%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE131+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 : n018.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 12:58:01 PM UTC 2026
% Result : Theorem 0.22s 5.54s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 47 unt; 0 def)
% Number of atoms : 69 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 6 |; 4 &)
% ( 1 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 57 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
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(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,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [X0] :
( divergence(X0) = zero
<= ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [X0] :
( divergence(X0) = zero
<= ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f40,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f42,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f43,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f49,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f55,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f56,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f60,plain,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f63,plain,
? [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
& divergence(X0) != zero ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f64,plain,
( ! [X1] : addition(domain(X1),forward_diamond(star(sK0_skl),domain_difference(domain(X1),forward_diamond(sK0_skl,domain(X1))))) = forward_diamond(star(sK0_skl),domain_difference(domain(X1),forward_diamond(sK0_skl,domain(X1))))
& divergence(sK0_skl) != zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f63]) ).
fof(f65,plain,
divergence(sK0_skl) != zero,
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0] : addition(domain(X0),forward_diamond(star(sK0_skl),domain_difference(domain(X0),forward_diamond(sK0_skl,domain(X0))))) = forward_diamond(star(sK0_skl),domain_difference(domain(X0),forward_diamond(sK0_skl,domain(X0)))),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f158,plain,
zero = antidomain(one),
inference(paramodulation,[status(thm)],[f46,f36]) ).
fof(f180,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f158,f49]) ).
fof(f182,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f49,f46]) ).
fof(f183,plain,
! [X0] : domain_difference(X0,X0) = zero,
inference(forward_demodulation,[status(thm)],[f55,f182]) ).
fof(f212,plain,
! [X0] : leq(domain(X0),forward_diamond(star(sK0_skl),domain_difference(domain(X0),forward_diamond(sK0_skl,domain(X0))))),
inference(resolution,[status(thm)],[f45,f66]) ).
fof(f346,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1))))))),
inference(paramodulation,[status(thm)],[f56,f212]) ).
fof(f353,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1))))))),
inference(forward_demodulation,[status(thm)],[f56,f346]) ).
fof(f354,plain,
! [X0,X1] : leq(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f56,f353]) ).
fof(f366,plain,
! [X0] : leq(divergence(X0),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0)))))),
inference(paramodulation,[status(thm)],[f60,f354]) ).
fof(f373,plain,
! [X0] : leq(divergence(X0),forward_diamond(star(sK0_skl),domain_difference(divergence(X0),forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0)))))),
inference(forward_demodulation,[status(thm)],[f60,f366]) ).
fof(f374,plain,
! [X0] : leq(divergence(X0),forward_diamond(star(sK0_skl),domain_difference(divergence(X0),forward_diamond(sK0_skl,divergence(X0))))),
inference(forward_demodulation,[status(thm)],[f60,f373]) ).
fof(f386,plain,
leq(divergence(sK0_skl),forward_diamond(star(sK0_skl),domain_difference(divergence(sK0_skl),divergence(sK0_skl)))),
inference(paramodulation,[status(thm)],[f60,f374]) ).
fof(f392,plain,
leq(divergence(sK0_skl),forward_diamond(star(sK0_skl),zero)),
inference(forward_demodulation,[status(thm)],[f183,f386]) ).
fof(f395,plain,
addition(divergence(sK0_skl),forward_diamond(star(sK0_skl),zero)) = forward_diamond(star(sK0_skl),zero),
inference(resolution,[status(thm)],[f392,f44]) ).
fof(f857,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f49,f48]) ).
fof(f862,plain,
addition(antidomain(zero),antidomain(one)) = one,
inference(paramodulation,[status(thm)],[f180,f857]) ).
fof(f880,plain,
addition(antidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f158,f862]) ).
fof(f881,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f33,f880]) ).
fof(f1016,plain,
domain(zero) = antidomain(one),
inference(paramodulation,[status(thm)],[f881,f49]) ).
fof(f1023,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f158,f1016]) ).
fof(f1114,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f1023,f56]) ).
fof(f1146,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f40,f1114]) ).
fof(f1147,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f1023,f1146]) ).
fof(f1320,plain,
addition(divergence(sK0_skl),forward_diamond(star(sK0_skl),zero)) = zero,
inference(backward_demodulation,[status(thm)],[f1147,f395]) ).
fof(f1335,plain,
addition(divergence(sK0_skl),zero) = zero,
inference(forward_demodulation,[status(thm)],[f1147,f1320]) ).
fof(f1336,plain,
divergence(sK0_skl) = zero,
inference(forward_demodulation,[status(thm)],[f33,f1335]) ).
fof(f1337,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1336,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE131+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n018.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Sun Sep 20 22:47:18 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.46 % Drodi V4.1.1
% 0.22/5.54 % Refutation found
% 0.22/5.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/5.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/5.57 % Elapsed time: 0.108904 seconds
% 0.22/5.57 % CPU time: 0.525725 seconds
% 0.22/5.57 % Total memory used: 76.510 MB
% 0.22/5.57 % Net memory used: 76.270 MB
%------------------------------------------------------------------------------