of connectives : 564 ( 90 ~; 190 |; 271 &)
% ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 12 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) = e10
& op1(e13,e12) = e14
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e14) = e13
& op1(e12,e13) = e11
& op1(e12,e12) = e10
& op1(e12,e11) = e14
& op1(e12,e10) = e12
& op1(e11,e14) = e12
& op1(e11,e13) = e14
& op1(e11,e12) = e13
& op1(e11,e11) = e10
& op1(e11,e10) = e11
& op1(e10,e14) = e14
& op1(e10,e13) = e13
& op1(e10,e12) = e12
& op1(e10,e11) = e11
& op1(e10,e10) = e10 ),
file('/export/starexec/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(f22,plain,
e21 != e22,
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(f65,plain,
op1(e12,e12) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f68,plain,
op1(e13,e10) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f71,plain,
op1(e13,e13) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f77,plain,
op1(e14,e14) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f84,plain,
op2(e21,e21) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f89,plain,
op2(e22,e21) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f90,plain,
op2(e22,e22) = 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(f111,plain,
( j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = 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(f129,plain,
h(op1(e13,e10)) = op2(h(e13),h(e10)),
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(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(f151,plain,
j(op2(e22,e22)) = op1(j(e22),j(e22)),
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(f171,plain,
j(h(e12)) = e12,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f177,definition,
( sQ1_spl
<=> h(e10) = e21 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ1_spl
| h(e10) = e21 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f179,plain,
( sQ1_spl
| h(e10) != e21 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
( sQ2_spl
<=> h(e10) = e22 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ2_spl
| h(e10) = e22 ),
inference(component_clause,[status(thm)],[f180]) ).
fof(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(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(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(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(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(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(f301,plain,
( sQ39_spl
| sQ38_spl
| sQ37_spl
| sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f111,f286,f289,f292,f295,f298]) ).
fof(f343,plain,
h(e10) = op2(h(e10),h(e10)),
inference(backward_demodulation,[status(thm)],[f53,f114]) ).
fof(f445,plain,
h(e13) = op2(h(e13),h(e10)),
inference(forward_demodulation,[status(thm)],[f68,f129]) ).
fof(f463,plain,
h(e10) = op2(h(e13),h(e13)),
inference(forward_demodulation,[status(thm)],[f71,f132]) ).
fof(f489,plain,
h(e10) = op2(h(e14),h(e14)),
inference(forward_demodulation,[status(thm)],[f77,f138]) ).
fof(f527,plain,
j(e22) = op1(j(e21),j(e21)),
inference(forward_demodulation,[status(thm)],[f84,f145]) ).
fof(f564,plain,
j(e21) = op1(j(e22),j(e22)),
inference(forward_demodulation,[status(thm)],[f90,f151]) ).
fof(f618,plain,
( ~ sQ30_spl
| h(e10) = e21 ),
inference(forward_demodulation,[status(thm)],[f271,f165]) ).
fof(f622,plain,
( ~ sQ30_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f618,f177,f270]) ).
fof(f626,plain,
( ~ sQ22_spl
| h(e10) = op2(e22,h(e14)) ),
inference(forward_demodulation,[status(thm)],[f245,f489]) ).
fof(f627,plain,
( ~ sQ22_spl
| h(e10) = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f245,f626]) ).
fof(f628,plain,
( ~ sQ22_spl
| h(e10) = e21 ),
inference(forward_demodulation,[status(thm)],[f90,f627]) ).
fof(f669,plain,
( ~ sQ22_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f628,f179]) ).
fof(f670,plain,
( ~ sQ22_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f669]) ).
fof(f688,plain,
( ~ sQ35_spl
| h(e10) = e22 ),
inference(forward_demodulation,[status(thm)],[f287,f166]) ).
fof(f722,plain,
( ~ sQ12_spl
| j(e22) = e12 ),
inference(forward_demodulation,[status(thm)],[f213,f171]) ).
fof(f730,plain,
( ~ sQ12_spl
| j(e21) = op1(e12,j(e22)) ),
inference(forward_demodulation,[status(thm)],[f722,f564]) ).
fof(f731,plain,
( ~ sQ12_spl
| j(e21) = op1(e12,e12) ),
inference(forward_demodulation,[status(thm)],[f722,f730]) ).
fof(f732,plain,
( ~ sQ12_spl
| j(e21) = e10 ),
inference(forward_demodulation,[status(thm)],[f65,f731]) ).
fof(f750,plain,
( ~ sQ35_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f688,f180,f286]) ).
fof(f838,plain,
( ~ sQ2_spl
| h(e10) = op2(h(e10),e22) ),
inference(backward_demodulation,[status(thm)],[f181,f343]) ).
fof(f840,plain,
( ~ sQ2_spl
| e22 = op2(h(e10),e22) ),
inference(forward_demodulation,[status(thm)],[f181,f838]) ).
fof(f841,plain,
( ~ sQ2_spl
| e22 = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f181,f840]) ).
fof(f842,plain,
( ~ sQ2_spl
| e22 = e21 ),
inference(forward_demodulation,[status(thm)],[f90,f841]) ).
fof(f843,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f842,f22]) ).
fof(f844,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f843]) ).
fof(f849,plain,
( ~ sQ37_spl
| h(e12) = e22 ),
inference(backward_demodulation,[status(thm)],[f293,f166]) ).
fof(f853,plain,
( ~ sQ37_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f849,f212,f292]) ).
fof(f891,plain,
( ~ sQ36_spl
| j(e21) = op1(e11,j(e22)) ),
inference(forward_demodulation,[status(thm)],[f290,f564]) ).
fof(f892,plain,
( ~ sQ36_spl
| j(e21) = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f290,f891]) ).
fof(f901,plain,
( ~ sQ36_spl
| j(e21) = e10 ),
inference(forward_demodulation,[status(thm)],[f59,f892]) ).
fof(f903,plain,
( ~ sQ36_spl
| e11 = op1(j(e21),j(e21)) ),
inference(forward_demodulation,[status(thm)],[f290,f527]) ).
fof(f904,plain,
( ~ sQ36_spl
| e11 = op1(e10,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f901,f903]) ).
fof(f905,plain,
( ~ sQ36_spl
| e11 = op1(e10,e10) ),
inference(forward_demodulation,[status(thm)],[f901,f904]) ).
fof(f906,plain,
( ~ sQ36_spl
| e11 = e10 ),
inference(forward_demodulation,[status(thm)],[f53,f905]) ).
fof(f907,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f906,f8]) ).
fof(f908,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f907]) ).
fof(f988,plain,
( ~ sQ1_spl
| e21 = op2(h(e10),h(e10)) ),
inference(forward_demodulation,[status(thm)],[f178,f343]) ).
fof(f989,plain,
( ~ sQ1_spl
| e21 = op2(e21,h(e10)) ),
inference(forward_demodulation,[status(thm)],[f178,f988]) ).
fof(f990,plain,
( ~ sQ1_spl
| e21 = e22 ),
inference(backward_demodulation,[status(thm)],[f991,f84]) ).
fof(f991,plain,
( ~ sQ1_spl
| e21 = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f178,f989]) ).
fof(f992,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f990,f22]) ).
fof(f993,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f992]) ).
fof(f1011,plain,
( ~ sQ38_spl
| h(e13) = e22 ),
inference(forward_demodulation,[status(thm)],[f296,f166]) ).
fof(f1023,plain,
( ~ sQ17_spl
| h(e10) = op2(e22,h(e13)) ),
inference(forward_demodulation,[status(thm)],[f229,f463]) ).
fof(f1024,plain,
( ~ sQ17_spl
| h(e10) = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f229,f1023]) ).
fof(f1025,plain,
( ~ sQ17_spl
| h(e10) = e21 ),
inference(forward_demodulation,[status(thm)],[f90,f1024]) ).
fof(f1026,plain,
( ~ sQ17_spl
| e22 = op2(h(e13),h(e10)) ),
inference(forward_demodulation,[status(thm)],[f229,f445]) ).
fof(f1027,plain,
( ~ sQ17_spl
| e22 = op2(e22,h(e10)) ),
inference(forward_demodulation,[status(thm)],[f229,f1026]) ).
fof(f1028,plain,
( ~ sQ17_spl
| e22 = e24 ),
inference(backward_demodulation,[status(thm)],[f1029,f89]) ).
fof(f1029,plain,
( ~ sQ17_spl
| e22 = op2(e22,e21) ),
inference(forward_demodulation,[status(thm)],[f1025,f1027]) ).
fof(f1030,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1028,f26]) ).
fof(f1031,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f1030]) ).
fof(f1034,plain,
( ~ sQ38_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f1011,f228,f295]) ).
fof(f1050,plain,
( ~ sQ12_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f732,f270,f212]) ).
fof(f1240,plain,
( ~ sQ39_spl
| h(e14) = e22 ),
inference(forward_demodulation,[status(thm)],[f299,f166]) ).
fof(f1241,plain,
( ~ sQ39_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1240,f246]) ).
fof(f1242,plain,
( ~ sQ39_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1241]) ).
fof(f1243,plain,
$false,
inference(sat_refutation,[status(thm)],[f301,f622,f670,f750,f844,f853,f908,f993,f1031,f1034,f1050,f1242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG088+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 12:57:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.15/0.42 % Refutation found
% 0.15/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.45 % Elapsed time: 0.076347 seconds
% 0.15/0.45 % CPU time: 0.261988 seconds
% 0.15/0.45 % Total memory used: 112.800 MB
% 0.15/0.45 % Net memory used: 112.632 MB
%------------------------------------------------------------------------------