%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE072+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:57:55 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(negated_conjecture,[status(cth)],[f18]) ).
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(f36,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
? [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) != addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
domain(multiplication(addition(sK0_skl,sK1_skl),domain(sK2_skl))) != addition(domain(multiplication(sK0_skl,domain(sK2_skl))),domain(multiplication(sK1_skl,domain(sK2_skl)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl)],[f40]) ).
fof(f42,plain,
domain(multiplication(addition(sK0_skl,sK1_skl),domain(sK2_skl))) != addition(domain(multiplication(sK0_skl,domain(sK2_skl))),domain(multiplication(sK1_skl,domain(sK2_skl)))),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
domain(multiplication(addition(sK0_skl,sK1_skl),sK2_skl)) != addition(domain(multiplication(sK0_skl,domain(sK2_skl))),domain(multiplication(sK1_skl,domain(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f36,f42]) ).
fof(f44,plain,
domain(multiplication(addition(sK0_skl,sK1_skl),sK2_skl)) != domain(addition(multiplication(sK0_skl,domain(sK2_skl)),multiplication(sK1_skl,domain(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f39,f43]) ).
fof(f45,plain,
domain(multiplication(addition(sK0_skl,sK1_skl),sK2_skl)) != domain(multiplication(addition(sK0_skl,sK1_skl),domain(sK2_skl))),
inference(forward_demodulation,[status(thm)],[f28,f44]) ).
fof(f46,plain,
domain(multiplication(addition(sK0_skl,sK1_skl),sK2_skl)) != domain(multiplication(addition(sK0_skl,sK1_skl),sK2_skl)),
inference(forward_demodulation,[status(thm)],[f36,f45]) ).
fof(f47,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE072+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:42:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.048674 seconds
% 0.10/0.43 % CPU time: 0.138424 seconds
% 0.10/0.43 % Total memory used: 66.663 MB
% 0.10/0.43 % Net memory used: 66.268 MB
%------------------------------------------------------------------------------