%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG082+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 12:53:22 PM UTC 2026
% Result : Theorem 2.43s 1.17s
% Output : CNFRefutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 88 ( 78 unt; 10 def)
% Number of atoms : 643 ( 592 equ)
% Maximal formula atoms : 110 ( 7 avg)
% Number of connectives : 522 ( 17 ~; 172 |; 331 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 74 ( 5 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 : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f4,axiom,
( op1(e14,e14) = e12
& op1(e14,e13) = e10
& op1(e14,e12) = e11
& op1(e14,e11) = e13
& op1(e14,e10) = e14
& op1(e13,e14) = e10
& op1(e13,e13) = e11
& op1(e13,e12) = e14
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e14) = e11
& op1(e12,e13) = e14
& op1(e12,e12) = e13
& op1(e12,e11) = e10
& op1(e12,e10) = e12
& op1(e11,e14) = e13
& op1(e11,e13) = e12
& op1(e11,e12) = e10
& 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/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,axiom,
( op2(e24,e24) = e20
& op2(e24,e23) = e22
& op2(e24,e22) = e21
& op2(e24,e21) = e23
& op2(e24,e20) = e24
& op2(e23,e24) = e21
& op2(e23,e23) = e24
& op2(e23,e22) = e20
& op2(e23,e21) = e22
& op2(e23,e20) = e23
& op2(e22,e24) = e23
& op2(e22,e23) = e21
& op2(e22,e22) = e24
& op2(e22,e21) = e20
& op2(e22,e20) = e22
& op2(e21,e24) = e22
& op2(e21,e23) = e20
& op2(e21,e22) = e23
& op2(e21,e21) = e24
& 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/sandbox2/benchmark/theBenchmark.p',ax5) ).
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/sandbox2/benchmark/theBenchmark.p',co1) ).
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,
( ( 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(ennf_transformation,[],[f7]) ).
fof(f9,plain,
( ( 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(flattening,[],[f8]) ).
fof(f20,plain,
e23 != e24,
inference(cnf_transformation,[],[f2]) ).
fof(f26,plain,
e20 != e24,
inference(cnf_transformation,[],[f2]) ).
fof(f55,plain,
e12 = op1(e14,e14),
inference(cnf_transformation,[],[f4]) ).
fof(f57,plain,
e11 = op1(e14,e12),
inference(cnf_transformation,[],[f4]) ).
fof(f61,plain,
e11 = op1(e13,e13),
inference(cnf_transformation,[],[f4]) ).
fof(f63,plain,
e12 = op1(e13,e11),
inference(cnf_transformation,[],[f4]) ).
fof(f67,plain,
e13 = op1(e12,e12),
inference(cnf_transformation,[],[f4]) ).
fof(f68,plain,
e10 = op1(e12,e11),
inference(cnf_transformation,[],[f4]) ).
fof(f73,plain,
e14 = op1(e11,e11),
inference(cnf_transformation,[],[f4]) ).
fof(f79,plain,
e10 = op1(e10,e10),
inference(cnf_transformation,[],[f4]) ).
fof(f80,plain,
e20 = op2(e24,e24),
inference(cnf_transformation,[],[f5]) ).
fof(f83,plain,
e23 = op2(e24,e21),
inference(cnf_transformation,[],[f5]) ).
fof(f84,plain,
e24 = op2(e24,e20),
inference(cnf_transformation,[],[f5]) ).
fof(f85,plain,
e21 = op2(e23,e24),
inference(cnf_transformation,[],[f5]) ).
fof(f86,plain,
e24 = op2(e23,e23),
inference(cnf_transformation,[],[f5]) ).
fof(f98,plain,
e24 = op2(e21,e21),
inference(cnf_transformation,[],[f5]) ).
fof(f106,plain,
( e14 = j(e23)
| e13 = j(e23)
| e12 = j(e23)
| e11 = j(e23)
| e10 = j(e23) ),
inference(cnf_transformation,[],[f9]) ).
fof(f120,plain,
e24 = h(j(e24)),
inference(cnf_transformation,[],[f9]) ).
fof(f121,plain,
e23 = h(j(e23)),
inference(cnf_transformation,[],[f9]) ).
fof(f125,plain,
j(op2(e24,e24)) = op1(j(e24),j(e24)),
inference(cnf_transformation,[],[f9]) ).
fof(f128,plain,
j(op2(e24,e21)) = op1(j(e24),j(e21)),
inference(cnf_transformation,[],[f9]) ).
fof(f129,plain,
j(op2(e24,e20)) = op1(j(e24),j(e20)),
inference(cnf_transformation,[],[f9]) ).
fof(f130,plain,
j(op2(e23,e24)) = op1(j(e23),j(e24)),
inference(cnf_transformation,[],[f9]) ).
fof(f131,plain,
j(op2(e23,e23)) = op1(j(e23),j(e23)),
inference(cnf_transformation,[],[f9]) ).
fof(f143,plain,
j(op2(e21,e21)) = op1(j(e21),j(e21)),
inference(cnf_transformation,[],[f9]) ).
fof(f174,plain,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_62,plain,
e20 != e24,
inference(cnf_transformation,[],[f26]) ).
tcf(c_68,plain,
e23 != e24,
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,plain,
op1(e10,e10) = e10,
inference(cnf_transformation,[],[f79]) ).
tcf(c_100,plain,
op1(e11,e11) = e14,
inference(cnf_transformation,[],[f73]) ).
tcf(c_105,plain,
op1(e12,e11) = e10,
inference(cnf_transformation,[],[f68]) ).
tcf(c_106,plain,
op1(e12,e12) = e13,
inference(cnf_transformation,[],[f67]) ).
tcf(c_110,plain,
op1(e13,e11) = e12,
inference(cnf_transformation,[],[f63]) ).
tcf(c_112,plain,
op1(e13,e13) = e11,
inference(cnf_transformation,[],[f61]) ).
tcf(c_116,plain,
op1(e14,e12) = e11,
inference(cnf_transformation,[],[f57]) ).
tcf(c_118,plain,
op1(e14,e14) = e12,
inference(cnf_transformation,[],[f55]) ).
tcf(c_125,plain,
op2(e21,e21) = e24,
inference(cnf_transformation,[],[f98]) ).
tcf(c_137,plain,
op2(e23,e23) = e24,
inference(cnf_transformation,[],[f86]) ).
tcf(c_138,plain,
op2(e23,e24) = e21,
inference(cnf_transformation,[],[f85]) ).
tcf(c_139,plain,
op2(e24,e20) = e24,
inference(cnf_transformation,[],[f84]) ).
tcf(c_140,plain,
op2(e24,e21) = e23,
inference(cnf_transformation,[],[f83]) ).
tcf(c_143,plain,
op2(e24,e24) = e20,
inference(cnf_transformation,[],[f80]) ).
tcf(c_144,negated_conjecture,
op2(h(e10),h(e10)) = h(op1(e10,e10)),
inference(cnf_transformation,[],[f174]) ).
tcf(c_175,negated_conjecture,
op1(j(e21),j(e21)) = j(op2(e21,e21)),
inference(cnf_transformation,[],[f143]) ).
tcf(c_187,negated_conjecture,
op1(j(e23),j(e23)) = j(op2(e23,e23)),
inference(cnf_transformation,[],[f131]) ).
tcf(c_188,negated_conjecture,
op1(j(e23),j(e24)) = j(op2(e23,e24)),
inference(cnf_transformation,[],[f130]) ).
tcf(c_189,negated_conjecture,
op1(j(e24),j(e20)) = j(op2(e24,e20)),
inference(cnf_transformation,[],[f129]) ).
tcf(c_190,negated_conjecture,
op1(j(e24),j(e21)) = j(op2(e24,e21)),
inference(cnf_transformation,[],[f128]) ).
tcf(c_193,negated_conjecture,
op1(j(e24),j(e24)) = j(op2(e24,e24)),
inference(cnf_transformation,[],[f125]) ).
tcf(c_197,negated_conjecture,
h(j(e23)) = e23,
inference(cnf_transformation,[],[f121]) ).
tcf(c_198,negated_conjecture,
h(j(e24)) = e24,
inference(cnf_transformation,[],[f120]) ).
tcf(c_212,negated_conjecture,
( ( j(e23) = e14 )
| ( j(e23) = e13 )
| ( j(e23) = e12 )
| ( j(e23) = e11 )
| ( j(e23) = e10 ) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_624,plain,
op1(j(e24),j(e24)) = j(e20),
inference(light_normalisation,[status(thm)],[c_193,c_143]) ).
tcf(c_627,plain,
op1(j(e24),j(e21)) = j(e23),
inference(light_normalisation,[status(thm)],[c_190,c_140]) ).
tcf(c_628,plain,
op1(j(e24),j(e20)) = j(e24),
inference(light_normalisation,[status(thm)],[c_189,c_139]) ).
tcf(c_629,plain,
op1(j(e23),j(e24)) = j(e21),
inference(light_normalisation,[status(thm)],[c_188,c_138]) ).
tcf(c_630,plain,
op1(j(e23),j(e23)) = j(e24),
inference(light_normalisation,[status(thm)],[c_187,c_137]) ).
tcf(c_642,plain,
op1(j(e21),j(e21)) = j(e24),
inference(light_normalisation,[status(thm)],[c_175,c_125]) ).
tcf(c_673,plain,
op2(h(e10),h(e10)) = h(e10),
inference(light_normalisation,[status(thm)],[c_144,c_94]) ).
tcf(c_775,definition,
iPr_def_10 = h(e10),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_776,definition,
iPr_def_11 = op2(iPr_def_10,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_816,definition,
iPr_def_51 = op1(iPr_def_42,iPr_def_42),
introduced(definition,[new_symbols(definition,[iPr_def_51])],[]) ).
tcf(c_828,definition,
iPr_def_63 = op1(iPr_def_46,iPr_def_46),
introduced(definition,[new_symbols(definition,[iPr_def_63])],[]) ).
tcf(c_829,definition,
iPr_def_64 = op1(iPr_def_46,iPr_def_48),
introduced(definition,[new_symbols(definition,[iPr_def_64])],[]) ).
tcf(c_830,definition,
iPr_def_65 = op1(iPr_def_48,iPr_def_40),
introduced(definition,[new_symbols(definition,[iPr_def_65])],[]) ).
tcf(c_831,definition,
iPr_def_66 = op1(iPr_def_48,iPr_def_42),
introduced(definition,[new_symbols(definition,[iPr_def_66])],[]) ).
tcf(c_834,definition,
iPr_def_69 = op1(iPr_def_48,iPr_def_48),
introduced(definition,[new_symbols(definition,[iPr_def_69])],[]) ).
tcf(c_840,definition,
iPr_def_75 = h(iPr_def_48),
introduced(definition,[new_symbols(definition,[iPr_def_75])],[]) ).
tcf(c_841,definition,
iPr_def_76 = h(iPr_def_46),
introduced(definition,[new_symbols(definition,[iPr_def_76])],[]) ).
tcf(c_845,plain,
iPr_def_11 = iPr_def_10,
inference(demodulation,[status(thm)],[c_673,c_775,c_776]) ).
tcf(c_876,plain,
iPr_def_51 = iPr_def_48,
inference(demodulation,[status(thm)],[c_642,c_816]) ).
tcf(c_888,plain,
iPr_def_63 = iPr_def_48,
inference(demodulation,[status(thm)],[c_630,c_828]) ).
tcf(c_889,plain,
iPr_def_64 = iPr_def_42,
inference(demodulation,[status(thm)],[c_629,c_829]) ).
tcf(c_890,plain,
iPr_def_65 = iPr_def_48,
inference(demodulation,[status(thm)],[c_628,c_830]) ).
tcf(c_891,plain,
iPr_def_66 = iPr_def_46,
inference(demodulation,[status(thm)],[c_627,c_831]) ).
tcf(c_894,plain,
iPr_def_69 = iPr_def_40,
inference(demodulation,[status(thm)],[c_624,c_834]) ).
tcf(c_896,negated_conjecture,
( ( iPr_def_46 = e14 )
| ( iPr_def_46 = e13 )
| ( iPr_def_46 = e12 )
| ( iPr_def_46 = e11 )
| ( iPr_def_46 = e10 ) ),
inference(demodulation,[status(thm)],[c_212]) ).
tcf(c_910,negated_conjecture,
iPr_def_75 = e24,
inference(demodulation,[status(thm)],[c_198,c_840]) ).
tcf(c_911,negated_conjecture,
iPr_def_76 = e23,
inference(demodulation,[status(thm)],[c_197,c_841]) ).
tcf(c_1736,plain,
op2(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_776,c_845]) ).
tcf(c_5316,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_1736,c_911,c_910,c_896,c_894,c_891,c_890,c_889,c_888,c_876,c_841,c_840,c_834,c_831,c_830,c_829,c_828,c_816,c_775,c_143,c_118,c_116,c_112,c_110,c_106,c_105,c_100,c_94,c_68,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG082+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 04:43:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.43/1.17 % SZS status Started for theBenchmark.p
% 2.43/1.17 % SZS status Theorem for theBenchmark.p
% 2.43/1.17
% 2.43/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.43/1.17
% 2.43/1.17 % ------ iProver source info
% 2.43/1.17
% 2.43/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.43/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.43/1.17 % git: non_committed_changes: false
% 2.43/1.17
% 2.43/1.17 % ------ Parsing...
% 2.43/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.43/1.17
% 2.43/1.17 % ------ Preprocessing... sup_sim: 50 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.43/1.17
% 2.43/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.43/1.17
% 2.43/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.43/1.17 % ------ Proving...
% 2.43/1.17 % ------ Problem Properties
% 2.43/1.17
% 2.43/1.17 %
% 2.43/1.17 % clauses 235
% 2.43/1.17 % conjectures 20
% 2.43/1.17 % EPR 115
% 2.43/1.17 % Horn 225
% 2.43/1.17 % unary 225
% 2.43/1.17 % binary 0
% 2.43/1.17 % lits 275
% 2.43/1.17 % lits eq 275
% 2.43/1.17 % fd_pure 0
% 2.43/1.17 % fd_pseudo 0
% 2.43/1.17 % fd_cond 0
% 2.43/1.17 % fd_pseudo_cond 0
% 2.43/1.17 % AC symbols 0
% 2.43/1.17
% 2.43/1.17 % ------ Schedule dynamic 5 is on
% 2.43/1.17
% 2.43/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.43/1.17
% 2.43/1.17
% 2.43/1.17 % ------
% 2.43/1.17 % Current options:
% 2.43/1.17 % ------
% 2.43/1.17
% 2.43/1.17
% 2.43/1.17 %
% 2.43/1.17
% 2.43/1.17 % ------ Proving...
% 2.43/1.17 %
% 2.43/1.17
% 2.43/1.17 % SZS status Theorem for theBenchmark.p
% 2.43/1.17
% 2.43/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.43/1.17
% 2.43/1.17
%------------------------------------------------------------------------------