TSTP Solution File: KLE133+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE133+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:15:51 EDT 2023
% Result : Theorem 0.15s 0.34s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 58 unt; 0 def)
% Number of atoms : 70 ( 69 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 : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 68 (; 66 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [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))))
& ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) )
=> ! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [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))))
& ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) )
=> ! [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(esa)],[f1]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f40,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f46,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f48,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f49,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f55,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f56,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f23]) ).
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))))
& ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
& ? [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(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f64,plain,
( ! [X1] : addition(domain(X1),forward_diamond(star(sk0_0),domain_difference(domain(X1),forward_diamond(sk0_0,domain(X1))))) = forward_diamond(star(sk0_0),domain_difference(domain(X1),forward_diamond(sk0_0,domain(X1))))
& ! [X2] : forward_diamond(sk0_0,forward_diamond(sk0_0,domain(X2))) = forward_diamond(sk0_0,domain(X2))
& addition(forward_diamond(sk0_0,domain(sk0_1)),forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1)))) ),
inference(skolemization,[status(esa)],[f63]) ).
fof(f65,plain,
! [X0] : addition(domain(X0),forward_diamond(star(sk0_0),domain_difference(domain(X0),forward_diamond(sk0_0,domain(X0))))) = forward_diamond(star(sk0_0),domain_difference(domain(X0),forward_diamond(sk0_0,domain(X0)))),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [X0] : forward_diamond(sk0_0,forward_diamond(sk0_0,domain(X0))) = forward_diamond(sk0_0,domain(X0)),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f67,plain,
addition(forward_diamond(sk0_0,domain(sk0_1)),forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1)))),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f124,plain,
! [X0,X1] : addition(domain(multiplication(X0,domain(X1))),forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,domain(multiplication(X0,domain(X1)))))),
inference(paramodulation,[status(thm)],[f56,f65]) ).
fof(f125,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,domain(multiplication(X0,domain(X1)))))),
inference(forward_demodulation,[status(thm)],[f56,f124]) ).
fof(f126,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,domain(multiplication(X0,domain(X1)))))),
inference(forward_demodulation,[status(thm)],[f56,f125]) ).
fof(f127,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,domain(multiplication(X0,domain(X1)))))),
inference(forward_demodulation,[status(thm)],[f56,f126]) ).
fof(f128,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,forward_diamond(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f56,f127]) ).
fof(f389,plain,
! [X0] : addition(zero,X0) = X0,
inference(paramodulation,[status(thm)],[f31,f33]) ).
fof(f434,plain,
antidomain(one) = zero,
inference(paramodulation,[status(thm)],[f36,f46]) ).
fof(f441,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f434,f49]) ).
fof(f442,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f49,f46]) ).
fof(f443,plain,
! [X0] : domain_difference(X0,X0) = zero,
inference(forward_demodulation,[status(thm)],[f55,f442]) ).
fof(f608,plain,
! [X0] : addition(forward_diamond(sk0_0,domain(X0)),forward_diamond(star(sk0_0),domain_difference(forward_diamond(sk0_0,domain(X0)),forward_diamond(sk0_0,domain(X0))))) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(sk0_0,domain(X0)),forward_diamond(sk0_0,forward_diamond(sk0_0,domain(X0))))),
inference(paramodulation,[status(thm)],[f66,f128]) ).
fof(f609,plain,
! [X0] : addition(forward_diamond(sk0_0,domain(X0)),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(sk0_0,domain(X0)),forward_diamond(sk0_0,forward_diamond(sk0_0,domain(X0))))),
inference(forward_demodulation,[status(thm)],[f443,f608]) ).
fof(f610,plain,
! [X0] : addition(forward_diamond(sk0_0,domain(X0)),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(sk0_0,domain(X0)),forward_diamond(sk0_0,domain(X0)))),
inference(forward_demodulation,[status(thm)],[f66,f609]) ).
fof(f611,plain,
! [X0] : addition(forward_diamond(sk0_0,domain(X0)),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),zero),
inference(forward_demodulation,[status(thm)],[f443,f610]) ).
fof(f638,plain,
! [X0] : addition(forward_diamond(star(sk0_0),zero),forward_diamond(sk0_0,domain(X0))) = forward_diamond(star(sk0_0),zero),
inference(paramodulation,[status(thm)],[f31,f611]) ).
fof(f960,plain,
! [X0] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f31,f48]) ).
fof(f961,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f49,f960]) ).
fof(f964,plain,
addition(zero,domain(one)) = one,
inference(paramodulation,[status(thm)],[f434,f961]) ).
fof(f965,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f389,f964]) ).
fof(f966,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f441,f965]) ).
fof(f1089,plain,
domain(zero) = antidomain(one),
inference(paramodulation,[status(thm)],[f966,f49]) ).
fof(f1090,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f434,f1089]) ).
fof(f1092,plain,
! [X0] : domain_difference(X0,zero) = multiplication(domain(X0),one),
inference(paramodulation,[status(thm)],[f966,f55]) ).
fof(f1093,plain,
! [X0] : domain_difference(X0,zero) = domain(X0),
inference(forward_demodulation,[status(thm)],[f36,f1092]) ).
fof(f1171,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f1090,f56]) ).
fof(f1172,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f40,f1171]) ).
fof(f1173,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f1090,f1172]) ).
fof(f1344,plain,
! [X0] : addition(forward_diamond(star(sk0_0),zero),forward_diamond(sk0_0,domain(X0))) = zero,
inference(backward_demodulation,[status(thm)],[f1173,f638]) ).
fof(f1345,plain,
! [X0] : addition(zero,forward_diamond(sk0_0,domain(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f1173,f1344]) ).
fof(f1346,plain,
! [X0] : forward_diamond(sk0_0,domain(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f389,f1345]) ).
fof(f1484,plain,
addition(forward_diamond(sk0_0,domain(sk0_1)),forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
inference(backward_demodulation,[status(thm)],[f1346,f67]) ).
fof(f1485,plain,
addition(zero,forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
inference(forward_demodulation,[status(thm)],[f1346,f1484]) ).
fof(f1486,plain,
forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1)))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
inference(forward_demodulation,[status(thm)],[f389,f1485]) ).
fof(f1487,plain,
forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
inference(forward_demodulation,[status(thm)],[f1346,f1486]) ).
fof(f1488,plain,
forward_diamond(star(sk0_0),domain(domain(sk0_1))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
inference(forward_demodulation,[status(thm)],[f1093,f1487]) ).
fof(f1489,plain,
forward_diamond(star(sk0_0),domain(domain(sk0_1))) != forward_diamond(star(sk0_0),domain(domain(sk0_1))),
inference(forward_demodulation,[status(thm)],[f1093,f1488]) ).
fof(f1490,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f1489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : KLE133+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n026.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 12:02:43 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.15/0.34 % Refutation found
% 0.15/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.29/0.57 % Elapsed time: 0.055846 seconds
% 0.29/0.57 % CPU time: 0.127841 seconds
% 0.29/0.57 % Memory used: 12.769 MB
%------------------------------------------------------------------------------