%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE081+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Thu Sep 24 12:57:56 PM UTC 2026
% Result : Theorem 20.28s 3.08s
% Output : CNFRefutation 20.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 54 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 98 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> multiplication(antidomain(X0),X0) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> multiplication(antidomain(X0),X0) = zero ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f26,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f37,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f39,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
? [X0] :
( multiplication(antidomain(X0),X0) != zero
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( ? [X0] : multiplication(antidomain(X0),X0) != zero
& ! [X1] : multiplication(domain(X1),antidomain(X1)) = zero
& ! [X1] : addition(domain(X1),antidomain(X1)) = one ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( multiplication(antidomain(sK0_skl),sK0_skl) != zero
& ! [X1] : multiplication(domain(X1),antidomain(X1)) = zero
& ! [X1] : addition(domain(X1),antidomain(X1)) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f41]) ).
fof(f43,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
multiplication(antidomain(sK0_skl),sK0_skl) != zero,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f63,plain,
! [X0,X1] : addition(domain(X0),addition(antidomain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f43,f21]) ).
fof(f97,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(paramodulation,[status(thm)],[f20,f37]) ).
fof(f108,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f44,f24]) ).
fof(f117,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f108]) ).
fof(f135,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f166,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f172,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f217,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = addition(one,antidomain(X0)),
inference(paramodulation,[status(thm)],[f23,f63]) ).
fof(f222,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f43,f217]) ).
fof(f1804,plain,
! [X0,X1] : multiplication(X0,one) = addition(multiplication(X0,domain(X1)),X0),
inference(paramodulation,[status(thm)],[f37,f135]) ).
fof(f1871,plain,
! [X0,X1] : X0 = addition(multiplication(X0,domain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f25,f1804]) ).
fof(f3511,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f222,f166]) ).
fof(f3528,plain,
! [X0] : multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f35,f166]) ).
fof(f3590,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f26,f3511]) ).
fof(f3617,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f97,f3528]) ).
fof(f3638,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f3617]) ).
fof(f3924,plain,
! [X0,X1] : multiplication(one,X0) = addition(multiplication(multiplication(one,domain(X1)),X0),X0),
inference(paramodulation,[status(thm)],[f1871,f172]) ).
fof(f4024,plain,
! [X0,X1] : X0 = addition(multiplication(multiplication(one,domain(X1)),X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f3924]) ).
fof(f4025,plain,
! [X0,X1] : X0 = addition(multiplication(one,multiplication(domain(X1),X0)),X0),
inference(forward_demodulation,[status(thm)],[f24,f4024]) ).
fof(f4026,plain,
! [X0,X1] : X0 = addition(multiplication(domain(X1),X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f4025]) ).
fof(f4435,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f3638,f28]) ).
fof(f17637,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = addition(multiplication(domain(X0),X1),X1),
inference(paramodulation,[status(thm)],[f39,f4435]) ).
fof(f17805,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f4026,f17637]) ).
fof(f18087,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),X0)) = multiplication(antidomain(X1),X0),
inference(paramodulation,[status(thm)],[f3590,f17805]) ).
fof(f26112,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f117,f18087]) ).
fof(f26210,plain,
zero != zero,
inference(backward_demodulation,[status(thm)],[f26112,f45]) ).
fof(f26312,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f26210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE081+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n017.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 22:37:26 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 20.28/3.08 % Refutation found
% 20.28/3.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.28/3.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.63/3.16 % Elapsed time: 2.701734 seconds
% 4.63/3.16 % CPU time: 20.903976 seconds
% 4.63/3.16 % Total memory used: 211.686 MB
% 4.63/3.16 % Net memory used: 208.225 MB
%------------------------------------------------------------------------------