%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE099+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 : 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 12:57:58 PM UTC 2026
% Result : Theorem 33.97s 4.81s
% Output : CNFRefutation 31.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 73 unt; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 95 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = 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(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
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] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f47,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f52,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f53,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f54,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
? [X0,X1,X2] :
( multiplication(antidomain(X2),multiplication(X0,domain(X1))) != zero
& addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f59,plain,
( multiplication(antidomain(sK2_skl),multiplication(sK0_skl,domain(sK1_skl))) != zero
& addition(forward_diamond(sK0_skl,domain(sK1_skl)),domain(sK2_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)],[f58]) ).
fof(f60,plain,
addition(forward_diamond(sK0_skl,domain(sK1_skl)),domain(sK2_skl)) = domain(sK2_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
multiplication(antidomain(sK2_skl),multiplication(sK0_skl,domain(sK1_skl))) != zero,
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f29,f46]) ).
fof(f63,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f47,f62]) ).
fof(f68,plain,
addition(domain(sK2_skl),forward_diamond(sK0_skl,domain(sK1_skl))) = domain(sK2_skl),
inference(forward_demodulation,[status(thm)],[f29,f60]) ).
fof(f69,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f29,f63]) ).
fof(f75,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f31,f29]) ).
fof(f95,plain,
! [X0] : domain(antidomain(X0)) = antidomain(domain(X0)),
inference(paramodulation,[status(thm)],[f47,f47]) ).
fof(f97,plain,
! [X0] : domain(antidomain(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f52,f95]) ).
fof(f99,plain,
! [X0] : domain(domain(X0)) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f47,f97]) ).
fof(f226,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f44,f36]) ).
fof(f247,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f75,f226]) ).
fof(f277,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f44,f37]) ).
fof(f297,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f277]) ).
fof(f657,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f69,f297]) ).
fof(f676,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f35,f657]) ).
fof(f1191,plain,
! [X0] : forward_diamond(one,X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f35,f54]) ).
fof(f1199,plain,
! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(forward_diamond(X0,X1),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f54,f676]) ).
fof(f1215,plain,
! [X0] : forward_diamond(one,X0) = c(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f99,f1191]) ).
fof(f1282,plain,
! [X0] : domain_difference(antidomain(X0),X0) = antidomain(X0),
inference(paramodulation,[status(thm)],[f676,f53]) ).
fof(f1286,plain,
! [X0,X1] : domain_difference(antidomain(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f97,f53]) ).
fof(f6234,plain,
multiplication(antidomain(domain(sK2_skl)),domain(sK2_skl)) = multiplication(antidomain(domain(sK2_skl)),forward_diamond(sK0_skl,domain(sK1_skl))),
inference(paramodulation,[status(thm)],[f68,f247]) ).
fof(f6236,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f69,f247]) ).
fof(f6307,plain,
zero = multiplication(antidomain(domain(sK2_skl)),forward_diamond(sK0_skl,domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f44,f6234]) ).
fof(f6308,plain,
zero = multiplication(c(sK2_skl),forward_diamond(sK0_skl,domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f52,f6307]) ).
fof(f6311,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f6236]) ).
fof(f6312,plain,
! [X0] : c(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f6311]) ).
fof(f6313,plain,
! [X0] : c(X0) = multiplication(c(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f6312]) ).
fof(f6314,plain,
! [X0] : c(X0) = domain_difference(antidomain(X0),X0),
inference(forward_demodulation,[status(thm)],[f1286,f6313]) ).
fof(f6316,plain,
! [X0] : c(X0) = c(domain(X0)),
inference(backward_demodulation,[status(thm)],[f6418,f52]) ).
fof(f6319,plain,
! [X0] : domain(X0) = c(antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f6418,f47]) ).
fof(f6320,plain,
multiplication(c(sK2_skl),multiplication(sK0_skl,domain(sK1_skl))) != zero,
inference(backward_demodulation,[status(thm)],[f6418,f61]) ).
fof(f6403,plain,
! [X0] : forward_diamond(one,X0) = c(c(X0)),
inference(backward_demodulation,[status(thm)],[f6418,f1215]) ).
fof(f6418,plain,
! [X0] : c(X0) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f1282,f6314]) ).
fof(f6479,plain,
! [X0] : domain(X0) = forward_diamond(one,X0),
inference(forward_demodulation,[status(thm)],[f1215,f6319]) ).
fof(f6561,plain,
! [X0] : domain(X0) = c(c(X0)),
inference(forward_demodulation,[status(thm)],[f6479,f6403]) ).
fof(f6615,plain,
! [X0] : domain(domain(X0)) = c(c(X0)),
inference(paramodulation,[status(thm)],[f6316,f6561]) ).
fof(f6636,plain,
! [X0] : domain(domain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f6561,f6615]) ).
fof(f6656,plain,
! [X0,X1] : forward_diamond(X0,domain(X1)) = domain(multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f6636,f54]) ).
fof(f6676,plain,
zero = multiplication(c(sK2_skl),forward_diamond(sK0_skl,sK1_skl)),
inference(backward_demodulation,[status(thm)],[f6693,f6308]) ).
fof(f6693,plain,
! [X0,X1] : forward_diamond(X0,domain(X1)) = forward_diamond(X0,X1),
inference(forward_demodulation,[status(thm)],[f54,f6656]) ).
fof(f7054,plain,
! [X0] : multiplication(c(sK2_skl),multiplication(forward_diamond(sK0_skl,sK1_skl),X0)) = multiplication(zero,X0),
inference(paramodulation,[status(thm)],[f6676,f33]) ).
fof(f7060,plain,
! [X0] : multiplication(c(sK2_skl),multiplication(forward_diamond(sK0_skl,sK1_skl),X0)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f7054]) ).
fof(f15431,plain,
multiplication(c(sK2_skl),multiplication(sK0_skl,domain(sK1_skl))) = zero,
inference(paramodulation,[status(thm)],[f1199,f7060]) ).
fof(f15526,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f15431,f6320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE099+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 22:43:00 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 33.97/4.81 % Refutation found
% 33.97/4.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 33.97/4.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 31.59/4.89 % Elapsed time: 4.502302 seconds
% 31.59/4.89 % CPU time: 35.421118 seconds
% 31.59/4.89 % Total memory used: 420.013 MB
% 31.59/4.89 % Net memory used: 407.432 MB
%------------------------------------------------------------------------------