%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG182+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 06:47:43 AM UTC 2026
% Result : Theorem 17.00s 2.98s
% Output : CNFRefutation 17.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 20 unt; 0 def)
% Number of atoms : 418 ( 417 equ)
% Maximal formula atoms : 110 ( 7 avg)
% Number of connectives : 379 ( 14 ~; 170 |; 193 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 6 avg)
% Maximal term depth : 3 ( 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 ) ).
fof(ax4,axiom,
( op1(e14,e14) = e11
& op1(e14,e13) = e13
& op1(e14,e12) = e14
& op1(e14,e11) = e10
& op1(e14,e10) = e12
& op1(e13,e14) = e12
& op1(e13,e13) = e10
& op1(e13,e12) = e13
& op1(e13,e11) = e11
& op1(e13,e10) = e14
& op1(e12,e14) = e10
& op1(e12,e13) = e14
& op1(e12,e12) = e12
& op1(e12,e11) = e13
& op1(e12,e10) = e11
& op1(e11,e14) = e13
& op1(e11,e13) = e12
& op1(e11,e12) = e11
& op1(e11,e11) = e14
& op1(e11,e10) = e10
& op1(e10,e14) = e14
& op1(e10,e13) = e11
& op1(e10,e12) = e10
& op1(e10,e11) = e12
& op1(e10,e10) = e13 ) ).
fof(ax5,axiom,
( op2(e24,e24) = e24
& op2(e24,e23) = e21
& op2(e24,e22) = e20
& op2(e24,e21) = e22
& op2(e24,e20) = e23
& op2(e23,e24) = e22
& op2(e23,e23) = e23
& op2(e23,e22) = e21
& op2(e23,e21) = e20
& op2(e23,e20) = e24
& op2(e22,e24) = e23
& op2(e22,e23) = e20
& op2(e22,e22) = e22
& op2(e22,e21) = e24
& op2(e22,e20) = e21
& op2(e21,e24) = e20
& op2(e21,e23) = e24
& op2(e21,e22) = e23
& op2(e21,e21) = e21
& op2(e21,e20) = e22
& op2(e20,e24) = e21
& op2(e20,e23) = e22
& op2(e20,e22) = e24
& op2(e20,e21) = e23
& op2(e20,e20) = e20 ) ).
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)) ) ) ).
fof(negated_conjecture,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(negate_conjecture,[status(cth)],[co1]) ).
cnf(c2,plain,
e10 != e13,
inference(clausification,[status(esa)],[ax1]) ).
cnf(c45,plain,
op1(e10,e10) = e13,
inference(clausification,[status(esa)],[ax4]) ).
cnf(c70,plain,
op2(e20,e20) = e20,
inference(clausification,[status(esa)],[ax5]) ).
cnf(c76,plain,
op2(e21,e21) = e21,
inference(clausification,[status(esa)],[ax5]) ).
cnf(c82,plain,
op2(e22,e22) = e22,
inference(clausification,[status(esa)],[ax5]) ).
cnf(c88,plain,
op2(e23,e23) = e23,
inference(clausification,[status(esa)],[ax5]) ).
cnf(c94,plain,
op2(e24,e24) = e24,
inference(clausification,[status(esa)],[ax5]) ).
cnf(c95,plain,
( h(e10) = e22
| h(e10) = e23
| h(e10) = e21
| h(e10) = e20
| h(e10) = e24 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c105,plain,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c130,plain,
j(op2(e20,e20)) = op1(j(e20),j(e20)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c160,plain,
j(h(e10)) = e10,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c163,plain,
j(h(e13)) = e13,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
h(e13) = op2(h(e10),h(e10)),
inference(demodulation,[status(thm)],[c105,c45]) ).
cnf(d1,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e13) = op2(e24,h(e10)) ),
inference(superposition,[status(thm)],[c95,d0]) ).
cnf(d2,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e13) = op2(e24,e24) ),
inference(superposition,[status(thm)],[c95,d1]) ).
cnf(d3,plain,
( h(e13) = e24
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(demodulation,[status(thm)],[d2,c94]) ).
cnf(d4,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| j(e24) = e13 ),
inference(superposition,[status(thm)],[d3,c163]) ).
cnf(d5,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| j(e24) = e10 ),
inference(superposition,[status(thm)],[c95,c160]) ).
cnf(d6,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| e10 = e13 ),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(resolution,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e13) = op2(e23,h(e10)) ),
inference(superposition,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e13) = op2(e23,e23) ),
inference(superposition,[status(thm)],[d7,d8]) ).
cnf(d10,plain,
( h(e13) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(demodulation,[status(thm)],[d9,c88]) ).
cnf(d11,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| j(e23) = e13 ),
inference(superposition,[status(thm)],[d10,c163]) ).
cnf(d12,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| j(e23) = e10 ),
inference(superposition,[status(thm)],[d7,c160]) ).
cnf(d13,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| e10 = e13 ),
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(resolution,[status(thm)],[c2,d13]) ).
cnf(d15,plain,
( h(e10) = e21
| h(e10) = e20
| h(e13) = op2(e22,h(e10)) ),
inference(superposition,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
( h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20
| h(e13) = op2(e22,e22) ),
inference(superposition,[status(thm)],[d14,d15]) ).
cnf(d17,plain,
( h(e13) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(demodulation,[status(thm)],[d16,c82]) ).
cnf(d18,plain,
( h(e10) = e21
| h(e10) = e20
| j(e22) = e13 ),
inference(superposition,[status(thm)],[d17,c163]) ).
cnf(d19,plain,
( h(e10) = e21
| h(e10) = e20
| j(e22) = e10 ),
inference(superposition,[status(thm)],[d14,c160]) ).
cnf(d20,plain,
( h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20
| e10 = e13 ),
inference(superposition,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( h(e10) = e21
| h(e10) = e20 ),
inference(resolution,[status(thm)],[c2,d20]) ).
cnf(d22,plain,
( h(e10) = e20
| h(e13) = op2(e21,h(e10)) ),
inference(superposition,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( h(e10) = e20
| h(e10) = e20
| h(e13) = op2(e21,e21) ),
inference(superposition,[status(thm)],[d21,d22]) ).
cnf(d24,plain,
( h(e13) = e21
| h(e10) = e20 ),
inference(demodulation,[status(thm)],[d23,c76]) ).
cnf(d25,plain,
( h(e10) = e20
| j(e21) = e13 ),
inference(superposition,[status(thm)],[d24,c163]) ).
cnf(d26,plain,
( h(e10) = e20
| j(e21) = e10 ),
inference(superposition,[status(thm)],[d21,c160]) ).
cnf(d27,plain,
( h(e10) = e20
| h(e10) = e20
| e10 = e13 ),
inference(superposition,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
h(e10) = e20,
inference(resolution,[status(thm)],[c2,d27]) ).
cnf(d29,plain,
j(e20) = e10,
inference(demodulation,[status(thm)],[c160,d28]) ).
cnf(d30,plain,
j(e20) = op1(j(e20),j(e20)),
inference(demodulation,[status(thm)],[c130,c70]) ).
cnf(d31,plain,
e10 = op1(j(e20),j(e20)),
inference(demodulation,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
e10 = op1(e10,j(e20)),
inference(demodulation,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
e10 = op1(e10,e10),
inference(demodulation,[status(thm)],[d32,d29]) ).
cnf(d34,plain,
e10 = e13,
inference(demodulation,[status(thm)],[c45,d33]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[c2,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG182+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 21:23:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.00/2.98 % SZS status Theorem for theBenchmark.p
% 17.00/2.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------