%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE098+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 12:57:58 PM UTC 2026
% Result : Theorem 118.14s 20.49s
% Output : CNFRefutation 111.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 94 ( 90 unt; 0 def)
% Number of atoms : 98 ( 97 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 115 ( 112 !; 3 ?)
% 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(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(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,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) = multiplication(domain(X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) = multiplication(domain(X2),X0) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f30,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0] : X0 = addition(X0,zero),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [X0] : X0 = multiplication(one,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] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
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] : antidomain(antidomain(X0)) = domain(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] : multiplication(domain(X0),antidomain(X1)) = domain_difference(X0,X1),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f54,plain,
! [X0,X1] : domain(multiplication(X0,domain(X1))) = forward_diamond(X0,X1),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
? [X0,X1,X2] :
( addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) != multiplication(domain(X2),X0)
& addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f59,plain,
( addition(multiplication(sK0_skl,domain(sK1_skl)),multiplication(domain(sK2_skl),sK0_skl)) != multiplication(domain(sK2_skl),sK0_skl)
& 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,
domain(sK2_skl) = addition(forward_diamond(sK0_skl,domain(sK1_skl)),domain(sK2_skl)),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
addition(multiplication(sK0_skl,domain(sK1_skl)),multiplication(domain(sK2_skl),sK0_skl)) != multiplication(domain(sK2_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,plain,
! [X0] : one = addition(domain(X0),antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f47,f46]) ).
fof(f68,plain,
domain(sK2_skl) = addition(domain(sK2_skl),forward_diamond(sK0_skl,domain(sK1_skl))),
inference(backward_demodulation,[status(thm)],[f29,f60]) ).
fof(f81,plain,
! [X0] : antidomain(domain(X0)) = domain(antidomain(X0)),
inference(paramodulation,[status(thm)],[f47,f47]) ).
fof(f82,plain,
! [X0] : c(X0) = domain(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f81]) ).
fof(f88,plain,
! [X0,X1] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(paramodulation,[status(thm)],[f34,f36]) ).
fof(f117,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f36,f29]) ).
fof(f122,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f125,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f36,f117]) ).
fof(f149,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f32,f30]) ).
fof(f226,plain,
! [X0] : one = addition(c(X0),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f82,f63]) ).
fof(f231,plain,
! [X0] : one = addition(c(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f47,f226]) ).
fof(f232,plain,
! [X0] : addition(domain(X0),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f29,f231]) ).
fof(f238,plain,
! [X0] : forward_diamond(one,X0) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f35,f54]) ).
fof(f242,plain,
! [X0,X1] : one = addition(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))),
inference(paramodulation,[status(thm)],[f54,f63]) ).
fof(f276,plain,
! [X0] : addition(domain(sK2_skl),X0) = addition(domain(sK2_skl),addition(forward_diamond(sK0_skl,domain(sK1_skl)),X0)),
inference(paramodulation,[status(thm)],[f68,f30]) ).
fof(f284,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(addition(X0,antidomain(X1)),X1),
inference(paramodulation,[status(thm)],[f44,f37]) ).
fof(f286,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f44,f36]) ).
fof(f287,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(paramodulation,[status(thm)],[f44,f36]) ).
fof(f289,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f31,f286]) ).
fof(f290,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[status(thm)],[f31,f284]) ).
fof(f295,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f122,f287]) ).
fof(f413,plain,
! [X0,X1] : domain_difference(antidomain(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f82,f53]) ).
fof(f416,plain,
! [X0,X1] : domain_difference(X0,antidomain(X1)) = multiplication(domain(X0),domain(X1)),
inference(paramodulation,[status(thm)],[f47,f53]) ).
fof(f833,plain,
! [X0] : addition(domain(X0),c(X0)) = addition(domain(X0),one),
inference(paramodulation,[status(thm)],[f232,f149]) ).
fof(f854,plain,
! [X0] : one = addition(domain(X0),one),
inference(forward_demodulation,[status(thm)],[f232,f833]) ).
fof(f855,plain,
! [X0] : one = addition(one,domain(X0)),
inference(forward_demodulation,[status(thm)],[f29,f854]) ).
fof(f4349,plain,
addition(domain(sK2_skl),antidomain(multiplication(sK0_skl,domain(domain(sK1_skl))))) = addition(domain(sK2_skl),one),
inference(paramodulation,[status(thm)],[f242,f276]) ).
fof(f4394,plain,
addition(domain(sK2_skl),antidomain(multiplication(sK0_skl,forward_diamond(one,sK1_skl)))) = addition(domain(sK2_skl),one),
inference(forward_demodulation,[status(thm)],[f238,f4349]) ).
fof(f4395,plain,
addition(domain(sK2_skl),antidomain(multiplication(sK0_skl,forward_diamond(one,sK1_skl)))) = addition(one,domain(sK2_skl)),
inference(forward_demodulation,[status(thm)],[f29,f4394]) ).
fof(f4396,plain,
addition(domain(sK2_skl),antidomain(multiplication(sK0_skl,forward_diamond(one,sK1_skl)))) = one,
inference(forward_demodulation,[status(thm)],[f855,f4395]) ).
fof(f5810,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),domain(X0)) = multiplication(antidomain(antidomain(X0)),one),
inference(paramodulation,[status(thm)],[f63,f289]) ).
fof(f5863,plain,
! [X0] : multiplication(domain(X0),domain(X0)) = multiplication(antidomain(antidomain(X0)),one),
inference(forward_demodulation,[status(thm)],[f47,f5810]) ).
fof(f5864,plain,
! [X0] : domain_difference(X0,antidomain(X0)) = multiplication(antidomain(antidomain(X0)),one),
inference(forward_demodulation,[status(thm)],[f416,f5863]) ).
fof(f5865,plain,
! [X0] : domain_difference(X0,antidomain(X0)) = antidomain(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f5864]) ).
fof(f5868,plain,
! [X0] : domain_difference(X0,antidomain(X0)) = domain(X0),
inference(forward_demodulation,[status(thm)],[f47,f5865]) ).
fof(f5919,plain,
! [X0] : domain_difference(domain(X0),c(X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f52,f5868]) ).
fof(f5923,plain,
! [X0] : forward_diamond(one,X0) = domain_difference(domain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f238,f5919]) ).
fof(f5935,plain,
multiplication(domain(sK2_skl),multiplication(sK0_skl,forward_diamond(one,sK1_skl))) = multiplication(one,multiplication(sK0_skl,forward_diamond(one,sK1_skl))),
inference(paramodulation,[status(thm)],[f4396,f290]) ).
fof(f5936,plain,
! [X0] : multiplication(domain(X0),X0) = multiplication(one,X0),
inference(paramodulation,[status(thm)],[f63,f290]) ).
fof(f5982,plain,
multiplication(sK0_skl,forward_diamond(one,sK1_skl)) = multiplication(domain(sK2_skl),multiplication(sK0_skl,forward_diamond(one,sK1_skl))),
inference(forward_demodulation,[status(thm)],[f35,f5935]) ).
fof(f6015,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f35,f5936]) ).
fof(f6163,plain,
! [X0] : multiplication(antidomain(domain(X0)),antidomain(X0)) = multiplication(antidomain(domain(X0)),one),
inference(paramodulation,[status(thm)],[f63,f295]) ).
fof(f6266,plain,
! [X0] : multiplication(c(X0),antidomain(X0)) = multiplication(antidomain(domain(X0)),one),
inference(forward_demodulation,[status(thm)],[f52,f6163]) ).
fof(f6267,plain,
! [X0] : domain_difference(antidomain(X0),X0) = multiplication(antidomain(domain(X0)),one),
inference(forward_demodulation,[status(thm)],[f413,f6266]) ).
fof(f6268,plain,
! [X0] : domain_difference(antidomain(X0),X0) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f6267]) ).
fof(f6269,plain,
! [X0] : c(X0) = domain_difference(antidomain(X0),X0),
inference(forward_demodulation,[status(thm)],[f52,f6268]) ).
fof(f6364,plain,
! [X0] : domain_difference(domain(X0),antidomain(X0)) = domain(X0),
inference(paramodulation,[status(thm)],[f416,f6015]) ).
fof(f6378,plain,
! [X0] : antidomain(X0) = domain_difference(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f6015,f53]) ).
fof(f6496,plain,
! [X0] : forward_diamond(one,X0) = domain_difference(domain(X0),antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f6624,f5923]) ).
fof(f6624,plain,
! [X0] : c(X0) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f6269,f6378]) ).
fof(f6813,plain,
multiplication(sK0_skl,forward_diamond(one,sK1_skl)) = multiplication(domain(sK2_skl),multiplication(sK0_skl,domain(sK1_skl))),
inference(backward_demodulation,[status(thm)],[f6836,f5982]) ).
fof(f6836,plain,
! [X0] : domain(X0) = forward_diamond(one,X0),
inference(forward_demodulation,[status(thm)],[f6364,f6496]) ).
fof(f6843,plain,
multiplication(domain(sK2_skl),multiplication(sK0_skl,domain(sK1_skl))) = multiplication(sK0_skl,domain(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f6836,f6813]) ).
fof(f6975,plain,
! [X0] : addition(multiplication(sK0_skl,domain(sK1_skl)),multiplication(domain(sK2_skl),X0)) = multiplication(domain(sK2_skl),addition(multiplication(sK0_skl,domain(sK1_skl)),X0)),
inference(paramodulation,[status(thm)],[f6843,f36]) ).
fof(f6977,plain,
multiplication(domain(sK2_skl),addition(multiplication(sK0_skl,domain(sK1_skl)),sK0_skl)) != multiplication(domain(sK2_skl),sK0_skl),
inference(backward_demodulation,[status(thm)],[f6975,f61]) ).
fof(f7005,plain,
multiplication(domain(sK2_skl),addition(sK0_skl,multiplication(sK0_skl,domain(sK1_skl)))) != multiplication(domain(sK2_skl),sK0_skl),
inference(forward_demodulation,[status(thm)],[f125,f6977]) ).
fof(f7006,plain,
multiplication(domain(sK2_skl),multiplication(sK0_skl,addition(one,domain(sK1_skl)))) != multiplication(domain(sK2_skl),sK0_skl),
inference(forward_demodulation,[status(thm)],[f88,f7005]) ).
fof(f7007,plain,
multiplication(domain(sK2_skl),multiplication(sK0_skl,one)) != multiplication(domain(sK2_skl),sK0_skl),
inference(forward_demodulation,[status(thm)],[f855,f7006]) ).
fof(f7008,plain,
multiplication(domain(sK2_skl),sK0_skl) != multiplication(domain(sK2_skl),sK0_skl),
inference(forward_demodulation,[status(thm)],[f34,f7007]) ).
fof(f7009,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f7008]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE098+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n016.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sun Sep 20 22:48:15 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.46 % Drodi V4.1.1
% 118.14/20.49 % Refutation found
% 118.14/20.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 118.14/20.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 45.77/20.68 % Elapsed time: 15.201906 seconds
% 45.77/20.68 % CPU time: 120.242071 seconds
% 45.77/20.68 % Total memory used: 641.643 MB
% 45.77/20.68 % Net memory used: 617.541 MB
%------------------------------------------------------------------------------