%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE133+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 : n013.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 0.20s 5.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 62 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 68 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(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(f29,conjecture,
! [X0] :
( ( ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
& ! [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)))) )
=> ! [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ( ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
& ! [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)))) )
=> ! [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(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(f54,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[status(thm)],[f21]) ).
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(f63,plain,
? [X0] :
( ? [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) != forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))
& ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
& ! [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(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f64,plain,
( addition(forward_diamond(sK0_skl,domain(sK1_skl)),forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))))) != forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))))
& ! [X2] : forward_diamond(sK0_skl,forward_diamond(sK0_skl,domain(X2))) = forward_diamond(sK0_skl,domain(X2))
& ! [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)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X3,sK1_skl)],[f63]) ).
fof(f65,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(f66,plain,
! [X0] : forward_diamond(sK0_skl,forward_diamond(sK0_skl,domain(X0))) = forward_diamond(sK0_skl,domain(X0)),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
addition(forward_diamond(sK0_skl,domain(sK1_skl)),forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))))) != forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl)))),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f49,f48]) ).
fof(f80,plain,
! [X0,X1] : addition(domain(multiplication(X0,domain(X1))),forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,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,f65]) ).
fof(f84,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,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(forward_demodulation,[status(thm)],[f56,f80]) ).
fof(f85,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,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(forward_demodulation,[status(thm)],[f56,f84]) ).
fof(f86,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,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,f85]) ).
fof(f87,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(X0,X1),forward_diamond(sK0_skl,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,f86]) ).
fof(f113,plain,
! [X0] : addition(zero,X0) = X0,
inference(paramodulation,[status(thm)],[f31,f33]) ).
fof(f240,plain,
! [X0] : addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,domain(X0))))) = forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,forward_diamond(sK0_skl,domain(X0))))),
inference(paramodulation,[status(thm)],[f66,f87]) ).
fof(f278,plain,
! [X0] : addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,domain(X0))))) = forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f66,f240]) ).
fof(f575,plain,
antidomain(one) = zero,
inference(paramodulation,[status(thm)],[f36,f46]) ).
fof(f603,plain,
! [X0] : domain(antidomain(X0)) = antidomain(domain(X0)),
inference(paramodulation,[status(thm)],[f49,f49]) ).
fof(f604,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f575,f49]) ).
fof(f605,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f49,f46]) ).
fof(f607,plain,
! [X0] : domain(antidomain(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f54,f603]) ).
fof(f608,plain,
! [X0] : addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),domain_difference(forward_diamond(sK0_skl,domain(X0)),forward_diamond(sK0_skl,domain(X0))))) = forward_diamond(star(sK0_skl),zero),
inference(backward_demodulation,[status(thm)],[f610,f278]) ).
fof(f610,plain,
! [X0] : domain_difference(X0,X0) = zero,
inference(forward_demodulation,[status(thm)],[f55,f605]) ).
fof(f611,plain,
! [X0] : addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),zero)) = forward_diamond(star(sK0_skl),zero),
inference(forward_demodulation,[status(thm)],[f610,f608]) ).
fof(f1002,plain,
domain(zero) = c(one),
inference(paramodulation,[status(thm)],[f575,f607]) ).
fof(f1550,plain,
addition(domain(one),zero) = one,
inference(paramodulation,[status(thm)],[f575,f68]) ).
fof(f1564,plain,
one = antidomain(zero),
inference(backward_demodulation,[status(thm)],[f1567,f604]) ).
fof(f1567,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f33,f1550]) ).
fof(f1582,plain,
c(one) = antidomain(one),
inference(paramodulation,[status(thm)],[f1567,f54]) ).
fof(f1641,plain,
domain(zero) = antidomain(one),
inference(forward_demodulation,[status(thm)],[f1002,f1582]) ).
fof(f1656,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f575,f1641]) ).
fof(f1747,plain,
! [X0] : domain_difference(X0,zero) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f1564,f55]) ).
fof(f1752,plain,
! [X0] : domain_difference(X0,zero) = domain(X0),
inference(forward_demodulation,[status(thm)],[f36,f1747]) ).
fof(f2301,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f1656,f56]) ).
fof(f2409,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f40,f2301]) ).
fof(f2412,plain,
! [X0] : addition(forward_diamond(sK0_skl,domain(X0)),forward_diamond(star(sK0_skl),zero)) = zero,
inference(backward_demodulation,[status(thm)],[f2437,f611]) ).
fof(f2437,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f1656,f2409]) ).
fof(f2455,plain,
! [X0] : addition(forward_diamond(sK0_skl,domain(X0)),zero) = zero,
inference(forward_demodulation,[status(thm)],[f2437,f2412]) ).
fof(f2457,plain,
addition(forward_diamond(sK0_skl,domain(sK1_skl)),forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))))) != forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero)),
inference(backward_demodulation,[status(thm)],[f2487,f67]) ).
fof(f2487,plain,
! [X0] : forward_diamond(sK0_skl,domain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f33,f2455]) ).
fof(f2540,plain,
addition(zero,forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))))) != forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero)),
inference(forward_demodulation,[status(thm)],[f2487,f2457]) ).
fof(f2541,plain,
forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl)))) != forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero)),
inference(forward_demodulation,[status(thm)],[f113,f2540]) ).
fof(f2542,plain,
forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero)) != forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero)),
inference(forward_demodulation,[status(thm)],[f2487,f2541]) ).
fof(f2543,plain,
forward_diamond(star(sK0_skl),domain(domain(sK1_skl))) != forward_diamond(star(sK0_skl),domain_difference(domain(sK1_skl),zero)),
inference(forward_demodulation,[status(thm)],[f1752,f2542]) ).
fof(f2544,plain,
forward_diamond(star(sK0_skl),domain(domain(sK1_skl))) != forward_diamond(star(sK0_skl),domain(domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f1752,f2543]) ).
fof(f2545,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE133+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.42 % Computer : n013.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sun Sep 20 22:44:42 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.44 % Drodi V4.1.1
% 0.20/5.62 % Refutation found
% 0.20/5.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/5.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/5.67 % Elapsed time: 0.227215 seconds
% 0.20/5.67 % CPU time: 1.439881 seconds
% 0.20/5.67 % Total memory used: 90.381 MB
% 0.20/5.67 % Net memory used: 89.627 MB
%------------------------------------------------------------------------------