%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE021+3 : 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 : n005.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 07:43:26 AM UTC 2026
% Result : Theorem 24.24s 4.00s
% Output : CNFRefutation 24.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 45 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 13 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
fof(left_distributivity,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ).
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,
! [X0,X1] :
( test(X1)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(clausification,[status(esa)],[left_distributivity]) ).
cnf(c17,plain,
( addition(X1,X0) = one
| ~ 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(c24,plain,
test(sK35),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c25,plain,
sK34 != addition(multiplication(sK35,sK34),multiplication(c(sK35),sK34)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d1,plain,
sK34 != multiplication(addition(sK35,c(sK35)),sK34),
inference(demodulation,[status(thm)],[c25,c8]) ).
cnf(d2,plain,
( ~ complement(sK35,X0)
| ~ test(sK35)
| sK34 != multiplication(addition(sK35,X0),sK34) ),
inference(superposition,[status(thm)],[c20,d1]) ).
cnf(d3,plain,
( ~ complement(sK35,X0)
| sK34 != multiplication(addition(sK35,X0),sK34) ),
inference(resolution,[status(thm)],[c24,d2]) ).
cnf(d4,plain,
( ~ complement(sK35,X0)
| sK34 != multiplication(addition(X0,sK35),sK34) ),
inference(superposition,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( ~ complement(sK35,X0)
| ~ complement(sK35,X0)
| sK34 != multiplication(one,sK34) ),
inference(superposition,[status(thm)],[c17,d4]) ).
cnf(d6,plain,
( ~ complement(sK35,X0)
| sK34 != sK34 ),
inference(demodulation,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
~ complement(sK35,X0),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
~ test(sK35),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c24,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE021+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.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 : Fri Sep 25 19:14:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.24/4.00 % SZS status Theorem for theBenchmark.p
% 24.24/4.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------