%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG042+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 : Fri Sep 25 12:53:15 PM UTC 2026
% Result : Theorem 2.37s 1.28s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 160 ( 136 unt; 21 def)
% Number of atoms : 731 ( 537 equ)
% Maximal formula atoms : 72 ( 4 avg)
% Number of connectives : 408 ( 30 ~; 150 |; 226 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 51 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 27 ( 25 usr; 26 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( e12 != e13
& e11 != e13
& e11 != e12
& e10 != e13
& e10 != e12
& e10 != e11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f2,axiom,
( e22 != e23
& e21 != e23
& e21 != e22
& e20 != e23
& e20 != e22
& e20 != e21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f4,axiom,
( op1(e13,e13) = e10
& op1(e13,e12) = e11
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e13) = e11
& op1(e12,e12) = e10
& op1(e12,e11) = e13
& op1(e12,e10) = e12
& op1(e11,e13) = e12
& op1(e11,e12) = e13
& op1(e11,e11) = e10
& op1(e11,e10) = e11
& op1(e10,e13) = e13
& op1(e10,e12) = e12
& op1(e10,e11) = e11
& op1(e10,e10) = e10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f5,axiom,
( op2(e23,e23) = e20
& op2(e23,e22) = e21
& op2(e23,e21) = e22
& op2(e23,e20) = e23
& op2(e22,e23) = e21
& op2(e22,e22) = e23
& op2(e22,e21) = e20
& op2(e22,e20) = e22
& op2(e21,e23) = e22
& op2(e21,e22) = e20
& op2(e21,e21) = e23
& op2(e21,e20) = e21
& op2(e20,e23) = e23
& op2(e20,e22) = e22
& op2(e20,e21) = e21
& op2(e20,e20) = e20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f6,conjecture,
( ( ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& 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,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,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,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(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,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,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,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',co1) ).
fof(f7,negated_conjecture,
~ ( ( ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& 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,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,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,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(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,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,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,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,
( ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 )
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& 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,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,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,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(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,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,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,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(ennf_transformation,[],[f7]) ).
fof(f9,plain,
( ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 )
& j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& 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,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,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,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(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,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,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,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(flattening,[],[f8]) ).
fof(f13,plain,
e10 != e13,
inference(cnf_transformation,[],[f1]) ).
fof(f14,plain,
e10 != e12,
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
e10 != e11,
inference(cnf_transformation,[],[f1]) ).
fof(f18,plain,
e21 != e22,
inference(cnf_transformation,[],[f2]) ).
fof(f19,plain,
e20 != e23,
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
e10 = op1(e13,e13),
inference(cnf_transformation,[],[f4]) ).
fof(f43,plain,
e10 = op1(e12,e12),
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
e13 = op1(e12,e11),
inference(cnf_transformation,[],[f4]) ).
fof(f45,plain,
e12 = op1(e12,e10),
inference(cnf_transformation,[],[f4]) ).
fof(f48,plain,
e10 = op1(e11,e11),
inference(cnf_transformation,[],[f4]) ).
fof(f53,plain,
e10 = op1(e10,e10),
inference(cnf_transformation,[],[f4]) ).
fof(f54,plain,
e20 = op2(e23,e23),
inference(cnf_transformation,[],[f5]) ).
fof(f56,plain,
e22 = op2(e23,e21),
inference(cnf_transformation,[],[f5]) ).
fof(f58,plain,
e21 = op2(e22,e23),
inference(cnf_transformation,[],[f5]) ).
fof(f59,plain,
e23 = op2(e22,e22),
inference(cnf_transformation,[],[f5]) ).
fof(f60,plain,
e20 = op2(e22,e21),
inference(cnf_transformation,[],[f5]) ).
fof(f62,plain,
e22 = op2(e21,e23),
inference(cnf_transformation,[],[f5]) ).
fof(f64,plain,
e23 = op2(e21,e21),
inference(cnf_transformation,[],[f5]) ).
fof(f69,plain,
e20 = op2(e20,e20),
inference(cnf_transformation,[],[f5]) ).
fof(f72,plain,
( e13 = j(e21)
| e12 = j(e21)
| e11 = j(e21)
| e10 = j(e21) ),
inference(cnf_transformation,[],[f9]) ).
fof(f73,plain,
( e13 = j(e20)
| e12 = j(e20)
| e11 = j(e20)
| e10 = j(e20) ),
inference(cnf_transformation,[],[f9]) ).
fof(f75,plain,
( e23 = h(e12)
| e22 = h(e12)
| e21 = h(e12)
| e20 = h(e12) ),
inference(cnf_transformation,[],[f9]) ).
fof(f78,plain,
e13 = j(h(e13)),
inference(cnf_transformation,[],[f9]) ).
fof(f79,plain,
e12 = j(h(e12)),
inference(cnf_transformation,[],[f9]) ).
fof(f80,plain,
e11 = j(h(e11)),
inference(cnf_transformation,[],[f9]) ).
fof(f81,plain,
e10 = j(h(e10)),
inference(cnf_transformation,[],[f9]) ).
fof(f82,plain,
e23 = h(j(e23)),
inference(cnf_transformation,[],[f9]) ).
fof(f83,plain,
e22 = h(j(e22)),
inference(cnf_transformation,[],[f9]) ).
fof(f84,plain,
e21 = h(j(e21)),
inference(cnf_transformation,[],[f9]) ).
fof(f85,plain,
e20 = h(j(e20)),
inference(cnf_transformation,[],[f9]) ).
fof(f86,plain,
j(op2(e23,e23)) = op1(j(e23),j(e23)),
inference(cnf_transformation,[],[f9]) ).
fof(f88,plain,
j(op2(e23,e21)) = op1(j(e23),j(e21)),
inference(cnf_transformation,[],[f9]) ).
fof(f90,plain,
j(op2(e22,e23)) = op1(j(e22),j(e23)),
inference(cnf_transformation,[],[f9]) ).
fof(f91,plain,
j(op2(e22,e22)) = op1(j(e22),j(e22)),
inference(cnf_transformation,[],[f9]) ).
fof(f92,plain,
j(op2(e22,e21)) = op1(j(e22),j(e21)),
inference(cnf_transformation,[],[f9]) ).
fof(f96,plain,
j(op2(e21,e21)) = op1(j(e21),j(e21)),
inference(cnf_transformation,[],[f9]) ).
fof(f101,plain,
j(op2(e20,e20)) = op1(j(e20),j(e20)),
inference(cnf_transformation,[],[f9]) ).
fof(f107,plain,
h(op1(e12,e12)) = op2(h(e12),h(e12)),
inference(cnf_transformation,[],[f9]) ).
fof(f109,plain,
h(op1(e12,e10)) = op2(h(e12),h(e10)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_49,plain,
e10 != e11,
inference(cnf_transformation,[],[f15]) ).
tcf(c_50,plain,
e10 != e12,
inference(cnf_transformation,[],[f14]) ).
tcf(c_51,plain,
e10 != e13,
inference(cnf_transformation,[],[f13]) ).
tcf(c_57,plain,
e20 != e23,
inference(cnf_transformation,[],[f19]) ).
tcf(c_58,plain,
e21 != e22,
inference(cnf_transformation,[],[f18]) ).
tcf(c_77,plain,
op1(e10,e10) = e10,
inference(cnf_transformation,[],[f53]) ).
tcf(c_82,plain,
op1(e11,e11) = e10,
inference(cnf_transformation,[],[f48]) ).
tcf(c_85,plain,
op1(e12,e10) = e12,
inference(cnf_transformation,[],[f45]) ).
tcf(c_86,plain,
op1(e12,e11) = e13,
inference(cnf_transformation,[],[f44]) ).
tcf(c_87,plain,
op1(e12,e12) = e10,
inference(cnf_transformation,[],[f43]) ).
tcf(c_92,plain,
op1(e13,e13) = e10,
inference(cnf_transformation,[],[f38]) ).
tcf(c_93,plain,
op2(e20,e20) = e20,
inference(cnf_transformation,[],[f69]) ).
tcf(c_98,plain,
op2(e21,e21) = e23,
inference(cnf_transformation,[],[f64]) ).
tcf(c_100,plain,
op2(e21,e23) = e22,
inference(cnf_transformation,[],[f62]) ).
tcf(c_102,plain,
op2(e22,e21) = e20,
inference(cnf_transformation,[],[f60]) ).
tcf(c_103,plain,
op2(e22,e22) = e23,
inference(cnf_transformation,[],[f59]) ).
tcf(c_104,plain,
op2(e22,e23) = e21,
inference(cnf_transformation,[],[f58]) ).
tcf(c_106,plain,
op2(e23,e21) = e22,
inference(cnf_transformation,[],[f56]) ).
tcf(c_108,plain,
op2(e23,e23) = e20,
inference(cnf_transformation,[],[f54]) ).
tcf(c_117,negated_conjecture,
op2(h(e12),h(e10)) = h(op1(e12,e10)),
inference(cnf_transformation,[],[f109]) ).
tcf(c_119,negated_conjecture,
op2(h(e12),h(e12)) = h(op1(e12,e12)),
inference(cnf_transformation,[],[f107]) ).
tcf(c_125,negated_conjecture,
op1(j(e20),j(e20)) = j(op2(e20,e20)),
inference(cnf_transformation,[],[f101]) ).
tcf(c_130,negated_conjecture,
op1(j(e21),j(e21)) = j(op2(e21,e21)),
inference(cnf_transformation,[],[f96]) ).
tcf(c_134,negated_conjecture,
op1(j(e22),j(e21)) = j(op2(e22,e21)),
inference(cnf_transformation,[],[f92]) ).
tcf(c_135,negated_conjecture,
op1(j(e22),j(e22)) = j(op2(e22,e22)),
inference(cnf_transformation,[],[f91]) ).
tcf(c_136,negated_conjecture,
op1(j(e22),j(e23)) = j(op2(e22,e23)),
inference(cnf_transformation,[],[f90]) ).
tcf(c_138,negated_conjecture,
op1(j(e23),j(e21)) = j(op2(e23,e21)),
inference(cnf_transformation,[],[f88]) ).
tcf(c_140,negated_conjecture,
op1(j(e23),j(e23)) = j(op2(e23,e23)),
inference(cnf_transformation,[],[f86]) ).
tcf(c_141,negated_conjecture,
h(j(e20)) = e20,
inference(cnf_transformation,[],[f85]) ).
tcf(c_142,negated_conjecture,
h(j(e21)) = e21,
inference(cnf_transformation,[],[f84]) ).
tcf(c_143,negated_conjecture,
h(j(e22)) = e22,
inference(cnf_transformation,[],[f83]) ).
tcf(c_144,negated_conjecture,
h(j(e23)) = e23,
inference(cnf_transformation,[],[f82]) ).
tcf(c_145,negated_conjecture,
j(h(e10)) = e10,
inference(cnf_transformation,[],[f81]) ).
tcf(c_146,negated_conjecture,
j(h(e11)) = e11,
inference(cnf_transformation,[],[f80]) ).
tcf(c_147,negated_conjecture,
j(h(e12)) = e12,
inference(cnf_transformation,[],[f79]) ).
tcf(c_148,negated_conjecture,
j(h(e13)) = e13,
inference(cnf_transformation,[],[f78]) ).
tcf(c_151,negated_conjecture,
( ( h(e12) = e23 )
| ( h(e12) = e22 )
| ( h(e12) = e21 )
| ( h(e12) = e20 ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_153,negated_conjecture,
( ( j(e20) = e13 )
| ( j(e20) = e12 )
| ( j(e20) = e11 )
| ( j(e20) = e10 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_154,negated_conjecture,
( ( j(e21) = e13 )
| ( j(e21) = e12 )
| ( j(e21) = e11 )
| ( j(e21) = e10 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_421,plain,
op1(j(e23),j(e23)) = j(e20),
inference(light_normalisation,[status(thm)],[c_140,c_108]) ).
tcf(c_423,plain,
op1(j(e23),j(e21)) = j(e22),
inference(light_normalisation,[status(thm)],[c_138,c_106]) ).
tcf(c_425,plain,
op1(j(e22),j(e23)) = j(e21),
inference(light_normalisation,[status(thm)],[c_136,c_104]) ).
tcf(c_426,plain,
op1(j(e22),j(e22)) = j(e23),
inference(light_normalisation,[status(thm)],[c_135,c_103]) ).
tcf(c_427,plain,
op1(j(e22),j(e21)) = j(e20),
inference(light_normalisation,[status(thm)],[c_134,c_102]) ).
tcf(c_431,plain,
op1(j(e21),j(e21)) = j(e23),
inference(light_normalisation,[status(thm)],[c_130,c_98]) ).
tcf(c_436,plain,
op1(j(e20),j(e20)) = j(e20),
inference(light_normalisation,[status(thm)],[c_125,c_93]) ).
tcf(c_442,plain,
op2(h(e12),h(e12)) = h(e10),
inference(light_normalisation,[status(thm)],[c_119,c_87]) ).
tcf(c_444,plain,
op2(h(e12),h(e10)) = h(e12),
inference(light_normalisation,[status(thm)],[c_117,c_85]) ).
tcf(c_519,definition,
iPr_def_10 = h(e10),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_531,definition,
iPr_def_22 = op2(iPr_def_14,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_533,definition,
iPr_def_24 = op2(iPr_def_14,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_539,definition,
iPr_def_30 = j(e20),
introduced(definition,[new_symbols(definition,[iPr_def_30])],[]) ).
tcf(c_540,definition,
iPr_def_31 = op1(iPr_def_30,iPr_def_30),
introduced(definition,[new_symbols(definition,[iPr_def_31])],[]) ).
tcf(c_543,definition,
iPr_def_34 = j(e22),
introduced(definition,[new_symbols(definition,[iPr_def_34])],[]) ).
tcf(c_545,definition,
iPr_def_36 = j(e23),
introduced(definition,[new_symbols(definition,[iPr_def_36])],[]) ).
tcf(c_548,definition,
iPr_def_39 = op1(iPr_def_32,iPr_def_32),
introduced(definition,[new_symbols(definition,[iPr_def_39])],[]) ).
tcf(c_552,definition,
iPr_def_43 = op1(iPr_def_34,iPr_def_32),
introduced(definition,[new_symbols(definition,[iPr_def_43])],[]) ).
tcf(c_553,definition,
iPr_def_44 = op1(iPr_def_34,iPr_def_34),
introduced(definition,[new_symbols(definition,[iPr_def_44])],[]) ).
tcf(c_554,definition,
iPr_def_45 = op1(iPr_def_34,iPr_def_36),
introduced(definition,[new_symbols(definition,[iPr_def_45])],[]) ).
tcf(c_556,definition,
iPr_def_47 = op1(iPr_def_36,iPr_def_32),
introduced(definition,[new_symbols(definition,[iPr_def_47])],[]) ).
tcf(c_558,definition,
iPr_def_49 = op1(iPr_def_36,iPr_def_36),
introduced(definition,[new_symbols(definition,[iPr_def_49])],[]) ).
tcf(c_559,definition,
iPr_def_50 = j(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_50])],[]) ).
tcf(c_560,definition,
iPr_def_51 = j(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_51])],[]) ).
tcf(c_561,definition,
iPr_def_52 = j(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_52])],[]) ).
tcf(c_562,definition,
iPr_def_53 = j(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_53])],[]) ).
tcf(c_563,definition,
iPr_def_54 = h(iPr_def_36),
introduced(definition,[new_symbols(definition,[iPr_def_54])],[]) ).
tcf(c_564,definition,
iPr_def_55 = h(iPr_def_34),
introduced(definition,[new_symbols(definition,[iPr_def_55])],[]) ).
tcf(c_565,definition,
iPr_def_56 = h(iPr_def_32),
introduced(definition,[new_symbols(definition,[iPr_def_56])],[]) ).
tcf(c_566,definition,
iPr_def_57 = h(iPr_def_30),
introduced(definition,[new_symbols(definition,[iPr_def_57])],[]) ).
tcf(c_575,plain,
iPr_def_22 = iPr_def_14,
inference(demodulation,[status(thm)],[c_444,c_531]) ).
tcf(c_577,plain,
iPr_def_24 = iPr_def_10,
inference(demodulation,[status(thm)],[c_442,c_533]) ).
tcf(c_583,plain,
iPr_def_31 = iPr_def_30,
inference(demodulation,[status(thm)],[c_436,c_539,c_540]) ).
tcf(c_588,plain,
iPr_def_39 = iPr_def_36,
inference(demodulation,[status(thm)],[c_431,c_548]) ).
tcf(c_592,plain,
iPr_def_43 = iPr_def_30,
inference(demodulation,[status(thm)],[c_427,c_552]) ).
tcf(c_593,plain,
iPr_def_44 = iPr_def_36,
inference(demodulation,[status(thm)],[c_426,c_553]) ).
tcf(c_594,plain,
iPr_def_45 = iPr_def_32,
inference(demodulation,[status(thm)],[c_425,c_554]) ).
tcf(c_596,plain,
iPr_def_47 = iPr_def_34,
inference(demodulation,[status(thm)],[c_423,c_556]) ).
tcf(c_598,plain,
iPr_def_49 = iPr_def_30,
inference(demodulation,[status(thm)],[c_421,c_558]) ).
tcf(c_601,negated_conjecture,
( ( iPr_def_32 = e13 )
| ( iPr_def_32 = e12 )
| ( iPr_def_32 = e11 )
| ( iPr_def_32 = e10 ) ),
inference(demodulation,[status(thm)],[c_154]) ).
tcf(c_602,negated_conjecture,
( ( iPr_def_30 = e13 )
| ( iPr_def_30 = e12 )
| ( iPr_def_30 = e11 )
| ( iPr_def_30 = e10 ) ),
inference(demodulation,[status(thm)],[c_153]) ).
tcf(c_604,negated_conjecture,
( ( iPr_def_14 = e23 )
| ( iPr_def_14 = e22 )
| ( iPr_def_14 = e21 )
| ( iPr_def_14 = e20 ) ),
inference(demodulation,[status(thm)],[c_151]) ).
tcf(c_607,negated_conjecture,
iPr_def_50 = e13,
inference(demodulation,[status(thm)],[c_148,c_559]) ).
tcf(c_608,negated_conjecture,
iPr_def_51 = e12,
inference(demodulation,[status(thm)],[c_147,c_560]) ).
tcf(c_609,negated_conjecture,
iPr_def_52 = e11,
inference(demodulation,[status(thm)],[c_146,c_561]) ).
tcf(c_610,negated_conjecture,
iPr_def_53 = e10,
inference(demodulation,[status(thm)],[c_145,c_562]) ).
tcf(c_611,negated_conjecture,
iPr_def_54 = e23,
inference(demodulation,[status(thm)],[c_144,c_563]) ).
tcf(c_612,negated_conjecture,
iPr_def_55 = e22,
inference(demodulation,[status(thm)],[c_143,c_564]) ).
tcf(c_613,negated_conjecture,
iPr_def_56 = e21,
inference(demodulation,[status(thm)],[c_142,c_565]) ).
tcf(c_614,negated_conjecture,
iPr_def_57 = e20,
inference(demodulation,[status(thm)],[c_141,c_566]) ).
tcf(c_1014,plain,
h(iPr_def_53) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_519,c_610]) ).
tcf(c_1054,plain,
( ( iPr_def_32 = iPr_def_53 )
| ( iPr_def_32 = iPr_def_52 )
| ( iPr_def_32 = iPr_def_51 )
| ( iPr_def_32 = iPr_def_50 ) ),
inference(light_normalisation,[status(thm)],[c_601,c_607,c_608,c_609,c_610]) ).
tcf(c_1091,plain,
( ( iPr_def_30 = iPr_def_53 )
| ( iPr_def_30 = iPr_def_52 )
| ( iPr_def_30 = iPr_def_51 )
| ( iPr_def_30 = iPr_def_50 ) ),
inference(light_normalisation,[status(thm)],[c_602,c_607,c_608,c_609,c_610]) ).
tcf(c_1107,plain,
( ( iPr_def_32 = iPr_def_52 )
| ( iPr_def_32 = iPr_def_51 )
| ( iPr_def_32 = iPr_def_50 )
| ( iPr_def_30 = iPr_def_52 )
| ( iPr_def_30 = iPr_def_51 )
| ( iPr_def_30 = iPr_def_50 )
| ( iPr_def_30 = iPr_def_32 ) ),
inference(superposition,[status(thm)],[c_1091,c_1054]) ).
tcf(c_1150,plain,
( ( iPr_def_14 = iPr_def_57 )
| ( iPr_def_14 = iPr_def_56 )
| ( iPr_def_14 = iPr_def_55 )
| ( iPr_def_14 = iPr_def_54 ) ),
inference(light_normalisation,[status(thm)],[c_604,c_611,c_612,c_613,c_614]) ).
tcf(c_1565,plain,
iPr_def_52 != iPr_def_53,
inference(light_normalisation,[status(thm)],[c_49,c_609,c_610]) ).
tcf(c_1570,plain,
iPr_def_51 != iPr_def_53,
inference(light_normalisation,[status(thm)],[c_50,c_608,c_610]) ).
tcf(c_1575,plain,
iPr_def_50 != iPr_def_53,
inference(light_normalisation,[status(thm)],[c_51,c_607,c_610]) ).
tcf(c_1929,plain,
iPr_def_54 != iPr_def_57,
inference(light_normalisation,[status(thm)],[c_57,c_611,c_614]) ).
tcf(c_1939,plain,
iPr_def_55 != iPr_def_56,
inference(light_normalisation,[status(thm)],[c_58,c_612,c_613]) ).
tcf(c_2811,plain,
j(iPr_def_57) = iPr_def_30,
inference(light_normalisation,[status(thm)],[c_539,c_614]) ).
tcf(c_2815,plain,
( ( iPr_def_14 = iPr_def_56 )
| ( iPr_def_14 = iPr_def_55 )
| ( iPr_def_14 = iPr_def_54 )
| ( j(iPr_def_14) = iPr_def_30 ) ),
inference(superposition,[status(thm)],[c_1150,c_2811]) ).
tcf(c_2822,plain,
( ( iPr_def_30 = iPr_def_51 )
| ( iPr_def_14 = iPr_def_56 )
| ( iPr_def_14 = iPr_def_55 )
| ( iPr_def_14 = iPr_def_54 ) ),
inference(light_normalisation,[status(thm)],[c_2815,c_560]) ).
tcf(c_2895,plain,
j(iPr_def_55) = iPr_def_34,
inference(light_normalisation,[status(thm)],[c_543,c_612]) ).
tcf(c_2898,plain,
j(iPr_def_54) = iPr_def_36,
inference(light_normalisation,[status(thm)],[c_545,c_611]) ).
tcf(c_3361,plain,
op1(iPr_def_53,iPr_def_53) = iPr_def_53,
inference(light_normalisation,[status(thm)],[c_77,c_610]) ).
tcf(c_3599,plain,
op1(iPr_def_52,iPr_def_52) = iPr_def_53,
inference(light_normalisation,[status(thm)],[c_82,c_609,c_610]) ).
tcf(c_3819,plain,
op1(iPr_def_51,iPr_def_52) = iPr_def_50,
inference(light_normalisation,[status(thm)],[c_86,c_607,c_608,c_609]) ).
tcf(c_3822,plain,
( ( iPr_def_32 = iPr_def_51 )
| ( iPr_def_32 = iPr_def_50 )
| ( iPr_def_30 = iPr_def_52 )
| ( iPr_def_30 = iPr_def_51 )
| ( iPr_def_30 = iPr_def_50 )
| ( iPr_def_30 = iPr_def_32 )
| ( op1(iPr_def_51,iPr_def_32) = iPr_def_50 ) ),
inference(superposition,[status(thm)],[c_1107,c_3819]) ).
tcf(c_3863,plain,
op1(iPr_def_51,iPr_def_51) = iPr_def_53,
inference(light_normalisation,[status(thm)],[c_87,c_608,c_610]) ).
tcf(c_3945,plain,
op1(iPr_def_50,iPr_def_50) = iPr_def_53,
inference(light_normalisation,[status(thm)],[c_92,c_607,c_610]) ).
tcf(c_4089,plain,
op2(iPr_def_57,iPr_def_57) = iPr_def_57,
inference(light_normalisation,[status(thm)],[c_93,c_614]) ).
tcf(c_4363,plain,
op2(iPr_def_56,iPr_def_56) = iPr_def_54,
inference(light_normalisation,[status(thm)],[c_98,c_611,c_613]) ).
tcf(c_4464,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_4363,c_4089,c_3945,c_3863,c_3822,c_3599,c_3361,c_2898,c_2895,c_2822,c_2811,c_1939,c_1929,c_1575,c_1570,c_1565,c_1014,c_614,c_613,c_612,c_611,c_610,c_609,c_607,c_604,c_598,c_596,c_594,c_593,c_592,c_588,c_583,c_577,c_575,c_566,c_563,c_562,c_560,c_558,c_556,c_554,c_553,c_552,c_548,c_540,c_533,c_531,c_108,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG042+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 04:37:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.37/1.28 % SZS status Started for theBenchmark.p
% 2.37/1.28 % SZS status Theorem for theBenchmark.p
% 2.37/1.28
% 2.37/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.37/1.28
% 2.37/1.28 % ------ iProver source info
% 2.37/1.28
% 2.37/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.37/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.37/1.28 % git: non_committed_changes: false
% 2.37/1.28
% 2.37/1.28 % ------ Parsing...
% 2.37/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.37/1.28
% 2.37/1.28 % ------ Preprocessing... sup_sim: 32 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.37/1.28
% 2.37/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.37/1.28
% 2.37/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.37/1.28 % ------ Proving...
% 2.37/1.28 % ------ Problem Properties
% 2.37/1.28
% 2.37/1.28 %
% 2.37/1.28 % clauses 156
% 2.37/1.28 % conjectures 16
% 2.37/1.28 % EPR 76
% 2.37/1.28 % Horn 148
% 2.37/1.28 % unary 148
% 2.37/1.28 % binary 0
% 2.37/1.28 % lits 180
% 2.37/1.28 % lits eq 180
% 2.37/1.28 % fd_pure 0
% 2.37/1.28 % fd_pseudo 0
% 2.37/1.28 % fd_cond 0
% 2.37/1.28 % fd_pseudo_cond 0
% 2.37/1.28 % AC symbols 0
% 2.37/1.28
% 2.37/1.28 % ------ Schedule dynamic 5 is on
% 2.37/1.28
% 2.37/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.37/1.28
% 2.37/1.28
% 2.37/1.28 % ------
% 2.37/1.28 % Current options:
% 2.37/1.28 % ------
% 2.37/1.28
% 2.37/1.28
% 2.37/1.28 %
% 2.37/1.28
% 2.37/1.28 % ------ Proving...
% 2.37/1.28 %
% 2.37/1.28
% 2.37/1.28 % SZS status Theorem for theBenchmark.p
% 2.37/1.28
% 2.37/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.37/1.28
% 2.37/1.28
%------------------------------------------------------------------------------