%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE078+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 : n016.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 35.76s 4.97s
% Output : CNFRefutation 29.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 98 ( 93 unt; 0 def)
% Number of atoms : 108 ( 107 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 : 6 ( 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 : 150 ( 148 !; 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(f3,axiom,
! [A] : addition(A,zero) = A,
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(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
domain(zero) = zero,
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 )
=> domain(antidomain(X0)) = antidomain(X0) ),
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 )
=> domain(antidomain(X0)) = antidomain(X0) ),
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(f22,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
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(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] :
( domain(antidomain(X0)) != antidomain(X0)
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( ? [X0] : domain(antidomain(X0)) != antidomain(X0)
& ! [X1] : multiplication(domain(X1),antidomain(X1)) = zero
& ! [X1] : addition(domain(X1),antidomain(X1)) = one ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( domain(antidomain(sK0_skl)) != antidomain(sK0_skl)
& ! [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,
domain(antidomain(sK0_skl)) != antidomain(sK0_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f49,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f92,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f109,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f92]) ).
fof(f133,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f44,f24]) ).
fof(f142,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f133]) ).
fof(f196,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f43,f109]) ).
fof(f214,plain,
! [X0] : addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f20,f196]) ).
fof(f215,plain,
! [X0] : addition(one,antidomain(X0)) = addition(domain(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f20,f214]) ).
fof(f216,plain,
! [X0] : addition(one,antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f43,f215]) ).
fof(f1197,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f1199,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = addition(zero,multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f44,f28]) ).
fof(f1205,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f24,f28]) ).
fof(f1242,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f49,f1199]) ).
fof(f1277,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f1283,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(f1292,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f1277]) ).
fof(f1296,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(domain(multiplication(X0,X1)),X0)),domain(X1)) = multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f1205,f1283]) ).
fof(f1297,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(domain(multiplication(X0,X1)),X0)),domain(X1)) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f36,f1296]) ).
fof(f1777,plain,
! [X0] : addition(domain(X0),antidomain(domain(X0))) = one,
inference(paramodulation,[status(thm)],[f1292,f43]) ).
fof(f2111,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f216,f1197]) ).
fof(f2112,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f46,f1197]) ).
fof(f2134,plain,
! [X0] : multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f35,f1197]) ).
fof(f2185,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f26,f2111]) ).
fof(f2187,plain,
! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(backward_demodulation,[status(thm)],[f2188,f1297]) ).
fof(f2188,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f26,f2112]) ).
fof(f2214,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f46,f2134]) ).
fof(f2220,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f2214]) ).
fof(f2307,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f2220,f28]) ).
fof(f2326,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f2307]) ).
fof(f4895,plain,
! [X0] : multiplication(one,antidomain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f1777,f1242]) ).
fof(f4957,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f4895]) ).
fof(f5982,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = addition(X1,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f39,f2326]) ).
fof(f6044,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f2188,f5982]) ).
fof(f6199,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),X0)) = multiplication(antidomain(X1),X0),
inference(paramodulation,[status(thm)],[f2185,f6044]) ).
fof(f8561,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f142,f6199]) ).
fof(f8724,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f8561,f27]) ).
fof(f8725,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f8561,f27]) ).
fof(f8770,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f22,f8724]) ).
fof(f8773,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f49,f8725]) ).
fof(f9522,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),one) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f43,f8770]) ).
fof(f9598,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f25,f9522]) ).
fof(f9659,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f43,f8773]) ).
fof(f9745,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f25,f9659]) ).
fof(f9789,plain,
! [X0] : antidomain(domain(X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f4957,f9745]) ).
fof(f10225,plain,
! [X0] : multiplication(domain(domain(X0)),antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f9598,f6199]) ).
fof(f10274,plain,
! [X0] : multiplication(domain(X0),antidomain(antidomain(X0))) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f1292,f10225]) ).
fof(f10275,plain,
! [X0] : multiplication(domain(X0),antidomain(antidomain(X0))) = antidomain(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f9598,f10274]) ).
fof(f15022,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f44,f2187]) ).
fof(f15187,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = multiplication(zero,multiplication(domain(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f38,f15022]) ).
fof(f15188,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f30,f15187]) ).
fof(f15381,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(antidomain(X0)),X1)) = addition(zero,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f15188,f27]) ).
fof(f15440,plain,
! [X0,X1] : multiplication(domain(X0),addition(domain(antidomain(X0)),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f49,f15381]) ).
fof(f21599,plain,
! [X0] : multiplication(domain(X0),one) = multiplication(domain(X0),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f43,f15440]) ).
fof(f21711,plain,
! [X0] : domain(X0) = multiplication(domain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f25,f21599]) ).
fof(f21901,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f10275,f21711]) ).
fof(f22207,plain,
! [X0] : domain(antidomain(X0)) = antidomain(domain(X0)),
inference(paramodulation,[status(thm)],[f21901,f21901]) ).
fof(f22283,plain,
antidomain(sK0_skl) != antidomain(sK0_skl),
inference(backward_demodulation,[status(thm)],[f22363,f45]) ).
fof(f22363,plain,
! [X0] : domain(antidomain(X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f9789,f22207]) ).
fof(f22433,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f22283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE078+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:47:09 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 35.76/4.97 % Refutation found
% 35.76/4.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 35.76/4.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.47/5.10 % Elapsed time: 4.748206 seconds
% 2.47/5.10 % CPU time: 36.954795 seconds
% 2.47/5.10 % Total memory used: 376.791 MB
% 2.47/5.10 % Net memory used: 363.371 MB
%------------------------------------------------------------------------------