%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG180+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 : n002.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 11:48:47 AM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 130 ( 49 unt; 6 def)
% Number of atoms : 603 ( 514 equ)
% Maximal formula atoms : 110 ( 4 avg)
% Number of connectives : 572 ( 99 ~; 194 |; 271 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 7 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) = e11
& op1(e14,e13) = e13
& op1(e14,e12) = e14
& op1(e14,e11) = e10
& op1(e14,e10) = e12
& op1(e13,e14) = e12
& op1(e13,e13) = e10
& op1(e13,e12) = e13
& op1(e13,e11) = e11
& op1(e13,e10) = e14
& op1(e12,e14) = e10
& op1(e12,e13) = e14
& op1(e12,e12) = e12
& op1(e12,e11) = e13
& op1(e12,e10) = e11
& op1(e11,e14) = e13
& op1(e11,e13) = e12
& op1(e11,e12) = e11
& op1(e11,e11) = e14
& op1(e11,e10) = e10
& op1(e10,e14) = e14
& op1(e10,e13) = e11
& op1(e10,e12) = e10
& op1(e10,e11) = e12
& op1(e10,e10) = e13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( op2(e24,e24) = e20
& op2(e24,e23) = e24
& op2(e24,e22) = e21
& op2(e24,e21) = e23
& op2(e24,e20) = e22
& op2(e23,e24) = e21
& op2(e23,e23) = e22
& op2(e23,e22) = e24
& op2(e23,e21) = e20
& op2(e23,e20) = e23
& op2(e22,e24) = e22
& op2(e22,e23) = e20
& op2(e22,e22) = e23
& op2(e22,e21) = e24
& op2(e22,e20) = e21
& op2(e21,e24) = e24
& op2(e21,e23) = e23
& op2(e21,e22) = e22
& op2(e21,e21) = e21
& op2(e21,e20) = e20
& op2(e20,e24) = e23
& op2(e20,e23) = e21
& op2(e20,e22) = e20
& op2(e20,e21) = e22
& op2(e20,e20) = e24 ),
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(f17,plain,
e13 != e14,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
e20 != e23,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
e20 != e24,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
e22 != e24,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f53,plain,
op1(e10,e10) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f56,plain,
op1(e10,e13) = e11,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f58,plain,
op1(e11,e10) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
op1(e11,e11) = e14,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f62,plain,
op1(e11,e14) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f65,plain,
op1(e12,e12) = e12,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f71,plain,
op1(e13,e13) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f74,plain,
op1(e14,e11) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f76,plain,
op1(e14,e13) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f77,plain,
op1(e14,e14) = e11,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f78,plain,
op2(e20,e20) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f82,plain,
op2(e20,e24) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f92,plain,
op2(e22,e24) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f93,plain,
op2(e23,e20) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f95,plain,
op2(e23,e22) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f98,plain,
op2(e24,e20) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f101,plain,
op2(e24,e23) = e24,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f102,plain,
op2(e24,e24) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f103,plain,
( j(h(e14)) = e14
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e24)) = e24
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e24,e24)) = op1(j(e24),j(e24))
& j(op2(e24,e23)) = op1(j(e24),j(e23))
& j(op2(e24,e22)) = op1(j(e24),j(e22))
& j(op2(e24,e21)) = op1(j(e24),j(e21))
& j(op2(e24,e20)) = op1(j(e24),j(e20))
& j(op2(e23,e24)) = op1(j(e23),j(e24))
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e24)) = op1(j(e22),j(e24))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e24)) = op1(j(e21),j(e24))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e24)) = op1(j(e20),j(e24))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e14,e14)) = op2(h(e14),h(e14))
& h(op1(e14,e13)) = op2(h(e14),h(e13))
& h(op1(e14,e12)) = op2(h(e14),h(e12))
& h(op1(e14,e11)) = op2(h(e14),h(e11))
& h(op1(e14,e10)) = op2(h(e14),h(e10))
& h(op1(e13,e14)) = op2(h(e13),h(e14))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e14)) = op2(h(e12),h(e14))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e14)) = op2(h(e11),h(e14))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e14)) = op2(h(e10),h(e14))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10))
& ( j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(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(f117,plain,
h(op1(e10,e13)) = op2(h(e10),h(e13)),
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(f126,plain,
h(op1(e12,e12)) = op2(h(e12),h(e12)),
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(f143,plain,
j(op2(e20,e24)) = op1(j(e20),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(f162,plain,
j(op2(e24,e23)) = op1(j(e24),j(e23)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f163,plain,
j(op2(e24,e24)) = op1(j(e24),j(e24)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f164,plain,
h(j(e20)) = e20,
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f168,plain,
h(j(e24)) = e24,
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(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(f334,plain,
h(e13) = op2(h(e10),h(e10)),
inference(forward_demodulation,[status(thm)],[f53,f114]) ).
fof(f337,plain,
h(e11) = op2(h(e10),h(e13)),
inference(forward_demodulation,[status(thm)],[f56,f117]) ).
fof(f339,plain,
h(e10) = op2(h(e11),h(e10)),
inference(forward_demodulation,[status(thm)],[f58,f119]) ).
fof(f346,plain,
h(e12) = op2(h(e12),h(e12)),
inference(forward_demodulation,[status(thm)],[f65,f126]) ).
fof(f359,plain,
j(e24) = op1(j(e20),j(e20)),
inference(forward_demodulation,[status(thm)],[f78,f139]) ).
fof(f363,plain,
j(e23) = op1(j(e20),j(e24)),
inference(forward_demodulation,[status(thm)],[f82,f143]) ).
fof(f376,plain,
j(e24) = op1(j(e23),j(e22)),
inference(forward_demodulation,[status(thm)],[f95,f156]) ).
fof(f382,plain,
j(e24) = op1(j(e24),j(e23)),
inference(forward_demodulation,[status(thm)],[f101,f162]) ).
fof(f383,plain,
j(e20) = op1(j(e24),j(e24)),
inference(forward_demodulation,[status(thm)],[f102,f163]) ).
fof(f386,plain,
( ~ sQ49_spl
| j(e24) = op1(e14,j(e23)) ),
inference(backward_demodulation,[status(thm)],[f331,f382]) ).
fof(f391,plain,
( ~ sQ49_spl
| e14 = op1(j(e23),j(e22)) ),
inference(backward_demodulation,[status(thm)],[f331,f376]) ).
fof(f595,plain,
( ~ sQ46_spl
| j(e20) = op1(e11,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f322,f383]) ).
fof(f596,plain,
( ~ sQ46_spl
| j(e20) = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f322,f595]) ).
fof(f608,plain,
( ~ sQ46_spl
| j(e20) = e14 ),
inference(forward_demodulation,[status(thm)],[f59,f596]) ).
fof(f619,plain,
( ~ sQ46_spl
| j(e23) = op1(e14,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f608,f363]) ).
fof(f620,plain,
( ~ sQ46_spl
| j(e23) = op1(e14,e11) ),
inference(forward_demodulation,[status(thm)],[f322,f619]) ).
fof(f628,plain,
( ~ sQ46_spl
| j(e23) = e10 ),
inference(forward_demodulation,[status(thm)],[f74,f620]) ).
fof(f633,plain,
( ~ sQ46_spl
| e11 = op1(j(e24),j(e23)) ),
inference(forward_demodulation,[status(thm)],[f322,f382]) ).
fof(f634,plain,
( ~ sQ46_spl
| e11 = op1(e11,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f322,f633]) ).
fof(f635,plain,
( ~ sQ46_spl
| e11 = op1(e11,e10) ),
inference(forward_demodulation,[status(thm)],[f628,f634]) ).
fof(f636,plain,
( ~ sQ46_spl
| e11 = e10 ),
inference(forward_demodulation,[status(thm)],[f58,f635]) ).
fof(f637,plain,
( ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f8]) ).
fof(f638,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f637]) ).
fof(f772,plain,
( ~ sQ45_spl
| h(e10) = e24 ),
inference(backward_demodulation,[status(thm)],[f319,f168]) ).
fof(f992,plain,
( ~ sQ47_spl
| h(e12) = e24 ),
inference(forward_demodulation,[status(thm)],[f325,f168]) ).
fof(f1017,plain,
( ~ sQ47_spl
| e24 = op2(h(e12),h(e12)) ),
inference(forward_demodulation,[status(thm)],[f992,f346]) ).
fof(f1018,plain,
( ~ sQ47_spl
| e24 = op2(e24,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f992,f1017]) ).
fof(f1019,plain,
( ~ sQ47_spl
| e24 = op2(e24,e24) ),
inference(forward_demodulation,[status(thm)],[f992,f1018]) ).
fof(f1020,plain,
( ~ sQ47_spl
| e24 = e20 ),
inference(forward_demodulation,[status(thm)],[f102,f1019]) ).
fof(f1021,plain,
( ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1020,f21]) ).
fof(f1022,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f1021]) ).
fof(f1040,plain,
( ~ sQ0_spl
| h(e13) = op2(h(e10),e20) ),
inference(backward_demodulation,[status(thm)],[f175,f334]) ).
fof(f1043,plain,
( ~ sQ0_spl
| h(e11) = op2(e20,h(e13)) ),
inference(backward_demodulation,[status(thm)],[f175,f337]) ).
fof(f1044,plain,
( ~ sQ0_spl
| h(e10) = op2(h(e11),e20) ),
inference(backward_demodulation,[status(thm)],[f175,f339]) ).
fof(f1108,plain,
( ~ sQ48_spl
| e13 = op1(j(e20),j(e20)) ),
inference(backward_demodulation,[status(thm)],[f328,f359]) ).
fof(f1109,plain,
( ~ sQ48_spl
| j(e20) = op1(j(e24),e13) ),
inference(backward_demodulation,[status(thm)],[f328,f383]) ).
fof(f1120,plain,
( ~ sQ0_spl
| h(e13) = op2(e20,e20) ),
inference(forward_demodulation,[status(thm)],[f175,f1040]) ).
fof(f1125,plain,
( ~ sQ0_spl
| h(e13) = e24 ),
inference(forward_demodulation,[status(thm)],[f78,f1120]) ).
fof(f1128,plain,
( ~ sQ0_spl
| h(e11) = op2(e20,e24) ),
inference(forward_demodulation,[status(thm)],[f1125,f1043]) ).
fof(f1137,plain,
( ~ sQ0_spl
| h(e11) = e23 ),
inference(forward_demodulation,[status(thm)],[f82,f1128]) ).
fof(f1138,plain,
( ~ sQ0_spl
| e20 = op2(h(e11),e20) ),
inference(forward_demodulation,[status(thm)],[f175,f1044]) ).
fof(f1139,plain,
( ~ sQ0_spl
| e20 = op2(e23,e20) ),
inference(forward_demodulation,[status(thm)],[f1137,f1138]) ).
fof(f1140,plain,
( ~ sQ0_spl
| e20 = e23 ),
inference(forward_demodulation,[status(thm)],[f93,f1139]) ).
fof(f1141,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1140,f20]) ).
fof(f1142,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1141]) ).
fof(f1263,plain,
( ~ sQ45_spl
| h(e10) = op2(h(e11),e24) ),
inference(backward_demodulation,[status(thm)],[f772,f339]) ).
fof(f1264,plain,
( ~ sQ45_spl
| h(e11) = op2(e24,h(e13)) ),
inference(backward_demodulation,[status(thm)],[f772,f337]) ).
fof(f1266,plain,
( ~ sQ45_spl
| h(e13) = op2(h(e10),e24) ),
inference(backward_demodulation,[status(thm)],[f772,f334]) ).
fof(f1386,plain,
( ~ sQ48_spl
| e13 = j(e24) ),
inference(forward_demodulation,[status(thm)],[f359,f1108]) ).
fof(f1387,plain,
( ~ sQ48_spl
| j(e20) = op1(e13,e13) ),
inference(forward_demodulation,[status(thm)],[f1386,f1109]) ).
fof(f1391,plain,
( ~ sQ48_spl
| h(e10) = e20 ),
inference(backward_demodulation,[status(thm)],[f1392,f164]) ).
fof(f1392,plain,
( ~ sQ48_spl
| j(e20) = e10 ),
inference(forward_demodulation,[status(thm)],[f71,f1387]) ).
fof(f1603,plain,
( ~ sQ48_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1391,f174,f327]) ).
fof(f1672,plain,
( ~ sQ45_spl
| h(e13) = op2(e24,e24) ),
inference(forward_demodulation,[status(thm)],[f772,f1266]) ).
fof(f1675,plain,
( ~ sQ45_spl
| h(e13) = e20 ),
inference(forward_demodulation,[status(thm)],[f102,f1672]) ).
fof(f1676,plain,
( ~ sQ45_spl
| h(e11) = op2(e24,e20) ),
inference(forward_demodulation,[status(thm)],[f1675,f1264]) ).
fof(f1679,plain,
( ~ sQ45_spl
| h(e11) = e22 ),
inference(forward_demodulation,[status(thm)],[f98,f1676]) ).
fof(f1680,plain,
( ~ sQ45_spl
| e24 = op2(h(e11),e24) ),
inference(forward_demodulation,[status(thm)],[f772,f1263]) ).
fof(f1681,plain,
( ~ sQ45_spl
| e24 = op2(e22,e24) ),
inference(forward_demodulation,[status(thm)],[f1679,f1680]) ).
fof(f1682,plain,
( ~ sQ45_spl
| e24 = e22 ),
inference(forward_demodulation,[status(thm)],[f92,f1681]) ).
fof(f1683,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1682,f26]) ).
fof(f1684,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f1683]) ).
fof(f1696,plain,
( ~ sQ49_spl
| e14 = op1(e14,j(e23)) ),
inference(backward_demodulation,[status(thm)],[f1710,f386]) ).
fof(f1710,plain,
( ~ sQ49_spl
| e14 = j(e24) ),
inference(forward_demodulation,[status(thm)],[f376,f391]) ).
fof(f1751,plain,
( ~ sQ49_spl
| j(e20) = op1(e14,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f1710,f383]) ).
fof(f1752,plain,
( ~ sQ49_spl
| j(e20) = op1(e14,e14) ),
inference(forward_demodulation,[status(thm)],[f1710,f1751]) ).
fof(f1761,plain,
( ~ sQ49_spl
| j(e20) = e11 ),
inference(forward_demodulation,[status(thm)],[f77,f1752]) ).
fof(f1763,plain,
( ~ sQ49_spl
| j(e23) = op1(e11,j(e24)) ),
inference(forward_demodulation,[status(thm)],[f1761,f363]) ).
fof(f1764,plain,
( ~ sQ49_spl
| j(e23) = op1(e11,e14) ),
inference(forward_demodulation,[status(thm)],[f1710,f1763]) ).
fof(f1772,plain,
( ~ sQ49_spl
| j(e23) = e13 ),
inference(forward_demodulation,[status(thm)],[f62,f1764]) ).
fof(f1824,plain,
( ~ sQ49_spl
| e14 = op1(e14,e13) ),
inference(forward_demodulation,[status(thm)],[f1772,f1696]) ).
fof(f1825,plain,
( ~ sQ49_spl
| e14 = e13 ),
inference(forward_demodulation,[status(thm)],[f76,f1824]) ).
fof(f1826,plain,
( ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1825,f17]) ).
fof(f1827,plain,
~ sQ49_spl,
inference(contradiction_clause,[status(thm)],[f1826]) ).
fof(f1828,plain,
$false,
inference(sat_refutation,[status(thm)],[f333,f638,f1022,f1142,f1603,f1684,f1827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG180+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 13:03:03 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.43 % Refutation found
% 0.12/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45 % Elapsed time: 0.090746 seconds
% 0.12/0.45 % CPU time: 0.413010 seconds
% 0.12/0.45 % Total memory used: 117.184 MB
% 0.12/0.45 % Net memory used: 116.912 MB
%------------------------------------------------------------------------------