%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE007+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 32.22s 9.56s
% Output : CNFRefutation 32.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 28 unt; 0 def)
% Number of atoms : 58 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 14 ~; 8 |; 4 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(additive_associativity,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ).
fof(additive_idempotence,axiom,
! [X0] : addition(X0,X0) = X0 ).
fof(multiplicative_right_identity,axiom,
! [X0] : multiplication(X0,one) = X0 ).
fof(right_distributivity,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ).
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,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c1,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[additive_idempotence]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c7,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(clausification,[status(esa)],[right_distributivity]) ).
cnf(c13,plain,
( complement(sK23(X0),X0)
| ~ test(X0) ),
inference(clausification,[status(esa)],[test_1]) ).
cnf(c16,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(c24,plain,
test(sK34),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c25,plain,
test(sK35),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c26,plain,
addition(multiplication(addition(sK34,c(sK34)),sK35),multiplication(addition(sK34,c(sK34)),c(sK35))) != 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,
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[d0,c16]) ).
cnf(d2,plain,
( ~ test(X0)
| addition(X0,c(X0)) = one ),
inference(demodulation,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
addition(sK34,c(sK34)) = one,
inference(resolution,[status(thm)],[d2,c24]) ).
cnf(d4,plain,
addition(sK35,c(sK35)) = one,
inference(resolution,[status(thm)],[d2,c25]) ).
cnf(d5,plain,
multiplication(addition(sK34,c(sK34)),addition(sK35,c(sK35))) != one,
inference(demodulation,[status(thm)],[c26,c7]) ).
cnf(d6,plain,
multiplication(addition(sK34,c(sK34)),one) != one,
inference(demodulation,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
addition(sK34,c(sK34)) != one,
inference(demodulation,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
one != one,
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( ~ test(X0)
| addition(X0,sK23(X0)) = one ),
inference(resolution,[status(thm)],[c16,c13]) ).
cnf(d10,plain,
addition(sK35,sK23(sK35)) = one,
inference(resolution,[status(thm)],[d9,c25]) ).
cnf(d11,plain,
addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d12,plain,
addition(sK35,sK23(sK35)) = addition(sK35,one),
inference(superposition,[status(thm)],[d10,d11]) ).
cnf(d13,plain,
one = addition(sK35,one),
inference(demodulation,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
one = addition(one,sK35),
inference(demodulation,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
addition(one,sK35) = addition(one,one),
inference(superposition,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
one = addition(one,one),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
one = one,
inference(demodulation,[status(thm)],[d16,c3]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE007+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n019.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Fri Sep 25 19:11:39 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.22/9.56 % SZS status Theorem for theBenchmark.p
% 32.22/9.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------