%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG042+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 : n009.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 06:47:08 AM UTC 2026
% Result : Theorem 14.66s 2.43s
% Output : CNFRefutation 14.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 4
% Syntax : Number of formulae : 67 ( 31 unt; 0 def)
% Number of atoms : 322 ( 321 equ)
% Maximal formula atoms : 72 ( 4 avg)
% Number of connectives : 268 ( 13 ~; 126 |; 127 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax2,axiom,
( e22 != e23
& e21 != e23
& e21 != e22
& e20 != e23
& e20 != e22
& e20 != e21 ) ).
fof(ax4,axiom,
( op1(e13,e13) = e10
& op1(e13,e12) = e11
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e13) = e11
& op1(e12,e12) = e10
& op1(e12,e11) = e13
& op1(e12,e10) = e12
& op1(e11,e13) = e12
& op1(e11,e12) = e13
& op1(e11,e11) = e10
& op1(e11,e10) = e11
& op1(e10,e13) = e13
& op1(e10,e12) = e12
& op1(e10,e11) = e11
& op1(e10,e10) = e10 ) ).
fof(ax5,axiom,
( op2(e23,e23) = e20
& op2(e23,e22) = e21
& op2(e23,e21) = e22
& op2(e23,e20) = e23
& op2(e22,e23) = e21
& op2(e22,e22) = e23
& op2(e22,e21) = e20
& op2(e22,e20) = e22
& op2(e21,e23) = e22
& op2(e21,e22) = e20
& op2(e21,e21) = e23
& op2(e21,e20) = e21
& op2(e20,e23) = e23
& op2(e20,e22) = e22
& op2(e20,e21) = e21
& op2(e20,e20) = e20 ) ).
fof(co1,conjecture,
( ( ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10)) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c7,plain,
e20 != e22,
inference(clausification,[status(esa)],[ax2]) ).
cnf(c8,plain,
e20 != e23,
inference(clausification,[status(esa)],[ax2]) ).
cnf(c10,plain,
e21 != e23,
inference(clausification,[status(esa)],[ax2]) ).
cnf(c11,plain,
e22 != e23,
inference(clausification,[status(esa)],[ax2]) ).
cnf(c28,plain,
op1(e10,e10) = e10,
inference(clausification,[status(esa)],[ax4]) ).
cnf(c33,plain,
op1(e11,e11) = e10,
inference(clausification,[status(esa)],[ax4]) ).
cnf(c38,plain,
op1(e12,e12) = e10,
inference(clausification,[status(esa)],[ax4]) ).
cnf(c43,plain,
op1(e13,e13) = e10,
inference(clausification,[status(esa)],[ax4]) ).
cnf(c49,plain,
op2(e21,e21) = e23,
inference(clausification,[status(esa)],[ax5]) ).
cnf(c54,plain,
op2(e22,e22) = e23,
inference(clausification,[status(esa)],[ax5]) ).
cnf(c59,plain,
op2(e23,e23) = e20,
inference(clausification,[status(esa)],[ax5]) ).
cnf(c60,plain,
( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c68,plain,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c73,plain,
h(op1(e11,e11)) = op2(h(e11),h(e11)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c78,plain,
h(op1(e12,e12)) = op2(h(e12),h(e12)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c83,plain,
h(op1(e13,e13)) = op2(h(e13),h(e13)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c102,plain,
h(j(e22)) = e22,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c104,plain,
j(h(e10)) = e10,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c107,plain,
j(h(e13)) = e13,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
h(e10) = op2(h(e10),h(e10)),
inference(demodulation,[status(thm)],[c68,c28]) ).
cnf(d1,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = op2(h(e10),e23) ),
inference(superposition,[status(thm)],[c60,d0]) ).
cnf(d2,plain,
( h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20
| h(e10) = op2(e23,e23) ),
inference(superposition,[status(thm)],[c60,d1]) ).
cnf(d3,plain,
( h(e10) = e20
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ),
inference(demodulation,[status(thm)],[d2,c59]) ).
cnf(d4,plain,
( h(e10) = e20
| h(e10) = e21
| h(e10) = e20
| h(e10) = op2(h(e10),e22) ),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( h(e10) = e20
| h(e10) = e21
| h(e10) = e20
| j(e22) = e10 ),
inference(superposition,[status(thm)],[d3,c104]) ).
cnf(d6,plain,
( h(e10) = e21
| h(e10) = e20
| h(e10) = e22 ),
inference(superposition,[status(thm)],[d5,c102]) ).
cnf(d7,plain,
( h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20
| h(e10) = op2(e22,e22) ),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( h(e10) = e23
| h(e10) = e21
| h(e10) = e20 ),
inference(demodulation,[status(thm)],[d7,c54]) ).
cnf(d9,plain,
( h(e10) = e21
| h(e10) = e20
| h(e10) = e21
| h(e10) = e20
| e22 = e23 ),
inference(superposition,[status(thm)],[d6,d8]) ).
cnf(d10,plain,
( h(e10) = e21
| h(e10) = e20 ),
inference(resolution,[status(thm)],[c11,d9]) ).
cnf(d11,plain,
( h(e10) = e20
| h(e10) = op2(h(e10),e21) ),
inference(superposition,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( h(e10) = e20
| h(e10) = e20
| h(e10) = op2(e21,e21) ),
inference(superposition,[status(thm)],[d10,d11]) ).
cnf(d13,plain,
( h(e10) = e23
| h(e10) = e20 ),
inference(demodulation,[status(thm)],[d12,c49]) ).
cnf(d14,plain,
( h(e10) = e20
| h(e10) = e20
| e21 = e23 ),
inference(superposition,[status(thm)],[d10,d13]) ).
cnf(d15,plain,
h(e10) = e20,
inference(resolution,[status(thm)],[c10,d14]) ).
cnf(d16,plain,
h(e10) = op2(h(e12),h(e12)),
inference(demodulation,[status(thm)],[c78,c38]) ).
cnf(d17,plain,
e20 = op2(h(e12),h(e12)),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
h(e10) = op2(h(e13),h(e13)),
inference(demodulation,[status(thm)],[c83,c43]) ).
cnf(d19,plain,
e20 = op2(h(e13),h(e13)),
inference(demodulation,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
( j(e22) = e12
| j(e22) = e11
| j(e22) = e10
| h(e13) = e22 ),
inference(superposition,[status(thm)],[c66,c102]) ).
cnf(d21,plain,
( j(e22) = e11
| j(e22) = e10
| h(e13) = e22
| h(e12) = e22 ),
inference(superposition,[status(thm)],[d20,c102]) ).
cnf(d22,plain,
( j(e22) = e10
| h(e13) = e22
| h(e12) = e22
| h(e11) = e22 ),
inference(superposition,[status(thm)],[d21,c102]) ).
cnf(d23,plain,
( h(e13) = e22
| h(e12) = e22
| h(e11) = e22
| h(e10) = e22 ),
inference(superposition,[status(thm)],[d22,c102]) ).
cnf(d24,plain,
( h(e12) = e22
| h(e11) = e22
| h(e10) = e22
| j(e22) = e13 ),
inference(superposition,[status(thm)],[d23,c107]) ).
cnf(d25,plain,
( j(e22) = e13
| h(e12) = e22
| h(e11) = e22
| e20 = e22 ),
inference(demodulation,[status(thm)],[d24,d15]) ).
cnf(d26,plain,
( j(e22) = e13
| h(e12) = e22
| h(e11) = e22 ),
inference(resolution,[status(thm)],[c7,d25]) ).
cnf(d27,plain,
( h(e12) = e22
| h(e11) = e22
| h(e13) = e22 ),
inference(superposition,[status(thm)],[d26,c102]) ).
cnf(d28,plain,
( h(e12) = e22
| h(e11) = e22
| e20 = op2(h(e13),e22) ),
inference(superposition,[status(thm)],[d27,d19]) ).
cnf(d29,plain,
( h(e12) = e22
| h(e11) = e22
| h(e12) = e22
| h(e11) = e22
| e20 = op2(e22,e22) ),
inference(superposition,[status(thm)],[d27,d28]) ).
cnf(d30,plain,
( h(e12) = e22
| h(e11) = e22
| e20 = e23 ),
inference(demodulation,[status(thm)],[d29,c54]) ).
cnf(d31,plain,
( h(e12) = e22
| h(e11) = e22 ),
inference(resolution,[status(thm)],[c8,d30]) ).
cnf(d32,plain,
( h(e11) = e22
| e20 = op2(h(e12),e22) ),
inference(superposition,[status(thm)],[d31,d17]) ).
cnf(d33,plain,
( h(e11) = e22
| h(e11) = e22
| e20 = op2(e22,e22) ),
inference(superposition,[status(thm)],[d31,d32]) ).
cnf(d34,plain,
( h(e11) = e22
| e20 = e23 ),
inference(demodulation,[status(thm)],[d33,c54]) ).
cnf(d35,plain,
h(e11) = e22,
inference(resolution,[status(thm)],[c8,d34]) ).
cnf(d36,plain,
h(e10) = op2(h(e11),h(e11)),
inference(demodulation,[status(thm)],[c73,c33]) ).
cnf(d37,plain,
e20 = op2(h(e11),h(e11)),
inference(demodulation,[status(thm)],[d36,d15]) ).
cnf(d38,plain,
e20 = op2(e22,h(e11)),
inference(demodulation,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
e20 = op2(e22,e22),
inference(demodulation,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
e20 = e23,
inference(demodulation,[status(thm)],[c54,d39]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[c8,d40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG042+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 21:01:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.66/2.43 % SZS status Theorem for theBenchmark.p
% 14.66/2.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------