%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE079+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 20.56s 3.04s
% Output : CNFRefutation 20.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 51 unt; 0 def)
% Number of atoms : 66 ( 65 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 : 86 ( 84 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
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(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
domain(zero) = zero,
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] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> multiplication(antidomain(X0),domain(X0)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> multiplication(antidomain(X0),domain(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(f24,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
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(f36,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f37,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
domain(zero) = zero,
inference(cnf_transformation,[status(thm)],[f16]) ).
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),domain(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),domain(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),domain(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),domain(sK0_skl)) != zero,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f868,plain,
! [X0,X1] : addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))) = multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f36,f35]) ).
fof(f891,plain,
! [X0,X1] : addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f36,f868]) ).
fof(f907,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f940,plain,
! [X0,X1] : multiplication(addition(one,domain(multiplication(X0,X1))),multiplication(X0,domain(X1))) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(backward_demodulation,[status(thm)],[f907,f891]) ).
fof(f965,plain,
! [X0,X1] : multiplication(one,multiplication(X0,domain(X1))) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f46,f940]) ).
fof(f966,plain,
! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f26,f965]) ).
fof(f1368,plain,
! [X0] : multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f35,f907]) ).
fof(f1422,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f46,f1368]) ).
fof(f1429,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f1422]) ).
fof(f1490,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f1429,f28]) ).
fof(f1491,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),X0) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f1429,f28]) ).
fof(f1502,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f1490]) ).
fof(f1510,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f46,f907]) ).
fof(f1521,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f26,f1510]) ).
fof(f2325,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f44,f24]) ).
fof(f2347,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f2325]) ).
fof(f6810,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = addition(X1,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f39,f1502]) ).
fof(f6890,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1521,f6810]) ).
fof(f9241,plain,
! [X0] : multiplication(one,X0) = addition(X0,multiplication(antidomain(X0),X0)),
inference(paramodulation,[status(thm)],[f43,f1491]) ).
fof(f9340,plain,
! [X0] : X0 = addition(X0,multiplication(antidomain(X0),X0)),
inference(forward_demodulation,[status(thm)],[f26,f9241]) ).
fof(f9578,plain,
! [X0] : multiplication(domain(X0),multiplication(antidomain(X0),X0)) = multiplication(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f9340,f6890]) ).
fof(f9690,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(forward_demodulation,[status(thm)],[f2347,f9578]) ).
fof(f10074,plain,
! [X0] : multiplication(antidomain(X0),domain(X0)) = multiplication(domain(zero),multiplication(antidomain(X0),domain(X0))),
inference(paramodulation,[status(thm)],[f9690,f966]) ).
fof(f10110,plain,
! [X0] : multiplication(antidomain(X0),domain(X0)) = multiplication(zero,multiplication(antidomain(X0),domain(X0))),
inference(forward_demodulation,[status(thm)],[f38,f10074]) ).
fof(f10111,plain,
zero != zero,
inference(backward_demodulation,[status(thm)],[f10113,f45]) ).
fof(f10113,plain,
! [X0] : multiplication(antidomain(X0),domain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f10110]) ).
fof(f10138,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f10111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE079+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 22:42:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 20.56/3.04 % Refutation found
% 20.56/3.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.56/3.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.76/3.13 % Elapsed time: 2.759065 seconds
% 3.76/3.13 % CPU time: 21.302619 seconds
% 3.76/3.13 % Total memory used: 234.994 MB
% 3.76/3.13 % Net memory used: 230.883 MB
%------------------------------------------------------------------------------