TSTP Solution File: NUN058+2 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUN058+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 : Tue Apr 30 20:36:18 EDT 2024
% Result : Theorem 42.99s 5.75s
% Output : CNFRefutation 43.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of formulae : 172 ( 85 unt; 0 def)
% Number of atoms : 430 ( 106 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 482 ( 224 ~; 170 |; 83 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 518 ( 458 !; 60 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ r2(X11,X12)
& X12 != Y21 )
| ( r2(X11,X12)
& X12 = Y21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ r3(X13,X14,X15)
& X15 != Y22 )
| ( r3(X13,X14,X15)
& X15 = Y22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ r4(X16,X17,X18)
& X18 != Y23 )
| ( r4(X16,X17,X18)
& X18 = Y23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) )
& Y5 = Y4 )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) )
& Y3 = Y2 )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) )
& Y9 = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& Y8 = Y18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X6] :
( ? [Y19] :
( r1(Y19)
& X6 = Y19 )
| ? [Y1,Y11] :
( r2(Y1,Y11)
& X6 = Y11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
( ? [Y2,Y4] :
( ? [Y6] :
( ? [Y10] :
( r4(Y10,Y2,Y6)
& ? [Y12] :
( r2(Y12,Y10)
& ? [Y14] :
( r1(Y14)
& r2(Y14,Y12) ) ) )
& Y6 = Y1 )
& ? [Y8] :
( r3(Y2,Y4,Y8)
& Y8 = Y1 ) )
& ? [Y3,Y5] :
( Y5 = Y1
& ? [Y7] :
( r3(Y3,Y7,Y5)
& ? [Y9] :
( r2(Y9,Y7)
& ? [Y11] :
( r2(Y11,Y9)
& ? [Y13] :
( r2(Y13,Y11)
& ? [Y15] :
( r1(Y15)
& r2(Y15,Y13) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ? [Y2,Y4] :
( ? [Y6] :
( ? [Y10] :
( r4(Y10,Y2,Y6)
& ? [Y12] :
( r2(Y12,Y10)
& ? [Y14] :
( r1(Y14)
& r2(Y14,Y12) ) ) )
& Y6 = Y1 )
& ? [Y8] :
( r3(Y2,Y4,Y8)
& Y8 = Y1 ) )
& ? [Y3,Y5] :
( Y5 = Y1
& ? [Y7] :
( r3(Y3,Y7,Y5)
& ? [Y9] :
( r2(Y9,Y7)
& ? [Y11] :
( r2(Y11,Y9)
& ? [Y13] :
( r2(Y13,Y11)
& ? [Y15] :
( r1(Y15)
& r2(Y15,Y13) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [Y24,X19] :
( pd0_0(X19,Y24)
=> ( ~ r1(X19)
& X19 != Y24 ) ),
introduced(predicate_definition,[f1]) ).
fof(f15,plain,
? [Y24] :
! [X19] :
( pd0_0(X19,Y24)
| ( r1(X19)
& X19 = Y24 ) ),
inference(formula_renaming,[status(thm)],[f1,f14]) ).
fof(f16,plain,
! [X19] :
( pd0_0(X19,sk0_0)
| ( r1(X19)
& X19 = sk0_0 ) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0] :
( pd0_0(X0,sk0_0)
| r1(X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0] :
( pd0_0(X0,sk0_0)
| X0 = sk0_0 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f19,plain,
! [X11,Y21,X12] :
( pd0_1(X12,Y21,X11)
=> ( ~ r2(X11,X12)
& X12 != Y21 ) ),
introduced(predicate_definition,[f2]) ).
fof(f20,plain,
! [X11] :
? [Y21] :
! [X12] :
( pd0_1(X12,Y21,X11)
| ( r2(X11,X12)
& X12 = Y21 ) ),
inference(formula_renaming,[status(thm)],[f2,f19]) ).
fof(f21,plain,
! [X11,X12] :
( pd0_1(X12,sk0_1(X11),X11)
| ( r2(X11,X12)
& X12 = sk0_1(X11) ) ),
inference(skolemization,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( pd0_1(X0,sk0_1(X1),X1)
| r2(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( pd0_1(X0,sk0_1(X1),X1)
| X0 = sk0_1(X1) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f24,plain,
! [X13,X14,Y22,X15] :
( pd0_2(X15,Y22,X14,X13)
=> ( ~ r3(X13,X14,X15)
& X15 != Y22 ) ),
introduced(predicate_definition,[f3]) ).
fof(f25,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( pd0_2(X15,Y22,X14,X13)
| ( r3(X13,X14,X15)
& X15 = Y22 ) ),
inference(formula_renaming,[status(thm)],[f3,f24]) ).
fof(f26,plain,
! [X13,X14,X15] :
( pd0_2(X15,sk0_2(X14,X13),X14,X13)
| ( r3(X13,X14,X15)
& X15 = sk0_2(X14,X13) ) ),
inference(skolemization,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0,X1,X2] :
( pd0_2(X0,sk0_2(X1,X2),X1,X2)
| X0 = sk0_2(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f29,plain,
! [X16,X17,Y23,X18] :
( pd0_3(X18,Y23,X17,X16)
=> ( ~ r4(X16,X17,X18)
& X18 != Y23 ) ),
introduced(predicate_definition,[f4]) ).
fof(f30,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( pd0_3(X18,Y23,X17,X16)
| ( r4(X16,X17,X18)
& X18 = Y23 ) ),
inference(formula_renaming,[status(thm)],[f4,f29]) ).
fof(f31,plain,
! [X16,X17,X18] :
( pd0_3(X18,sk0_3(X17,X16),X17,X16)
| ( r4(X16,X17,X18)
& X18 = sk0_3(X17,X16) ) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f33,plain,
! [X0,X1,X2] :
( pd0_3(X0,sk0_3(X1,X2),X1,X2)
| X0 = sk0_3(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X1,X8] :
( r2(X8,sk0_6(X8,X1))
& r3(X1,sk0_6(X8,X1),sk0_5(X8,X1))
& sk0_5(X8,X1) = sk0_4(X8,X1)
& r2(sk0_7(X8,X1),sk0_4(X8,X1))
& r3(X1,X8,sk0_7(X8,X1)) ),
inference(skolemization,[status(esa)],[f5]) ).
fof(f35,plain,
! [X0,X1] : r2(X0,sk0_6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
! [X0,X1] : r3(X0,sk0_6(X1,X0),sk0_5(X1,X0)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f37,plain,
! [X0,X1] : sk0_5(X0,X1) = sk0_4(X0,X1),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f38,plain,
! [X0,X1] : r2(sk0_7(X0,X1),sk0_4(X0,X1)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f39,plain,
! [X0,X1] : r3(X0,X1,sk0_7(X1,X0)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f40,plain,
! [X2,X9] :
( r2(X9,sk0_10(X9,X2))
& r4(X2,sk0_10(X9,X2),sk0_9(X9,X2))
& sk0_9(X9,X2) = sk0_8(X9,X2)
& r3(sk0_11(X9,X2),X2,sk0_8(X9,X2))
& r4(X2,X9,sk0_11(X9,X2)) ),
inference(skolemization,[status(esa)],[f6]) ).
fof(f41,plain,
! [X0,X1] : r2(X0,sk0_10(X0,X1)),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [X0,X1] : r4(X0,sk0_10(X1,X0),sk0_9(X1,X0)),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f43,plain,
! [X0,X1] : sk0_9(X0,X1) = sk0_8(X0,X1),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f44,plain,
! [X0,X1] : r3(sk0_11(X0,X1),X1,sk0_8(X0,X1)),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f45,plain,
! [X0,X1] : r4(X0,X1,sk0_11(X1,X0)),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f47,plain,
! [X4] :
( r1(sk0_13(X4))
& r3(X4,sk0_13(X4),sk0_12(X4))
& sk0_12(X4) = X4 ),
inference(skolemization,[status(esa)],[f8]) ).
fof(f48,plain,
! [X0] : r1(sk0_13(X0)),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0] : r3(X0,sk0_13(X0),sk0_12(X0)),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
! [X0] : sk0_12(X0) = X0,
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f51,plain,
! [X5] :
( r1(sk0_15(X5))
& r4(X5,sk0_15(X5),sk0_14(X5))
& r1(sk0_16(X5))
& sk0_14(X5) = sk0_16(X5) ),
inference(skolemization,[status(esa)],[f9]) ).
fof(f52,plain,
! [X0] : r1(sk0_15(X0)),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f53,plain,
! [X0] : r4(X0,sk0_15(X0),sk0_14(X0)),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f54,plain,
! [X0] : r1(sk0_16(X0)),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f55,plain,
! [X0] : sk0_14(X0) = sk0_16(X0),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f56,plain,
! [X6,Y19] :
( pd0_4(Y19,X6)
=> ( r1(Y19)
& X6 = Y19 ) ),
introduced(predicate_definition,[f10]) ).
fof(f57,plain,
! [X6] :
( ? [Y19] : pd0_4(Y19,X6)
| ? [Y1,Y11] :
( r2(Y1,Y11)
& X6 = Y11 ) ),
inference(formula_renaming,[status(thm)],[f10,f56]) ).
fof(f58,plain,
! [X6] :
( ? [Y19] : pd0_4(Y19,X6)
| ? [Y11] :
( ? [Y1] : r2(Y1,Y11)
& X6 = Y11 ) ),
inference(miniscoping,[status(esa)],[f57]) ).
fof(f59,plain,
! [X6] :
( pd0_4(sk0_17(X6),X6)
| ( r2(sk0_19(X6),sk0_18(X6))
& X6 = sk0_18(X6) ) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f61,plain,
! [X0] :
( pd0_4(sk0_17(X0),X0)
| X0 = sk0_18(X0) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f62,plain,
! [Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ! [X7] : ~ r2(X7,Y10) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| X0 != X1
| ~ r2(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f64,plain,
! [Y1] :
( ! [Y2,Y4] :
( ! [Y6] :
( ! [Y10] :
( ~ r4(Y10,Y2,Y6)
| ! [Y12] :
( ~ r2(Y12,Y10)
| ! [Y14] :
( ~ r1(Y14)
| ~ r2(Y14,Y12) ) ) )
| Y6 != Y1 )
| ! [Y8] :
( ~ r3(Y2,Y4,Y8)
| Y8 != Y1 ) )
| ! [Y3,Y5] :
( Y5 != Y1
| ! [Y7] :
( ~ r3(Y3,Y7,Y5)
| ! [Y9] :
( ~ r2(Y9,Y7)
| ! [Y11] :
( ~ r2(Y11,Y9)
| ! [Y13] :
( ~ r2(Y13,Y11)
| ! [Y15] :
( ~ r1(Y15)
| ~ r2(Y15,Y13) ) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f65,plain,
! [Y1] :
( ! [Y2] :
( ! [Y6] :
( ! [Y10] :
( ~ r4(Y10,Y2,Y6)
| ! [Y12] :
( ~ r2(Y12,Y10)
| ! [Y14] :
( ~ r1(Y14)
| ~ r2(Y14,Y12) ) ) )
| Y6 != Y1 )
| ! [Y8] :
( ! [Y4] : ~ r3(Y2,Y4,Y8)
| Y8 != Y1 ) )
| ! [Y5] :
( Y5 != Y1
| ! [Y7] :
( ! [Y3] : ~ r3(Y3,Y7,Y5)
| ! [Y9] :
( ~ r2(Y9,Y7)
| ! [Y11] :
( ~ r2(Y11,Y9)
| ! [Y13] :
( ~ r2(Y13,Y11)
| ! [Y15] :
( ~ r1(Y15)
| ~ r2(Y15,Y13) ) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f64]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14] :
( ~ r4(X0,X1,X2)
| ~ r2(X3,X0)
| ~ r1(X4)
| ~ r2(X4,X3)
| X2 != X5
| ~ r3(X1,X6,X7)
| X7 != X5
| X8 != X5
| ~ r3(X9,X10,X8)
| ~ r2(X11,X10)
| ~ r2(X12,X11)
| ~ r2(X13,X12)
| ~ r1(X14)
| ~ r2(X14,X13) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [Y24,X19] :
( ~ pd0_0(X19,Y24)
| ( ~ r1(X19)
& X19 != Y24 ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f68,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f70,plain,
! [X11,Y21,X12] :
( ~ pd0_1(X12,Y21,X11)
| ( ~ r2(X11,X12)
& X12 != Y21 ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| ~ r2(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
! [X13,X14,Y22,X15] :
( ~ pd0_2(X15,Y22,X14,X13)
| ( ~ r3(X13,X14,X15)
& X15 != Y22 ) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( ~ pd0_2(X0,X1,X2,X3)
| ~ r3(X3,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f73]) ).
fof(f76,plain,
! [X16,X17,Y23,X18] :
( ~ pd0_3(X18,Y23,X17,X16)
| ( ~ r4(X16,X17,X18)
& X18 != Y23 ) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ~ pd0_3(X0,X1,X2,X3)
| ~ r4(X3,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f79,plain,
! [X6,Y19] :
( ~ pd0_4(Y19,X6)
| ( r1(Y19)
& X6 = Y19 ) ),
inference(pre_NNF_transformation,[status(esa)],[f56]) ).
fof(f80,plain,
! [X0,X1] :
( ~ pd0_4(X0,X1)
| r1(X0) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ pd0_4(X0,X1)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f83,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ r2(X1,X0) ),
inference(destructive_equality_resolution,[status(esa)],[f63]) ).
fof(f84,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ r4(X0,X1,X2)
| ~ r2(X3,X0)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X1,X5,X2)
| ~ r3(X6,X7,X2)
| ~ r2(X8,X7)
| ~ r2(X9,X8)
| ~ r2(X10,X9)
| ~ r1(X11)
| ~ r2(X11,X10) ),
inference(destructive_equality_resolution,[status(esa)],[f66]) ).
fof(f85,plain,
! [X0] : ~ pd0_0(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f69]) ).
fof(f86,plain,
! [X0,X1] : ~ pd0_1(X0,X0,X1),
inference(destructive_equality_resolution,[status(esa)],[f72]) ).
fof(f89,plain,
r1(sk0_0),
inference(resolution,[status(thm)],[f17,f85]) ).
fof(f90,plain,
! [X0] : ~ r2(X0,sk0_0),
inference(resolution,[status(thm)],[f89,f83]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ r4(X0,X1,X2)
| ~ r2(X3,X0)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X1,X5,X2)
| ~ r3(X6,X7,X2)
| ~ r2(X8,X7)
| ~ r2(X9,X8)
| ~ r2(X10,X9)
| ~ r2(sk0_0,X10) ),
inference(resolution,[status(thm)],[f89,f84]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ pd0_4(X0,X1)
| ~ pd0_0(X0,X2) ),
inference(resolution,[status(thm)],[f80,f68]) ).
fof(f111,plain,
! [X0] : r3(X0,sk0_13(X0),X0),
inference(forward_demodulation,[status(thm)],[f50,f49]) ).
fof(f112,plain,
! [X0,X1,X2] : ~ pd0_1(sk0_10(X0,X1),X2,X0),
inference(resolution,[status(thm)],[f71,f41]) ).
fof(f113,plain,
! [X0,X1,X2] : ~ pd0_1(sk0_6(X0,X1),X2,X0),
inference(resolution,[status(thm)],[f71,f35]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( pd0_1(X0,sk0_1(sk0_0),sk0_0)
| ~ r4(X1,X2,X3)
| ~ r2(X4,X1)
| ~ r1(X5)
| ~ r2(X5,X4)
| ~ r3(X2,X6,X3)
| ~ r3(X7,X8,X3)
| ~ r2(X9,X8)
| ~ r2(X10,X9)
| ~ r2(X0,X10) ),
inference(resolution,[status(thm)],[f22,f91]) ).
fof(f123,plain,
! [X0,X1] : sk0_6(X0,X1) = sk0_1(X0),
inference(resolution,[status(thm)],[f23,f113]) ).
fof(f124,plain,
! [X0,X1] : sk0_10(X0,X1) = sk0_1(X0),
inference(resolution,[status(thm)],[f23,f112]) ).
fof(f173,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ r4(X0,X1,X2)
| ~ r2(X3,X0)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X1,X5,X2)
| ~ r3(X6,X7,X2)
| ~ r2(X8,X7)
| ~ r2(X9,X8)
| ~ r2(sk0_1(sk0_0),X9) ),
inference(resolution,[status(thm)],[f118,f86]) ).
fof(f174,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ r4(X0,X1,X2)
| ~ r2(X3,X0)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X1,X5,X2)
| ~ r3(X6,X7,X2)
| ~ r2(X8,X7)
| ~ r2(sk0_10(sk0_1(sk0_0),X9),X8) ),
inference(resolution,[status(thm)],[f173,f41]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r4(X0,X1,X2)
| ~ r2(X3,X0)
| ~ r2(sk0_0,X3)
| ~ r3(X1,X4,X2)
| ~ r3(X5,X6,X2)
| ~ r2(X7,X6)
| ~ r2(sk0_10(sk0_1(sk0_0),X8),X7) ),
inference(resolution,[status(thm)],[f174,f89]) ).
fof(f179,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r4(X0,X1,X2)
| ~ r2(sk0_10(sk0_0,X3),X0)
| ~ r3(X1,X4,X2)
| ~ r3(X5,X6,X2)
| ~ r2(X7,X6)
| ~ r2(sk0_10(sk0_1(sk0_0),X8),X7) ),
inference(resolution,[status(thm)],[f177,f41]) ).
fof(f182,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r4(X0,X1,X2)
| ~ r2(sk0_10(sk0_0,X3),X0)
| ~ r3(X1,X4,X2)
| ~ r3(X5,X6,X2)
| ~ r2(sk0_10(sk0_10(sk0_1(sk0_0),X7),X8),X6) ),
inference(resolution,[status(thm)],[f179,f41]) ).
fof(f185,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r4(sk0_10(sk0_10(sk0_0,X0),X1),X2,X3)
| ~ r3(X2,X4,X3)
| ~ r3(X5,X6,X3)
| ~ r2(sk0_10(sk0_10(sk0_1(sk0_0),X7),X8),X6) ),
inference(resolution,[status(thm)],[f182,f41]) ).
fof(f245,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r4(sk0_10(sk0_10(sk0_0,X0),X1),X2,X3)
| ~ r3(X2,X4,X3)
| ~ r3(X5,sk0_10(sk0_10(sk0_10(sk0_1(sk0_0),X6),X7),X8),X3) ),
inference(resolution,[status(thm)],[f185,f41]) ).
fof(f318,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ r4(sk0_10(sk0_10(sk0_0,X0),X1),X2,X3)
| ~ r3(X2,X4,X3)
| ~ r3(X5,sk0_10(sk0_10(sk0_1(sk0_1(sk0_0)),X6),X7),X3) ),
inference(backward_demodulation,[status(thm)],[f124,f245]) ).
fof(f319,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ r4(sk0_1(sk0_10(sk0_0,X0)),X1,X2)
| ~ r3(X1,X3,X2)
| ~ r3(X4,sk0_10(sk0_10(sk0_1(sk0_1(sk0_0)),X5),X6),X2) ),
inference(forward_demodulation,[status(thm)],[f124,f318]) ).
fof(f320,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,X1)
| ~ r3(X0,X2,X1)
| ~ r3(X3,sk0_10(sk0_10(sk0_1(sk0_1(sk0_0)),X4),X5),X1) ),
inference(forward_demodulation,[status(thm)],[f124,f319]) ).
fof(f321,plain,
! [X0,X1,X2,X3,X4] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,X1)
| ~ r3(X0,X2,X1)
| ~ r3(X3,sk0_1(sk0_10(sk0_1(sk0_1(sk0_0)),X4)),X1) ),
inference(forward_demodulation,[status(thm)],[f124,f320]) ).
fof(f322,plain,
! [X0,X1,X2,X3] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,X1)
| ~ r3(X0,X2,X1)
| ~ r3(X3,sk0_1(sk0_1(sk0_1(sk0_1(sk0_0)))),X1) ),
inference(forward_demodulation,[status(thm)],[f124,f321]) ).
fof(f356,plain,
! [X0,X1,X2] : ~ pd0_1(sk0_4(X0,X1),X2,sk0_7(X0,X1)),
inference(resolution,[status(thm)],[f38,f71]) ).
fof(f361,plain,
! [X0,X1] : r3(X0,sk0_1(X1),sk0_5(X1,X0)),
inference(forward_demodulation,[status(thm)],[f123,f36]) ).
fof(f362,plain,
! [X0,X1] : r3(X0,sk0_1(X1),sk0_4(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f361]) ).
fof(f363,plain,
! [X0,X1] : r4(X0,sk0_1(X1),sk0_9(X1,X0)),
inference(forward_demodulation,[status(thm)],[f124,f42]) ).
fof(f364,plain,
! [X0,X1] : r4(X0,sk0_1(X1),sk0_8(X1,X0)),
inference(forward_demodulation,[status(thm)],[f43,f363]) ).
fof(f365,plain,
! [X0,X1,X2] : ~ pd0_2(sk0_4(X0,X1),X2,sk0_1(X0),X1),
inference(resolution,[status(thm)],[f74,f362]) ).
fof(f366,plain,
! [X0,X1] : ~ pd0_2(X0,X1,sk0_13(X0),X0),
inference(resolution,[status(thm)],[f74,f111]) ).
fof(f367,plain,
! [X0,X1,X2] : ~ pd0_2(sk0_7(X0,X1),X2,X0,X1),
inference(resolution,[status(thm)],[f74,f39]) ).
fof(f370,plain,
! [X0,X1] : ~ pd0_3(sk0_14(X0),X1,sk0_15(X0),X0),
inference(resolution,[status(thm)],[f77,f53]) ).
fof(f371,plain,
! [X0,X1,X2] : ~ pd0_3(sk0_11(X0,X1),X2,X0,X1),
inference(resolution,[status(thm)],[f77,f45]) ).
fof(f372,plain,
! [X0] : X0 = sk0_2(sk0_13(X0),X0),
inference(resolution,[status(thm)],[f28,f366]) ).
fof(f466,plain,
! [X0,X1] : sk0_4(X0,X1) = sk0_1(sk0_7(X0,X1)),
inference(resolution,[status(thm)],[f356,f23]) ).
fof(f480,plain,
! [X0,X1] : sk0_4(X0,X1) = sk0_2(sk0_1(X0),X1),
inference(resolution,[status(thm)],[f365,f28]) ).
fof(f518,plain,
! [X0,X1,X2] : ~ pd0_2(sk0_8(X0,X1),X2,X1,sk0_11(X0,X1)),
inference(resolution,[status(thm)],[f44,f74]) ).
fof(f521,plain,
! [X0,X1] : ~ pd0_0(sk0_13(X0),X1),
inference(resolution,[status(thm)],[f48,f68]) ).
fof(f525,plain,
! [X0,X1] : ~ pd0_0(sk0_15(X0),X1),
inference(resolution,[status(thm)],[f52,f68]) ).
fof(f589,plain,
! [X0] : sk0_13(X0) = sk0_0,
inference(resolution,[status(thm)],[f521,f18]) ).
fof(f631,plain,
! [X0] : X0 = sk0_2(sk0_0,X0),
inference(backward_demodulation,[status(thm)],[f589,f372]) ).
fof(f634,plain,
! [X0] : sk0_15(X0) = sk0_0,
inference(resolution,[status(thm)],[f525,f18]) ).
fof(f642,plain,
! [X0,X1] : ~ pd0_3(sk0_14(X0),X1,sk0_0,X0),
inference(backward_demodulation,[status(thm)],[f634,f370]) ).
fof(f658,plain,
! [X0,X1] : sk0_8(X0,X1) = sk0_2(X1,sk0_11(X0,X1)),
inference(resolution,[status(thm)],[f518,f28]) ).
fof(f666,plain,
! [X0] : r1(sk0_14(X0)),
inference(forward_demodulation,[status(thm)],[f55,f54]) ).
fof(f668,plain,
! [X0,X1] : ~ pd0_0(sk0_14(X0),X1),
inference(resolution,[status(thm)],[f666,f68]) ).
fof(f734,plain,
! [X0] : sk0_14(X0) = sk0_0,
inference(resolution,[status(thm)],[f668,f18]) ).
fof(f772,plain,
! [X0,X1] : ~ pd0_3(sk0_0,X0,sk0_0,X1),
inference(backward_demodulation,[status(thm)],[f734,f642]) ).
fof(f783,plain,
! [X0] : sk0_0 = sk0_3(sk0_0,X0),
inference(resolution,[status(thm)],[f772,f33]) ).
fof(f868,plain,
! [X0,X1] :
( ~ pd0_0(sk0_17(X0),X1)
| X0 = sk0_18(X0) ),
inference(resolution,[status(thm)],[f107,f61]) ).
fof(f873,plain,
! [X0,X1] : sk0_7(X0,X1) = sk0_2(X0,X1),
inference(resolution,[status(thm)],[f367,f28]) ).
fof(f1124,plain,
! [X0,X1] : sk0_4(X0,X1) = sk0_1(sk0_2(X0,X1)),
inference(backward_demodulation,[status(thm)],[f873,f466]) ).
fof(f1128,plain,
! [X0,X1] : r2(sk0_2(X0,X1),sk0_4(X0,X1)),
inference(backward_demodulation,[status(thm)],[f873,f38]) ).
fof(f1136,plain,
! [X0] :
( X0 = sk0_18(X0)
| sk0_17(X0) = sk0_0 ),
inference(resolution,[status(thm)],[f868,f18]) ).
fof(f1200,plain,
! [X0] :
( pd0_4(sk0_0,X0)
| X0 = sk0_18(X0)
| X0 = sk0_18(X0) ),
inference(paramodulation,[status(thm)],[f1136,f61]) ).
fof(f1201,plain,
! [X0] :
( pd0_4(sk0_0,X0)
| X0 = sk0_18(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f1200]) ).
fof(f1221,plain,
! [X0] :
( X0 = sk0_18(X0)
| X0 = sk0_0 ),
inference(resolution,[status(thm)],[f1201,f81]) ).
fof(f1311,plain,
! [X0] : sk0_4(sk0_0,X0) = sk0_1(X0),
inference(paramodulation,[status(thm)],[f631,f1124]) ).
fof(f1312,plain,
! [X0,X1] : sk0_4(sk0_1(X0),X1) = sk0_1(sk0_4(X0,X1)),
inference(paramodulation,[status(thm)],[f480,f1124]) ).
fof(f1344,plain,
! [X0,X1] : ~ pd0_2(sk0_1(X0),X1,sk0_1(sk0_0),X0),
inference(paramodulation,[status(thm)],[f1311,f365]) ).
fof(f1355,plain,
! [X0,X1] :
( r2(sk0_2(X0,X1),sk0_0)
| sk0_4(X0,X1) = sk0_18(sk0_4(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1221,f1128]) ).
fof(f1356,plain,
! [X0,X1] : sk0_4(X0,X1) = sk0_18(sk0_4(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f1355,f90]) ).
fof(f1366,plain,
! [X0,X1] : sk0_11(X0,X1) = sk0_3(X0,X1),
inference(resolution,[status(thm)],[f371,f33]) ).
fof(f1590,plain,
! [X0,X1,X2] : ~ pd0_2(sk0_8(X0,X1),X2,X1,sk0_3(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1366,f518]) ).
fof(f2171,plain,
! [X0] : sk0_4(sk0_0,X0) = sk0_18(sk0_1(X0)),
inference(paramodulation,[status(thm)],[f1311,f1356]) ).
fof(f2173,plain,
! [X0,X1] : sk0_4(sk0_0,sk0_2(X0,X1)) = sk0_18(sk0_4(X0,X1)),
inference(paramodulation,[status(thm)],[f1124,f2171]) ).
fof(f2363,plain,
! [X0,X1] : ~ pd0_2(sk0_8(sk0_0,X0),X1,X0,sk0_0),
inference(paramodulation,[status(thm)],[f783,f1590]) ).
fof(f2535,plain,
! [X0] : sk0_1(X0) = sk0_2(sk0_1(sk0_0),X0),
inference(resolution,[status(thm)],[f1344,f28]) ).
fof(f2539,plain,
! [X0] : sk0_4(sk0_0,sk0_1(X0)) = sk0_18(sk0_4(sk0_1(sk0_0),X0)),
inference(paramodulation,[status(thm)],[f2535,f2173]) ).
fof(f4878,plain,
! [X0] : sk0_4(sk0_0,sk0_1(X0)) = sk0_4(sk0_1(sk0_0),X0),
inference(paramodulation,[status(thm)],[f1356,f2539]) ).
fof(f4940,plain,
! [X0] : r3(X0,sk0_1(sk0_1(sk0_0)),sk0_4(sk0_0,sk0_1(X0))),
inference(paramodulation,[status(thm)],[f4878,f362]) ).
fof(f4941,plain,
! [X0] : r3(X0,sk0_1(sk0_1(sk0_0)),sk0_1(sk0_1(X0))),
inference(forward_demodulation,[status(thm)],[f1311,f4940]) ).
fof(f4963,plain,
! [X0,X1] : ~ pd0_2(sk0_1(sk0_1(X0)),X1,sk0_1(sk0_1(sk0_0)),X0),
inference(resolution,[status(thm)],[f4941,f74]) ).
fof(f5015,plain,
! [X0] : sk0_1(sk0_1(X0)) = sk0_2(sk0_1(sk0_1(sk0_0)),X0),
inference(resolution,[status(thm)],[f4963,f28]) ).
fof(f5156,plain,
! [X0] : sk0_8(sk0_0,X0) = sk0_2(X0,sk0_0),
inference(resolution,[status(thm)],[f2363,f28]) ).
fof(f5164,plain,
! [X0] : r4(X0,sk0_1(sk0_0),sk0_2(X0,sk0_0)),
inference(paramodulation,[status(thm)],[f5156,f364]) ).
fof(f6170,plain,
! [X0,X1] : r3(X0,sk0_1(sk0_1(X1)),sk0_1(sk0_4(X1,X0))),
inference(paramodulation,[status(thm)],[f1312,f362]) ).
fof(f6187,plain,
! [X0,X1] : sk0_8(X0,X1) = sk0_2(X1,sk0_3(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1366,f658]) ).
fof(f6191,plain,
! [X0,X1] : sk0_8(X0,sk0_1(X1)) = sk0_4(X1,sk0_3(X0,sk0_1(X1))),
inference(paramodulation,[status(thm)],[f480,f6187]) ).
fof(f7039,plain,
r4(sk0_1(sk0_1(sk0_0)),sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))),
inference(paramodulation,[status(thm)],[f5015,f5164]) ).
fof(f8048,plain,
! [X0,X1,X2] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_4(sk0_1(sk0_1(sk0_0)),X1)))
| ~ r3(X0,X2,sk0_1(sk0_4(sk0_1(sk0_1(sk0_0)),X1))) ),
inference(resolution,[status(thm)],[f6170,f322]) ).
fof(f8049,plain,
! [X0,X1,X2] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_1(sk0_4(sk0_1(sk0_0),X1))))
| ~ r3(X0,X2,sk0_1(sk0_4(sk0_1(sk0_1(sk0_0)),X1))) ),
inference(forward_demodulation,[status(thm)],[f1312,f8048]) ).
fof(f8050,plain,
! [X0,X1,X2] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_1(sk0_4(sk0_0,sk0_1(X1)))))
| ~ r3(X0,X2,sk0_1(sk0_4(sk0_1(sk0_1(sk0_0)),X1))) ),
inference(forward_demodulation,[status(thm)],[f4878,f8049]) ).
fof(f8051,plain,
! [X0,X1,X2] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_1(sk0_1(sk0_1(X1)))))
| ~ r3(X0,X2,sk0_1(sk0_4(sk0_1(sk0_1(sk0_0)),X1))) ),
inference(forward_demodulation,[status(thm)],[f1311,f8050]) ).
fof(f8052,plain,
! [X0,X1,X2] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_1(sk0_1(sk0_1(X1)))))
| ~ r3(X0,X2,sk0_1(sk0_1(sk0_4(sk0_1(sk0_0),X1)))) ),
inference(forward_demodulation,[status(thm)],[f1312,f8051]) ).
fof(f8053,plain,
! [X0,X1,X2] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_1(sk0_1(sk0_1(X1)))))
| ~ r3(X0,X2,sk0_1(sk0_1(sk0_4(sk0_0,sk0_1(X1))))) ),
inference(forward_demodulation,[status(thm)],[f4878,f8052]) ).
fof(f8054,plain,
! [X0,X1,X2] :
( ~ r4(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_1(sk0_1(sk0_1(X1)))))
| ~ r3(X0,X2,sk0_1(sk0_1(sk0_1(sk0_1(X1))))) ),
inference(forward_demodulation,[status(thm)],[f1311,f8053]) ).
fof(f12610,plain,
! [X0] : ~ pd0_3(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))),
inference(resolution,[status(thm)],[f7039,f77]) ).
fof(f14811,plain,
sk0_1(sk0_1(sk0_0)) = sk0_3(sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))),
inference(resolution,[status(thm)],[f12610,f33]) ).
fof(f27623,plain,
sk0_8(sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))) = sk0_4(sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))),
inference(paramodulation,[status(thm)],[f14811,f6191]) ).
fof(f31846,plain,
r4(sk0_1(sk0_1(sk0_0)),sk0_1(sk0_1(sk0_0)),sk0_4(sk0_1(sk0_0),sk0_1(sk0_1(sk0_0)))),
inference(paramodulation,[status(thm)],[f27623,f364]) ).
fof(f31847,plain,
r4(sk0_1(sk0_1(sk0_0)),sk0_1(sk0_1(sk0_0)),sk0_4(sk0_0,sk0_1(sk0_1(sk0_1(sk0_0))))),
inference(forward_demodulation,[status(thm)],[f4878,f31846]) ).
fof(f31848,plain,
r4(sk0_1(sk0_1(sk0_0)),sk0_1(sk0_1(sk0_0)),sk0_1(sk0_1(sk0_1(sk0_1(sk0_0))))),
inference(forward_demodulation,[status(thm)],[f1311,f31847]) ).
fof(f31858,plain,
! [X0] : ~ r3(sk0_1(sk0_1(sk0_0)),X0,sk0_1(sk0_1(sk0_1(sk0_1(sk0_0))))),
inference(resolution,[status(thm)],[f31848,f8054]) ).
fof(f32981,plain,
$false,
inference(resolution,[status(thm)],[f31858,f4941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : NUN058+2 : TPTP v8.1.2. Released v7.3.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n009.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Apr 29 22:31:56 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.6.0
% 42.99/5.75 % Refutation found
% 42.99/5.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 42.99/5.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 43.94/5.86 % Elapsed time: 5.536320 seconds
% 43.94/5.86 % CPU time: 43.559927 seconds
% 43.94/5.86 % Total memory used: 336.642 MB
% 43.94/5.86 % Net memory used: 326.133 MB
%------------------------------------------------------------------------------