%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG077+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 11:51:27 AM UTC 2026
% Result : Theorem 0.16s 5.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 24 unt; 0 def)
% Number of atoms : 678 ( 660 equ)
% Maximal formula atoms : 110 ( 13 avg)
% Number of connectives : 712 ( 83 ~; 240 |; 384 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 10 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,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(ax2,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(ax4,axiom,
( op1(e14,e14) = e10
& op1(e14,e13) = e12
& op1(e14,e12) = e11
& op1(e14,e11) = e13
& op1(e14,e10) = e14
& op1(e13,e14) = e11
& op1(e13,e13) = e14
& op1(e13,e12) = e10
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e14) = e13
& op1(e12,e13) = e11
& op1(e12,e12) = e14
& op1(e12,e11) = e10
& op1(e12,e10) = e12
& op1(e11,e14) = e12
& op1(e11,e13) = e10
& op1(e11,e12) = e13
& op1(e11,e11) = e14
& op1(e11,e10) = e11
& op1(e10,e14) = e14
& op1(e10,e13) = e13
& op1(e10,e12) = e12
& op1(e10,e11) = e11
& op1(e10,e10) = e10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(ax5,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/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(ax1,axiom,
( e13 != e14
& e12 != e14
& e12 != e13
& e11 != e14
& e11 != e13
& e11 != e12
& e10 != e14
& e10 != e13
& e10 != e12
& e10 != e11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(c_0_5,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(assume_negation,[status(cth)],[co1]) ).
fof(c_0_6,plain,
( epred1_0
<=> ( ( 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 ) ) ),
introduced(definition) ).
fof(c_0_7,negated_conjecture,
~ ( epred1_0
=> ~ ( 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(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
fof(c_0_8,plain,
( epred1_0
=> ( ( 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(split_equiv,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
( 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))
& epred1_0 ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
( ( ~ epred1_0
| j(e24) = e14
| j(e24) = e13
| j(e24) = e12
| j(e24) = e11
| j(e24) = e10 )
& ( ~ epred1_0
| j(e23) = e14
| j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( ~ epred1_0
| j(e22) = e14
| j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( ~ epred1_0
| j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( ~ epred1_0
| j(e20) = e14
| j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( ~ epred1_0
| h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 )
& ( ~ epred1_0
| h(e13) = e24
| h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( ~ epred1_0
| h(e12) = e24
| h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( ~ epred1_0
| h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( ~ epred1_0
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
( e23 != e24
& e22 != e24
& e22 != e23
& e21 != e24
& e21 != e23
& e21 != e22
& e20 != e24
& e20 != e23
& e20 != e22
& e20 != e21 ),
inference(fof_simplification,[status(thm)],[ax2]) ).
cnf(c_0_12,negated_conjecture,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
op1(e10,e10) = e10,
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_14,plain,
( ~ epred1_0
| h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,plain,
( e23 != e24
& e22 != e24
& e22 != e23
& e21 != e24
& e21 != e23
& e21 != e22
& e20 != e24
& e20 != e23
& e20 != e22
& e20 != e21 ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
op2(h(e10),h(e10)) = h(e10),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( h(e10) = e20
| h(e10) = e21
| h(e10) = e22
| h(e10) = e23
| h(e10) = e24 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_19,plain,
op2(e24,e24) = e21,
inference(split_conjunct,[status(thm)],[ax5]) ).
cnf(c_0_20,plain,
e21 != e24,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( h(e10) = e20
| h(e10) = e21
| h(e10) = e22
| h(e10) = e23 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_22,plain,
op2(e23,e23) = e21,
inference(split_conjunct,[status(thm)],[ax5]) ).
cnf(c_0_23,plain,
e21 != e23,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_25,plain,
op2(e22,e22) = e21,
inference(split_conjunct,[status(thm)],[ax5]) ).
cnf(c_0_26,plain,
e21 != e22,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
h(op1(e14,e14)) = op2(h(e14),h(e14)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,plain,
op1(e14,e14) = e10,
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_29,negated_conjecture,
( h(e10) = e20
| h(e10) = e21 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
op2(e21,e21) = e22,
inference(split_conjunct,[status(thm)],[ax5]) ).
cnf(c_0_31,negated_conjecture,
op2(h(e14),h(e14)) = h(e10),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
h(e10) = e20,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_30]),c_0_26]) ).
cnf(c_0_33,plain,
( ~ epred1_0
| h(e14) = e24
| h(e14) = e23
| h(e14) = e22
| h(e14) = e21
| h(e14) = e20 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_34,negated_conjecture,
op2(h(e14),h(e14)) = e20,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( h(e14) = e20
| h(e14) = e21
| h(e14) = e22
| h(e14) = e23
| h(e14) = e24 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_15])]) ).
cnf(c_0_36,plain,
e20 != e21,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_37,negated_conjecture,
( h(e14) = e20
| h(e14) = e21
| h(e14) = e22
| h(e14) = e23 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_19]),c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( h(e14) = e22
| h(e14) = e21
| h(e14) = e20 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_37]),c_0_22]),c_0_36]) ).
fof(c_0_39,plain,
( e13 != e14
& e12 != e14
& e12 != e13
& e11 != e14
& e11 != e13
& e11 != e12
& e10 != e14
& e10 != e13
& e10 != e12
& e10 != e11 ),
inference(fof_simplification,[status(thm)],[ax1]) ).
cnf(c_0_40,negated_conjecture,
( h(e14) = e20
| h(e14) = e21 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_38]),c_0_25]),c_0_36]) ).
cnf(c_0_41,plain,
e20 != e22,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_42,negated_conjecture,
j(h(e10)) = e10,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_43,plain,
( e13 != e14
& e12 != e14
& e12 != e13
& e11 != e14
& e11 != e13
& e11 != e12
& e10 != e14
& e10 != e13
& e10 != e12
& e10 != e11 ),
inference(fof_nnf,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
j(h(e14)) = e14,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_45,negated_conjecture,
h(e14) = e20,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_40]),c_0_30]),c_0_41]) ).
cnf(c_0_46,negated_conjecture,
j(e20) = e10,
inference(rw,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_47,plain,
e10 != e14,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG077+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.39 % Computer : n008.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Mon Sep 21 12:56:14 UTC 2026
% 0.10/5.40 % CPUTime :
% 0.10/5.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.47 Running first-order theorem proving
% 0.16/5.47 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.50 % Version: 3.5.1
% 0.16/5.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.50 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.50 % Starting sh5l with 300s (1) cores
% 0.16/5.50 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1026073 completed with status 0
% 0.16/5.50 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.16/5.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.50 % No SInE strategy applied
% 0.16/5.50 % Search class: FGUSF-FFMM21-SFFFFFNN
% 0.16/5.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.50 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.16/5.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/5.50 % Starting new_bool_3 with 136s (1) cores
% 0.16/5.50 % Starting new_bool_1 with 136s (1) cores
% 0.16/5.50 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1026081 completed with status 0
% 0.16/5.50 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.16/5.50 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.50 % No SInE strategy applied
% 0.16/5.50 % Search class: FGUSF-FFMM21-SFFFFFNN
% 0.16/5.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.50 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.50 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.16/5.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/5.50 % Preprocessing time : 0.002 s
% 0.16/5.50 % Presaturation interreduction done
% 0.16/5.50
% 0.16/5.50 % Proof found!
% 0.16/5.50 % SZS status Theorem
% 0.16/5.50 % SZS output start CNFRefutation
% See solution above
% 0.16/5.50 % Parsed axioms : 6
% 0.16/5.50 % Removed by relevancy pruning/SinE : 0
% 0.16/5.50 % Initial clauses : 166
% 0.16/5.50 % Removed in clause preprocessing : 0
% 0.16/5.50 % Initial clauses in saturation : 166
% 0.16/5.50 % Processed clauses : 362
% 0.16/5.50 % ...of these trivial : 0
% 0.16/5.50 % ...subsumed : 2
% 0.16/5.50 % ...remaining for further processing : 360
% 0.16/5.50 % Other redundant clauses eliminated : 0
% 0.16/5.50 % Clauses deleted for lack of memory : 0
% 0.16/5.50 % Backward-subsumed : 6
% 0.16/5.50 % Backward-rewritten : 43
% 0.16/5.50 % Generated clauses : 146
% 0.16/5.50 % ...of the previous two non-redundant : 166
% 0.16/5.50 % ...aggressively subsumed : 0
% 0.16/5.50 % Contextual simplify-reflections : 0
% 0.16/5.50 % Paramodulations : 114
% 0.16/5.50 % Factorizations : 32
% 0.16/5.50 % NegExts : 0
% 0.16/5.50 % Equation resolutions : 0
% 0.16/5.50 % Disequality decompositions : 0
% 0.16/5.50 % Total rewrite steps : 148
% 0.16/5.50 % ...of those cached : 88
% 0.16/5.50 % Propositional unsat checks : 0
% 0.16/5.50 % Propositional check models : 0
% 0.16/5.50 % Propositional check unsatisfiable : 0
% 0.16/5.50 % Propositional clauses : 0
% 0.16/5.50 % Propositional clauses after purity: 0
% 0.16/5.50 % Propositional unsat core size : 0
% 0.16/5.50 % Propositional preprocessing time : 0.000
% 0.16/5.50 % Propositional encoding time : 0.000
% 0.16/5.50 % Propositional solver time : 0.000
% 0.16/5.50 % Success case prop preproc time : 0.000
% 0.16/5.50 % Success case prop encoding time : 0.000
% 0.16/5.50 % Success case prop solver time : 0.000
% 0.16/5.50 % Current number of processed clauses : 145
% 0.16/5.50 % Positive orientable unit clauses : 97
% 0.16/5.50 % Positive unorientable unit clauses: 0
% 0.16/5.50 % Negative unit clauses : 45
% 0.16/5.50 % Non-unit-clauses : 3
% 0.16/5.50 % Current number of unprocessed clauses: 106
% 0.16/5.50 % ...number of literals in the above : 454
% 0.16/5.50 % Current number of archived formulas : 0
% 0.16/5.50 % Current number of archived clauses : 215
% 0.16/5.50 % Clause-clause subsumption calls (NU) : 6
% 0.16/5.50 % Rec. Clause-clause subsumption calls : 6
% 0.16/5.50 % Non-unit clause-clause subsumptions : 6
% 0.16/5.50 % Unit Clause-clause subsumption calls : 1980
% 0.16/5.50 % Rewrite failures with RHS unbound : 0
% 0.16/5.50 % BW rewrite match attempts : 3
% 0.16/5.50 % BW rewrite match successes : 3
% 0.16/5.50 % Condensation attempts : 0
% 0.16/5.50 % Condensation successes : 0
% 0.16/5.50 % Termbank termtop insertions : 7448
% 0.16/5.50 % Search garbage collected termcells : 632
% 0.16/5.50
% 0.16/5.50 % -------------------------------------------------
% 0.16/5.50 % User time : 0.013 s
% 0.16/5.50 % System time : 0.006 s
% 0.16/5.50 % Total time : 0.019 s
% 0.16/5.50 % Maximum resident set size: 3696 pages
% 0.16/5.50
% 0.16/5.50 % -------------------------------------------------
% 0.16/5.50 % User time : 0.061 s
% 0.16/5.50 % System time : 0.015 s
% 0.16/5.50 % Total time : 0.076 s
% 0.16/5.50 % Maximum resident set size: 4864 pages
% 0.16/5.50 % E exiting
%------------------------------------------------------------------------------