%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE083+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 : n013.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 0.08s 0.45s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 32 ( 31 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
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(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [X0] : X0 = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [X0] : X0 = multiplication(domain(X0),X0),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
? [X0] : X0 != multiplication(domain(X0),X0),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
sK0_skl != multiplication(domain(sK0_skl),sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f46]) ).
fof(f48,plain,
sK0_skl != multiplication(domain(sK0_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f41,f40]) ).
fof(f72,plain,
! [X0] : one = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f49,f23]) ).
fof(f94,plain,
! [X0] : addition(zero,X0) = X0,
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f494,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f38,f31]) ).
fof(f528,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f94,f494]) ).
fof(f1918,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f72,f528]) ).
fof(f1949,plain,
sK0_skl != sK0_skl,
inference(backward_demodulation,[status(thm)],[f1950,f48]) ).
fof(f1950,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f29,f1918]) ).
fof(f1972,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1949]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE083+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n013.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 22:41:37 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.45 % Refutation found
% 0.08/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.47 % Elapsed time: 0.094473 seconds
% 0.08/0.47 % CPU time: 0.446842 seconds
% 0.08/0.47 % Total memory used: 74.140 MB
% 0.08/0.47 % Net memory used: 73.790 MB
%------------------------------------------------------------------------------