%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE082+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 : n012.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 12:57:56 PM UTC 2026
% Result : Theorem 10.69s 11.76s
% Output : CNFRefutation 10.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 82 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 135 ( 131 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
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(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(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] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
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(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(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(f39,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
? [X0,X1] :
( addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) != antidomain(multiplication(X0,domain(X1)))
& ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( ? [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) != antidomain(multiplication(X0,domain(X1)))
& ! [X2] : multiplication(domain(X2),antidomain(X2)) = zero
& ! [X2] : addition(domain(X2),antidomain(X2)) = one ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( addition(antidomain(multiplication(sK0_skl,sK1_skl)),antidomain(multiplication(sK0_skl,domain(sK1_skl)))) != antidomain(multiplication(sK0_skl,domain(sK1_skl)))
& ! [X2] : multiplication(domain(X2),antidomain(X2)) = zero
& ! [X2] : addition(domain(X2),antidomain(X2)) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_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,
addition(antidomain(multiplication(sK0_skl,sK1_skl)),antidomain(multiplication(sK0_skl,domain(sK1_skl)))) != antidomain(multiplication(sK0_skl,domain(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f47,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f20,f43]) ).
fof(f54,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f83,plain,
! [X0,X1] : addition(antidomain(X0),addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f47,f21]) ).
fof(f89,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f105,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f47,f89]) ).
fof(f120,plain,
! [X0] : addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f20,f105]) ).
fof(f121,plain,
! [X0] : addition(one,antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f47,f120]) ).
fof(f199,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f251,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f259,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f251]) ).
fof(f268,plain,
! [X0] : addition(antidomain(domain(X0)),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f259,f47]) ).
fof(f271,plain,
! [X0] : addition(domain(X0),antidomain(domain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f20,f268]) ).
fof(f310,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0)),
inference(paramodulation,[status(thm)],[f20,f39]) ).
fof(f325,plain,
! [X0,X1] : domain(addition(X0,X1)) = domain(addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f39,f310]) ).
fof(f346,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = addition(zero,multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f44,f28]) ).
fof(f348,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f371,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f54,f346]) ).
fof(f986,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(paramodulation,[status(thm)],[f25,f35]) ).
fof(f1007,plain,
one = multiplication(domain(one),one),
inference(forward_demodulation,[status(thm)],[f46,f986]) ).
fof(f1011,plain,
one = domain(one),
inference(forward_demodulation,[status(thm)],[f25,f1007]) ).
fof(f1044,plain,
! [X0] : domain(addition(one,X0)) = addition(one,domain(X0)),
inference(paramodulation,[status(thm)],[f1011,f39]) ).
fof(f1060,plain,
! [X0] : domain(addition(one,X0)) = one,
inference(forward_demodulation,[status(thm)],[f46,f1044]) ).
fof(f1157,plain,
! [X0,X1] : domain(multiplication(X0,addition(one,X1))) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f1060,f36]) ).
fof(f1184,plain,
! [X0,X1] : domain(multiplication(X0,addition(one,X1))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f25,f1157]) ).
fof(f1610,plain,
! [X0,X1] : addition(antidomain(X0),domain(addition(X0,X1))) = addition(one,domain(X1)),
inference(paramodulation,[status(thm)],[f39,f83]) ).
fof(f1654,plain,
! [X0,X1] : addition(antidomain(X0),domain(addition(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f46,f1610]) ).
fof(f1838,plain,
! [X0,X1] : addition(antidomain(X0),domain(addition(X1,X0))) = one,
inference(paramodulation,[status(thm)],[f325,f1654]) ).
fof(f3924,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f121,f199]) ).
fof(f3959,plain,
! [X0,X1] : domain(addition(X0,multiplication(X0,X1))) = domain(X0),
inference(paramodulation,[status(thm)],[f199,f1184]) ).
fof(f3989,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f25,f3924]) ).
fof(f4262,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f3959,f1838]) ).
fof(f4316,plain,
! [X0,X1] : addition(domain(X0),antidomain(multiplication(X0,X1))) = one,
inference(forward_demodulation,[status(thm)],[f20,f4262]) ).
fof(f6617,plain,
! [X0] : multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f35,f348]) ).
fof(f6726,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f46,f6617]) ).
fof(f6743,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f6726]) ).
fof(f19478,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = multiplication(antidomain(multiplication(X0,X1)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f4316,f371]) ).
fof(f19480,plain,
! [X0] : multiplication(one,antidomain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f271,f371]) ).
fof(f19600,plain,
! [X0,X1] : antidomain(X0) = multiplication(antidomain(multiplication(X0,X1)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f19478]) ).
fof(f19602,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f19480]) ).
fof(f19929,plain,
! [X0] : antidomain(domain(X0)) = addition(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f19602,f3989]) ).
fof(f20027,plain,
! [X0] : antidomain(domain(X0)) = addition(antidomain(X0),antidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f20,f19929]) ).
fof(f20081,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(X0),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f6743,f19600]) ).
fof(f22368,plain,
! [X0,X1] : antidomain(domain(multiplication(X0,domain(X1)))) = addition(antidomain(multiplication(X0,domain(X1))),antidomain(domain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f20027]) ).
fof(f22665,plain,
! [X0,X1] : antidomain(domain(multiplication(X0,X1))) = addition(antidomain(multiplication(X0,domain(X1))),antidomain(domain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f36,f22368]) ).
fof(f22666,plain,
! [X0,X1] : antidomain(domain(multiplication(X0,X1))) = addition(antidomain(domain(multiplication(X0,X1))),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f20,f22665]) ).
fof(f23011,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f20081,f3989]) ).
fof(f23261,plain,
! [X0,X1] : antidomain(domain(multiplication(X0,X1))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(backward_demodulation,[status(thm)],[f23493,f22666]) ).
fof(f23493,plain,
! [X0] : antidomain(X0) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f20027,f23011]) ).
fof(f23583,plain,
antidomain(multiplication(sK0_skl,sK1_skl)) != antidomain(multiplication(sK0_skl,domain(sK1_skl))),
inference(backward_demodulation,[status(thm)],[f23584,f45]) ).
fof(f23584,plain,
! [X0,X1] : antidomain(multiplication(X0,X1)) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f23493,f23261]) ).
fof(f23707,plain,
! [X0,X1] : antidomain(multiplication(X0,domain(X1))) = antidomain(domain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f23493]) ).
fof(f23939,plain,
antidomain(multiplication(sK0_skl,sK1_skl)) != antidomain(multiplication(sK0_skl,sK1_skl)),
inference(backward_demodulation,[status(thm)],[f23994,f23583]) ).
fof(f23994,plain,
! [X0,X1] : antidomain(multiplication(X0,domain(X1))) = antidomain(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23493,f23707]) ).
fof(f24082,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f23939]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE082+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/10.31 % Computer : n012.cluster.edu
% 0.03/10.31 % Model : x86_64 x86_64
% 0.03/10.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.31 % Memory : 8046.5625MB
% 0.03/10.31 % OS : Linux 6.8.0-71-generic
% 0.03/10.31 % CPULimit : 300
% 0.03/10.31 % WCLimit : 300
% 0.03/10.31 % DateTime : Sun Sep 20 22:42:19 UTC 2026
% 0.03/10.32 % CPUTime :
% 0.03/10.32 % Drodi V4.1.1
% 10.69/11.76 % Refutation found
% 10.69/11.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.69/11.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.22/11.81 % Elapsed time: 1.480041 seconds
% 1.22/11.81 % CPU time: 11.610361 seconds
% 1.22/11.81 % Total memory used: 273.735 MB
% 1.22/11.81 % Net memory used: 268.059 MB
%------------------------------------------------------------------------------