%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE088+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 : n017.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 78.69s 10.64s
% Output : CNFRefutation 74.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 61 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 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 : 71 ( 69 !; 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(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(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
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,conjecture,
! [X0,X1] :
( multiplication(domain(X0),X1) = zero
=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [X0,X1] :
( multiplication(domain(X0),X1) = zero
=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [X0] : X0 = multiplication(one,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
? [X0,X1] :
( addition(domain(X0),antidomain(X1)) != antidomain(X1)
& multiplication(domain(X0),X1) = zero ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
( addition(domain(sK0_skl),antidomain(sK1_skl)) != antidomain(sK1_skl)
& multiplication(domain(sK0_skl),sK1_skl) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f46]) ).
fof(f48,plain,
multiplication(domain(sK0_skl),sK1_skl) = zero,
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
addition(domain(sK0_skl),antidomain(sK1_skl)) != antidomain(sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0] : one = addition(domain(X0),antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f41,f40]) ).
fof(f51,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f41,f39]) ).
fof(f52,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f41,f51]) ).
fof(f54,plain,
addition(antidomain(sK1_skl),domain(sK0_skl)) != antidomain(sK1_skl),
inference(backward_demodulation,[status(thm)],[f23,f49]) ).
fof(f56,plain,
! [X0] : one = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f23,f50]) ).
fof(f62,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f24]) ).
fof(f73,plain,
antidomain(one) = zero,
inference(paramodulation,[status(thm)],[f38,f28]) ).
fof(f87,plain,
addition(antidomain(zero),antidomain(multiplication(domain(sK0_skl),domain(sK1_skl)))) = antidomain(multiplication(domain(sK0_skl),domain(sK1_skl))),
inference(paramodulation,[status(thm)],[f48,f52]) ).
fof(f169,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f30]) ).
fof(f179,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f235,plain,
antidomain(zero) = domain(one),
inference(paramodulation,[status(thm)],[f73,f41]) ).
fof(f250,plain,
one = addition(zero,domain(one)),
inference(paramodulation,[status(thm)],[f73,f56]) ).
fof(f257,plain,
antidomain(zero) = one,
inference(backward_demodulation,[status(thm)],[f258,f235]) ).
fof(f258,plain,
one = domain(one),
inference(forward_demodulation,[status(thm)],[f179,f250]) ).
fof(f260,plain,
addition(one,antidomain(multiplication(domain(sK0_skl),domain(sK1_skl)))) = antidomain(multiplication(domain(sK0_skl),domain(sK1_skl))),
inference(backward_demodulation,[status(thm)],[f257,f87]) ).
fof(f338,plain,
! [X0,X1] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f471,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = addition(antidomain(X0),one),
inference(paramodulation,[status(thm)],[f56,f62]) ).
fof(f476,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f23,f62]) ).
fof(f489,plain,
! [X0] : one = addition(antidomain(X0),one),
inference(forward_demodulation,[status(thm)],[f56,f471]) ).
fof(f490,plain,
one = antidomain(multiplication(domain(sK0_skl),domain(sK1_skl))),
inference(backward_demodulation,[status(thm)],[f497,f260]) ).
fof(f497,plain,
! [X0] : one = addition(one,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f23,f489]) ).
fof(f1120,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = addition(domain(X0),one),
inference(paramodulation,[status(thm)],[f56,f476]) ).
fof(f1144,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = addition(domain(X0),one),
inference(forward_demodulation,[status(thm)],[f23,f1120]) ).
fof(f1145,plain,
! [X0] : one = addition(domain(X0),one),
inference(forward_demodulation,[status(thm)],[f56,f1144]) ).
fof(f1146,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f23,f1145]) ).
fof(f3239,plain,
zero = multiplication(one,multiplication(domain(sK0_skl),domain(sK1_skl))),
inference(paramodulation,[status(thm)],[f490,f38]) ).
fof(f3265,plain,
zero = multiplication(domain(sK0_skl),domain(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f29,f3239]) ).
fof(f4618,plain,
! [X0] : multiplication(domain(sK0_skl),addition(X0,domain(sK1_skl))) = addition(zero,multiplication(domain(sK0_skl),X0)),
inference(paramodulation,[status(thm)],[f3265,f169]) ).
fof(f4642,plain,
! [X0] : multiplication(domain(sK0_skl),X0) = multiplication(domain(sK0_skl),addition(X0,domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f179,f4618]) ).
fof(f9626,plain,
multiplication(domain(sK0_skl),antidomain(sK1_skl)) = multiplication(domain(sK0_skl),one),
inference(paramodulation,[status(thm)],[f56,f4642]) ).
fof(f9705,plain,
multiplication(domain(sK0_skl),antidomain(sK1_skl)) = domain(sK0_skl),
inference(forward_demodulation,[status(thm)],[f28,f9626]) ).
fof(f9735,plain,
addition(antidomain(sK1_skl),domain(sK0_skl)) = multiplication(addition(one,domain(sK0_skl)),antidomain(sK1_skl)),
inference(paramodulation,[status(thm)],[f9705,f338]) ).
fof(f9766,plain,
addition(antidomain(sK1_skl),domain(sK0_skl)) = multiplication(one,antidomain(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f1146,f9735]) ).
fof(f9767,plain,
addition(antidomain(sK1_skl),domain(sK0_skl)) = antidomain(sK1_skl),
inference(forward_demodulation,[status(thm)],[f29,f9766]) ).
fof(f9768,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f9767,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 20 22:37:42 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 78.69/10.64 % Refutation found
% 78.69/10.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 78.69/10.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.50/11.30 % Elapsed time: 10.837483 seconds
% 5.50/11.30 % CPU time: 81.818597 seconds
% 5.50/11.30 % Total memory used: 482.355 MB
% 5.50/11.30 % Net memory used: 445.363 MB
%------------------------------------------------------------------------------