%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG078+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 : Sun Sep 27 06:49:25 AM UTC 2026
% Result : Theorem 2.15s 0.75s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 96
% Number of leaves : 5
% Syntax : Number of formulae : 210 ( 87 unt; 0 def)
% Number of atoms : 935 ( 934 equ)
% Maximal formula atoms : 110 ( 4 avg)
% Number of connectives : 755 ( 30 ~; 521 |; 202 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 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(ax1,axiom,
( e13 != e14
& e12 != e14
& e12 != e13
& e11 != e14
& e11 != e13
& e11 != e12
& e10 != e14
& e10 != e13
& e10 != e12
& e10 != e11 ),
file('theBenchmark.p',ax1) ).
fof(ax2,axiom,
( e23 != e24
& e22 != e24
& e22 != e23
& e21 != e24
& e21 != e23
& e21 != e22
& e20 != e24
& e20 != e23
& e20 != e22
& e20 != e21 ),
file('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('theBenchmark.p',ax4) ).
fof(ax5,axiom,
( op2(e24,e24) = e20
& op2(e24,e23) = e22
& op2(e24,e22) = e21
& op2(e24,e21) = e23
& op2(e24,e20) = e24
& op2(e23,e24) = e22
& op2(e23,e23) = e21
& op2(e23,e22) = e20
& op2(e23,e21) = e24
& op2(e23,e20) = e23
& op2(e22,e24) = e21
& op2(e22,e23) = e24
& op2(e22,e22) = e23
& op2(e22,e21) = e20
& op2(e22,e20) = e22
& op2(e21,e24) = e23
& op2(e21,e23) = e20
& op2(e21,e22) = e24
& 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('theBenchmark.p',ax5) ).
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('theBenchmark.p',co1) ).
fof(co1_neg,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]) ).
cnf(c_9,plain,
e13 != e10,
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_10,plain,
e14 != e10,
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_13,plain,
e14 != e11,
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_17,plain,
e21 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_18,plain,
e22 != e20,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_21,plain,
e22 != e21,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_24,plain,
e23 != e22,
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_52,plain,
op1(e10,e10) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_57,plain,
op1(e11,e10) = e11,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_58,plain,
op1(e11,e11) = e14,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_59,plain,
op1(e11,e12) = e13,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_60,plain,
op1(e11,e13) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_61,plain,
op1(e11,e14) = e12,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_65,plain,
op1(e12,e13) = e11,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_70,plain,
op1(e13,e13) = e14,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_73,plain,
op1(e14,e11) = e13,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_76,plain,
op1(e14,e14) = e10,
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_77,plain,
op2(e20,e20) = e20,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_82,plain,
op2(e21,e20) = e21,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_83,plain,
op2(e21,e21) = e22,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_84,plain,
op2(e21,e22) = e24,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_88,plain,
op2(e22,e21) = e20,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_89,plain,
op2(e22,e22) = e23,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_91,plain,
op2(e22,e24) = e21,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_95,plain,
op2(e23,e23) = e21,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_101,plain,
op2(e24,e24) = e20,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_102,negated_conjecture,
( h(e10) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_103,negated_conjecture,
( h(e11) = e24
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_108,negated_conjecture,
( j(e21) = e14
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_112,negated_conjecture,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2071,negated_conjecture,
h(e10) = op2(h(e10),h(e10)),
inference(paramod,[status(thm)],[c_52,c_112]) ).
cnf(c_113,negated_conjecture,
op2(h(e10),h(e10)) = h(e10),
inference(copy,[status(thm)],[c_2071]) ).
cnf(c_122,negated_conjecture,
h(op1(e11,e10)) = op2(h(e11),h(e10)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2072,negated_conjecture,
h(e11) = op2(h(e11),h(e10)),
inference(paramod,[status(thm)],[c_57,c_122]) ).
cnf(c_123,negated_conjecture,
op2(h(e11),h(e10)) = h(e11),
inference(copy,[status(thm)],[c_2072]) ).
cnf(c_124,negated_conjecture,
h(op1(e11,e11)) = op2(h(e11),h(e11)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_125,negated_conjecture,
h(e14) = op2(h(e11),h(e11)),
inference(paramod,[status(thm)],[c_58,c_124]) ).
cnf(c_126,negated_conjecture,
h(op1(e11,e12)) = op2(h(e11),h(e12)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_127,negated_conjecture,
h(e13) = op2(h(e11),h(e12)),
inference(paramod,[status(thm)],[c_59,c_126]) ).
cnf(c_128,negated_conjecture,
h(op1(e11,e13)) = op2(h(e11),h(e13)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2073,negated_conjecture,
h(e10) = op2(h(e11),h(e13)),
inference(paramod,[status(thm)],[c_60,c_128]) ).
cnf(c_2074,negated_conjecture,
h(e10) = op2(h(e11),op2(h(e11),h(e12))),
inference(paramod,[status(thm)],[c_127,c_2073]) ).
cnf(c_129,negated_conjecture,
op2(h(e11),op2(h(e11),h(e12))) = h(e10),
inference(copy,[status(thm)],[c_2074]) ).
cnf(c_130,negated_conjecture,
h(op1(e11,e14)) = op2(h(e11),h(e14)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2075,negated_conjecture,
h(e12) = op2(h(e11),h(e14)),
inference(paramod,[status(thm)],[c_61,c_130]) ).
cnf(c_131,negated_conjecture,
h(e12) = op2(h(e11),op2(h(e11),h(e11))),
inference(paramod,[status(thm)],[c_125,c_2075]) ).
cnf(c_138,negated_conjecture,
h(op1(e12,e13)) = op2(h(e12),h(e13)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2076,negated_conjecture,
h(e11) = op2(h(e12),h(e13)),
inference(paramod,[status(thm)],[c_65,c_138]) ).
cnf(c_2077,negated_conjecture,
h(e11) = op2(op2(h(e11),op2(h(e11),h(e11))),h(e13)),
inference(paramod,[status(thm)],[c_131,c_2076]) ).
cnf(c_2078,negated_conjecture,
h(e11) = op2(op2(h(e11),op2(h(e11),h(e11))),op2(h(e11),h(e12))),
inference(paramod,[status(thm)],[c_127,c_2077]) ).
cnf(c_2079,negated_conjecture,
h(e11) = op2(op2(h(e11),op2(h(e11),h(e11))),op2(h(e11),op2(h(e11),op2(h(e11),h(e11))))),
inference(paramod,[status(thm)],[c_131,c_2078]) ).
cnf(c_139,negated_conjecture,
op2(op2(h(e11),op2(h(e11),h(e11))),op2(h(e11),op2(h(e11),op2(h(e11),h(e11))))) = h(e11),
inference(copy,[status(thm)],[c_2079]) ).
cnf(c_172,negated_conjecture,
j(op2(e21,e20)) = op1(j(e21),j(e20)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2080,negated_conjecture,
j(e21) = op1(j(e21),j(e20)),
inference(paramod,[status(thm)],[c_82,c_172]) ).
cnf(c_173,negated_conjecture,
op1(j(e21),j(e20)) = j(e21),
inference(copy,[status(thm)],[c_2080]) ).
cnf(c_174,negated_conjecture,
j(op2(e21,e21)) = op1(j(e21),j(e21)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_175,negated_conjecture,
j(e22) = op1(j(e21),j(e21)),
inference(paramod,[status(thm)],[c_83,c_174]) ).
cnf(c_176,negated_conjecture,
j(op2(e21,e22)) = op1(j(e21),j(e22)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2081,negated_conjecture,
j(e24) = op1(j(e21),j(e22)),
inference(paramod,[status(thm)],[c_84,c_176]) ).
cnf(c_177,negated_conjecture,
j(e24) = op1(j(e21),op1(j(e21),j(e21))),
inference(paramod,[status(thm)],[c_175,c_2081]) ).
cnf(c_184,negated_conjecture,
j(op2(e22,e21)) = op1(j(e22),j(e21)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2082,negated_conjecture,
j(e20) = op1(j(e22),j(e21)),
inference(paramod,[status(thm)],[c_88,c_184]) ).
cnf(c_2083,negated_conjecture,
j(e20) = op1(op1(j(e21),j(e21)),j(e21)),
inference(paramod,[status(thm)],[c_175,c_2082]) ).
cnf(c_185,negated_conjecture,
op1(op1(j(e21),j(e21)),j(e21)) = j(e20),
inference(copy,[status(thm)],[c_2083]) ).
cnf(c_190,negated_conjecture,
j(op2(e22,e24)) = op1(j(e22),j(e24)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_2084,negated_conjecture,
j(e21) = op1(j(e22),j(e24)),
inference(paramod,[status(thm)],[c_91,c_190]) ).
cnf(c_2085,negated_conjecture,
j(e21) = op1(op1(j(e21),j(e21)),j(e24)),
inference(paramod,[status(thm)],[c_175,c_2084]) ).
cnf(c_2086,negated_conjecture,
j(e21) = op1(op1(j(e21),j(e21)),op1(j(e21),op1(j(e21),j(e21)))),
inference(paramod,[status(thm)],[c_177,c_2085]) ).
cnf(c_191,negated_conjecture,
op1(op1(j(e21),j(e21)),op1(j(e21),op1(j(e21),j(e21)))) = j(e21),
inference(copy,[status(thm)],[c_2086]) ).
cnf(c_213,negated_conjecture,
h(j(e21)) = e21,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_214,negated_conjecture,
h(j(e22)) = e22,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_215,negated_conjecture,
h(op1(j(e21),j(e21))) = e22,
inference(paramod,[status(thm)],[c_175,c_214]) ).
cnf(c_220,negated_conjecture,
j(h(e10)) = e10,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_221,negated_conjecture,
j(h(e11)) = e11,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_226,negated_conjecture,
j(h(e14)) = e14,
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_227,negated_conjecture,
j(op2(h(e11),h(e11))) = e14,
inference(paramod,[status(thm)],[c_125,c_226]) ).
cnf(c_232,negated_conjecture,
op2(h(e11),op2(h(e11),op2(h(e11),op2(h(e11),h(e11))))) = h(e10),
inference(paramod,[status(thm)],[c_131,c_129]) ).
cnf(c_243,plain,
( op2(e24,h(e10)) = h(e10)
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_102,c_113]) ).
cnf(c_2087,plain,
( h(e14) = op2(e24,h(e11))
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_103,c_125]) ).
cnf(c_249,plain,
( op2(h(e11),h(e11)) = op2(e24,h(e11))
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_125,c_2087]) ).
cnf(c_2088,plain,
( j(e22) = op1(e14,j(e21))
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_108,c_175]) ).
cnf(c_334,plain,
( op1(j(e21),j(e21)) = op1(e14,j(e21))
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_175,c_2088]) ).
cnf(c_2089,plain,
( op2(e24,e24) = h(e10)
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_102,c_243]) ).
cnf(c_2090,plain,
( e20 = h(e10)
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_101,c_2089]) ).
cnf(c_2091,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2090]) ).
cnf(c_2092,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2091]) ).
cnf(c_2093,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2092]) ).
cnf(c_2094,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2093]) ).
cnf(c_2095,plain,
( h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2094]) ).
cnf(c_549,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2095]) ).
cnf(c_697,plain,
( op2(e23,h(e10)) = h(e10)
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_549,c_113]) ).
cnf(c_2096,plain,
( op2(e23,e23) = h(e10)
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_549,c_697]) ).
cnf(c_2097,plain,
( e21 = h(e10)
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_95,c_2096]) ).
cnf(c_2098,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2097]) ).
cnf(c_2099,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2098]) ).
cnf(c_2100,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2099]) ).
cnf(c_2101,plain,
( h(e10) = e21
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2100]) ).
cnf(c_709,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2101]) ).
cnf(c_710,plain,
( op2(e22,h(e10)) = h(e10)
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_709,c_113]) ).
cnf(c_2102,plain,
( op2(e22,e22) = h(e10)
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_709,c_710]) ).
cnf(c_2103,plain,
( e23 = h(e10)
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_89,c_2102]) ).
cnf(c_2104,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2103]) ).
cnf(c_2105,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2104]) ).
cnf(c_722,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2105]) ).
cnf(c_2106,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_722,c_709]) ).
cnf(c_2107,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2106]) ).
cnf(c_2108,plain,
( e23 = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2107]) ).
cnf(c_735,plain,
( h(e10) = e21
| h(e10) = e20 ),
inference(resolve,[status(thm)],[c_24,c_2108]) ).
cnf(c_736,plain,
( op2(e21,h(e10)) = h(e10)
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_735,c_113]) ).
cnf(c_2109,plain,
( op2(h(e11),h(e11)) = op2(e24,e24)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_103,c_249]) ).
cnf(c_2110,plain,
( op2(h(e11),h(e11)) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_101,c_2109]) ).
cnf(c_2111,plain,
( op2(h(e11),h(e11)) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2110]) ).
cnf(c_2112,plain,
( op2(h(e11),h(e11)) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2111]) ).
cnf(c_2113,plain,
( op2(h(e11),h(e11)) = e20
| h(e11) = e23
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2112]) ).
cnf(c_749,plain,
( op2(h(e11),h(e11)) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2113]) ).
cnf(c_2114,plain,
( op2(e21,e21) = h(e10)
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_735,c_736]) ).
cnf(c_2115,plain,
( e22 = h(e10)
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_83,c_2114]) ).
cnf(c_2116,plain,
( h(e10) = e22
| h(e10) = e20
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2115]) ).
cnf(c_890,plain,
( h(e10) = e22
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2116]) ).
cnf(c_2117,plain,
( e22 = e21
| h(e10) = e20
| h(e10) = e20 ),
inference(paramod,[status(thm)],[c_890,c_735]) ).
cnf(c_2118,plain,
( e22 = e21
| h(e10) = e20 ),
inference(copy,[status(thm)],[c_2117]) ).
cnf(c_903,plain,
h(e10) = e20,
inference(resolve,[status(thm)],[c_21,c_2118]) ).
cnf(c_955,negated_conjecture,
op2(h(e11),op2(h(e11),op2(h(e11),op2(h(e11),h(e11))))) = e20,
inference(paramod,[status(thm)],[c_903,c_232]) ).
cnf(c_958,negated_conjecture,
j(e20) = e10,
inference(paramod,[status(thm)],[c_903,c_220]) ).
cnf(c_965,negated_conjecture,
op2(h(e11),e20) = h(e11),
inference(paramod,[status(thm)],[c_903,c_123]) ).
cnf(c_1024,negated_conjecture,
op1(op1(j(e21),j(e21)),j(e21)) = e10,
inference(paramod,[status(thm)],[c_958,c_185]) ).
cnf(c_1026,negated_conjecture,
op1(j(e21),e10) = j(e21),
inference(paramod,[status(thm)],[c_958,c_173]) ).
cnf(c_2119,plain,
( op2(op2(h(e11),e20),op2(h(e11),op2(h(e11),op2(h(e11),h(e11))))) = h(e11)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_749,c_139]) ).
cnf(c_2120,plain,
( op2(h(e11),op2(h(e11),op2(h(e11),op2(h(e11),h(e11))))) = h(e11)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_965,c_2119]) ).
cnf(c_2121,plain,
( e20 = h(e11)
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_955,c_2120]) ).
cnf(c_2122,plain,
( h(e11) = e20
| h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2121]) ).
cnf(c_1107,plain,
( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2122]) ).
cnf(c_2123,plain,
( op1(j(e21),j(e21)) = op1(e14,e14)
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_108,c_334]) ).
cnf(c_2124,plain,
( op1(j(e21),j(e21)) = e10
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_76,c_2123]) ).
cnf(c_2125,plain,
( op1(j(e21),j(e21)) = e10
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2124]) ).
cnf(c_2126,plain,
( op1(j(e21),j(e21)) = e10
| j(e21) = e13
| j(e21) = e12
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2125]) ).
cnf(c_2127,plain,
( op1(j(e21),j(e21)) = e10
| j(e21) = e13
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2126]) ).
cnf(c_1109,plain,
( op1(j(e21),j(e21)) = e10
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2127]) ).
cnf(c_2128,plain,
( h(e14) = op2(e23,h(e11))
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1107,c_125]) ).
cnf(c_1114,plain,
( op2(h(e11),h(e11)) = op2(e23,h(e11))
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_125,c_2128]) ).
cnf(c_2129,plain,
( op2(h(e11),h(e11)) = op2(e23,e23)
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1107,c_1114]) ).
cnf(c_2130,plain,
( op2(h(e11),h(e11)) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_95,c_2129]) ).
cnf(c_2131,plain,
( op2(h(e11),h(e11)) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2130]) ).
cnf(c_2132,plain,
( op2(h(e11),h(e11)) = e21
| h(e11) = e22
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2131]) ).
cnf(c_1187,plain,
( op2(h(e11),h(e11)) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2132]) ).
cnf(c_1208,plain,
( j(e21) = e14
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1187,c_227]) ).
cnf(c_2133,plain,
( j(e22) = op1(e14,j(e21))
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1208,c_175]) ).
cnf(c_1212,plain,
( op1(j(e21),j(e21)) = op1(e14,j(e21))
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_175,c_2133]) ).
cnf(c_2134,plain,
( op1(j(e21),j(e21)) = op1(e14,e14)
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1208,c_1212]) ).
cnf(c_2135,plain,
( op1(j(e21),j(e21)) = e10
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_76,c_2134]) ).
cnf(c_2136,plain,
( op1(j(e21),j(e21)) = e10
| h(e11) = e22
| h(e11) = e21
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2135]) ).
cnf(c_2137,plain,
( op1(j(e21),j(e21)) = e10
| h(e11) = e22
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2136]) ).
cnf(c_1295,plain,
( op1(j(e21),j(e21)) = e10
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2137]) ).
cnf(c_2138,plain,
( h(e10) = e22
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1295,c_215]) ).
cnf(c_2139,plain,
( e20 = e22
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_903,c_2138]) ).
cnf(c_2140,plain,
( e22 = e20
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2139]) ).
cnf(c_1305,plain,
( h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(resolve,[status(thm)],[c_18,c_2140]) ).
cnf(c_2141,plain,
( j(e22) = e11
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1305,c_221]) ).
cnf(c_1366,plain,
( op1(j(e21),j(e21)) = e11
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_175,c_2141]) ).
cnf(c_1401,plain,
( op1(e11,j(e21)) = e10
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1366,c_1024]) ).
cnf(c_2142,plain,
( op1(op1(j(e21),j(e21)),op1(j(e21),e10)) = j(e21)
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_1109,c_191]) ).
cnf(c_2143,plain,
( op1(op1(j(e21),j(e21)),j(e21)) = j(e21)
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_1026,c_2142]) ).
cnf(c_2144,plain,
( e10 = j(e21)
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_1024,c_2143]) ).
cnf(c_2145,plain,
( j(e21) = e10
| j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2144]) ).
cnf(c_1566,plain,
( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2145]) ).
cnf(c_2146,plain,
( j(e22) = op1(e13,j(e21))
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_1566,c_175]) ).
cnf(c_1567,plain,
( op1(j(e21),j(e21)) = op1(e13,j(e21))
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_175,c_2146]) ).
cnf(c_2147,plain,
( op1(j(e21),j(e21)) = op1(e13,e13)
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_1566,c_1567]) ).
cnf(c_2148,plain,
( op1(j(e21),j(e21)) = e14
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_70,c_2147]) ).
cnf(c_2149,plain,
( op1(j(e21),j(e21)) = e14
| j(e21) = e12
| j(e21) = e11
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2148]) ).
cnf(c_2150,plain,
( op1(j(e21),j(e21)) = e14
| j(e21) = e12
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2149]) ).
cnf(c_1650,plain,
( op1(j(e21),j(e21)) = e14
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2150]) ).
cnf(c_2151,plain,
( e14 = e11
| h(e11) = e21
| h(e11) = e20
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_1650,c_1366]) ).
cnf(c_1674,plain,
( h(e11) = e21
| h(e11) = e20
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(resolve,[status(thm)],[c_13,c_2151]) ).
cnf(c_2152,plain,
( op1(e11,e12) = e10
| h(e11) = e21
| h(e11) = e20
| h(e11) = e21
| h(e11) = e20
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_1674,c_1401]) ).
cnf(c_2153,plain,
( e13 = e10
| h(e11) = e21
| h(e11) = e20
| h(e11) = e21
| h(e11) = e20
| j(e21) = e11
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_59,c_2152]) ).
cnf(c_2154,plain,
( e13 = e10
| h(e11) = e21
| h(e11) = e21
| h(e11) = e20
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2153]) ).
cnf(c_2155,plain,
( e13 = e10
| h(e11) = e21
| h(e11) = e20
| j(e21) = e11
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2154]) ).
cnf(c_1744,plain,
( h(e11) = e21
| h(e11) = e20
| j(e21) = e11
| j(e21) = e10 ),
inference(resolve,[status(thm)],[c_9,c_2155]) ).
cnf(c_2156,plain,
( h(e11) = e21
| h(e11) = e21
| h(e11) = e20
| j(e21) = e10 ),
inference(paramod,[status(thm)],[c_1744,c_213]) ).
cnf(c_1805,plain,
( h(e11) = e21
| h(e11) = e20
| j(e21) = e10 ),
inference(copy,[status(thm)],[c_2156]) ).
cnf(c_2157,plain,
( h(e10) = e21
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1805,c_213]) ).
cnf(c_2158,plain,
( e20 = e21
| h(e11) = e21
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_903,c_2157]) ).
cnf(c_2159,plain,
( e21 = e20
| h(e11) = e21
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2158]) ).
cnf(c_1814,plain,
( h(e11) = e21
| h(e11) = e20 ),
inference(resolve,[status(thm)],[c_17,c_2159]) ).
cnf(c_2160,plain,
( h(e14) = op2(e21,h(e11))
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1814,c_125]) ).
cnf(c_1815,plain,
( op2(h(e11),h(e11)) = op2(e21,h(e11))
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_125,c_2160]) ).
cnf(c_1875,plain,
( j(e21) = e11
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1814,c_221]) ).
cnf(c_2161,plain,
( op2(h(e11),h(e11)) = op2(e21,e21)
| h(e11) = e20
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1814,c_1815]) ).
cnf(c_2162,plain,
( op2(h(e11),h(e11)) = e22
| h(e11) = e20
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_83,c_2161]) ).
cnf(c_2014,plain,
( op2(h(e11),h(e11)) = e22
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2162]) ).
cnf(c_2163,plain,
( j(e22) = e14
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_2014,c_227]) ).
cnf(c_2035,plain,
( op1(j(e21),j(e21)) = e14
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_175,c_2163]) ).
cnf(c_2060,plain,
( op1(e14,j(e21)) = e10
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_2035,c_1024]) ).
cnf(c_2164,plain,
( op1(e14,e11) = e10
| h(e11) = e20
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_1875,c_2060]) ).
cnf(c_2165,plain,
( e13 = e10
| h(e11) = e20
| h(e11) = e20 ),
inference(paramod,[status(thm)],[c_73,c_2164]) ).
cnf(c_2166,plain,
( e13 = e10
| h(e11) = e20 ),
inference(copy,[status(thm)],[c_2165]) ).
cnf(c_2065,plain,
h(e11) = e20,
inference(resolve,[status(thm)],[c_9,c_2166]) ).
cnf(c_2167,negated_conjecture,
j(op2(e20,h(e11))) = e14,
inference(paramod,[status(thm)],[c_2065,c_227]) ).
cnf(c_2168,negated_conjecture,
j(op2(e20,e20)) = e14,
inference(paramod,[status(thm)],[c_2065,c_2167]) ).
cnf(c_2169,negated_conjecture,
j(e20) = e14,
inference(paramod,[status(thm)],[c_77,c_2168]) ).
cnf(c_2170,negated_conjecture,
e10 = e14,
inference(paramod,[status(thm)],[c_958,c_2169]) ).
cnf(c_2171,negated_conjecture,
e14 = e10,
inference(copy,[status(thm)],[c_2170]) ).
cnf(c_2070,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_10,c_2171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG078+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 21:11:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2683698 was started by sandbox on n001,
% 0.10/0.37 % Sat Sep 26 21:11:58 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 2.15/0.75
% 2.15/0.75 % SZS status Theorem for theBenchmark
% 2.15/0.75
% 2.15/0.75 % Proof 1 at 0.32 (+ 0.03) seconds.
% 2.15/0.75 % Length of proof is 108.
% 2.15/0.75 % Level of proof is 31.
% 2.15/0.75 % Maximum clause weight is 78.000.
% 2.15/0.75 % Given clauses 259.
% 2.15/0.75
% 2.15/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------