%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE004+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:43:23 AM UTC 2026
% Result : Theorem 22.92s 5.53s
% Output : CNFRefutation 22.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 26 unt; 0 def)
% Number of atoms : 76 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 30 ~; 26 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 6 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X0] : addition(X0,zero) = X0 ).
fof(multiplicative_associativity,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ).
fof(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
fof(right_annihilation,axiom,
! [X0] : multiplication(X0,zero) = zero ).
fof(left_annihilation,axiom,
! [X0] : multiplication(zero,X0) = zero ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
c(zero) = one ).
fof(negated_conjecture,negated_conjecture,
c(zero) != one,
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_identity]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(clausification,[status(esa)],[multiplicative_associativity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c9,plain,
multiplication(X0,zero) = zero,
inference(clausification,[status(esa)],[right_annihilation]) ).
cnf(c10,plain,
multiplication(zero,X0) = zero,
inference(clausification,[status(esa)],[left_annihilation]) ).
cnf(c14,plain,
( ~ complement(X1,X0)
| test(X0) ),
inference(clausification,[status(esa)],[test_1]) ).
cnf(c16,plain,
( multiplication(X0,X1) = zero
| ~ complement(X0,X1) ),
inference(clausification,[status(esa)],[test_2]) ).
cnf(c18,plain,
( addition(X1,X0) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X0,X1) ),
inference(clausification,[status(esa)],[test_2]) ).
cnf(c19,plain,
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(clausification,[status(esa)],[test_3]) ).
cnf(c20,plain,
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(clausification,[status(esa)],[test_3]) ).
cnf(c22,plain,
c(zero) != one,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d1,plain,
( test(c(X0))
| ~ test(X0) ),
inference(resolution,[status(thm)],[d0,c14]) ).
cnf(d2,plain,
( multiplication(X0,c(X0)) = zero
| ~ test(X0) ),
inference(resolution,[status(thm)],[d0,c16]) ).
cnf(d3,plain,
( complement(zero,X0)
| multiplication(zero,X0) != zero
| addition(X0,zero) != one
| zero != zero ),
inference(superposition,[status(thm)],[c9,c18]) ).
cnf(d4,plain,
( complement(zero,X0)
| multiplication(zero,X0) != zero
| zero != zero
| X0 != one ),
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( complement(zero,X0)
| zero != zero
| zero != zero
| X0 != one ),
inference(demodulation,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
( complement(zero,X0)
| zero != zero
| X0 != one ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
multiplication(multiplication(X0,X1),multiplication(X2,X3)) = multiplication(multiplication(X0,multiplication(X1,X2)),X3),
inference(superposition,[status(thm)],[c4,c4]) ).
cnf(d8,plain,
multiplication(X0,multiplication(X1,multiplication(X2,X3))) = multiplication(multiplication(X0,multiplication(X1,X2)),X3),
inference(demodulation,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
multiplication(X0,multiplication(X1,multiplication(X2,X3))) = multiplication(X0,multiplication(multiplication(X1,X2),X3)),
inference(demodulation,[status(thm)],[d8,c4]) ).
cnf(d10,plain,
multiplication(X3,multiplication(X0,multiplication(X1,X2))) = multiplication(X3,multiplication(X0,multiplication(X1,X2))),
inference(demodulation,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
zero = multiplication(zero,multiplication(X0,multiplication(X1,X2))),
inference(superposition,[status(thm)],[c10,d10]) ).
cnf(d12,plain,
zero = zero,
inference(demodulation,[status(thm)],[d11,c10]) ).
cnf(d13,plain,
( complement(zero,X0)
| X0 != one ),
inference(resolution,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
complement(zero,one),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
test(one),
inference(resolution,[status(thm)],[d14,c14]) ).
cnf(d16,plain,
multiplication(one,c(one)) = zero,
inference(resolution,[status(thm)],[d15,d2]) ).
cnf(d17,plain,
c(one) = zero,
inference(demodulation,[status(thm)],[d16,c6]) ).
cnf(d18,plain,
( ~ test(one)
| test(zero) ),
inference(superposition,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( ~ test(zero)
| c(zero) = one ),
inference(resolution,[status(thm)],[d14,c20]) ).
cnf(d20,plain,
~ test(zero),
inference(resolution,[status(thm)],[c22,d19]) ).
cnf(d21,plain,
~ test(one),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d15,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 19:11:52 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.92/5.53 % SZS status Theorem for theBenchmark.p
% 22.92/5.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------