TSTP Solution File: KLE145+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : KLE145+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n024.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 : Thu Aug 31 05:37:01 EDT 2023
% Result : Theorem 4.63s 1.08s
% Output : Refutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of formulae : 160 ( 94 unt; 0 def)
% Number of atoms : 228 ( 170 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 138 ( 70 ~; 62 |; 1 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 163 (; 161 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25263,plain,
$false,
inference(subsumption_resolution,[],[f52,f25254]) ).
fof(f25254,plain,
sF1 = sF2,
inference(subsumption_resolution,[],[f21544,f25199]) ).
fof(f25199,plain,
sF2 = addition(one,multiplication(sK0,sF2)),
inference(backward_demodulation,[],[f10692,f25171]) ).
fof(f25171,plain,
sF2 = star(multiplication(sK0,sF1)),
inference(trivial_inequality_removal,[],[f25170]) ).
fof(f25170,plain,
( sF2 != sF2
| sF2 = star(multiplication(sK0,sF1)) ),
inference(forward_demodulation,[],[f25169,f417]) ).
fof(f417,plain,
sF2 = multiplication(sF2,sF1),
inference(forward_demodulation,[],[f414,f126]) ).
fof(f126,plain,
sF1 = addition(one,sF1),
inference(superposition,[],[f88,f73]) ).
fof(f73,plain,
sF1 = addition(one,multiplication(sK0,sF1)),
inference(superposition,[],[f53,f50]) ).
fof(f50,plain,
strong_iteration(sK0) = sF1,
introduced(function_definition,[]) ).
fof(f53,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(backward_demodulation,[],[f36,f40]) ).
fof(f40,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',additive_commutativity) ).
fof(f36,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',infty_unfold1) ).
fof(f88,plain,
! [X2,X3] : addition(X2,X3) = addition(X2,addition(X2,X3)),
inference(superposition,[],[f43,f35]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',idempotence) ).
fof(f43,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',additive_associativity) ).
fof(f414,plain,
sF2 = multiplication(sF2,addition(one,sF1)),
inference(backward_demodulation,[],[f207,f394]) ).
fof(f394,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f45,f33]) ).
fof(f33,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',multiplicative_right_identity) ).
fof(f45,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',distributivity1) ).
fof(f207,plain,
sF2 = addition(sF2,multiplication(sF2,sF1)),
inference(forward_demodulation,[],[f187,f40]) ).
fof(f187,plain,
sF2 = addition(multiplication(sF2,sF1),sF2),
inference(superposition,[],[f117,f69]) ).
fof(f69,plain,
sF2 = addition(one,multiplication(sF2,sF1)),
inference(superposition,[],[f38,f51]) ).
fof(f51,plain,
star(sF1) = sF2,
introduced(function_definition,[]) ).
fof(f38,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',star_unfold2) ).
fof(f117,plain,
! [X2,X1] : addition(X2,X1) = addition(X1,addition(X2,X1)),
inference(superposition,[],[f88,f40]) ).
fof(f25169,plain,
( sF2 != multiplication(sF2,sF1)
| sF2 = star(multiplication(sK0,sF1)) ),
inference(forward_demodulation,[],[f25168,f1556]) ).
fof(f1556,plain,
sF2 = addition(sF2,sK0),
inference(forward_demodulation,[],[f1555,f1446]) ).
fof(f1446,plain,
sF2 = multiplication(addition(sF2,sK0),sF1),
inference(backward_demodulation,[],[f1363,f1406]) ).
fof(f1406,plain,
! [X27] : multiplication(addition(sF2,X27),sF1) = addition(sF2,multiplication(X27,sF1)),
inference(superposition,[],[f46,f417]) ).
fof(f46,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',distributivity2) ).
fof(f1363,plain,
sF2 = addition(sF2,multiplication(sK0,sF1)),
inference(backward_demodulation,[],[f1315,f1350]) ).
fof(f1350,plain,
sF2 = multiplication(sF1,sF2),
inference(forward_demodulation,[],[f1342,f63]) ).
fof(f63,plain,
sF2 = addition(one,multiplication(sF1,sF2)),
inference(superposition,[],[f37,f51]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',star_unfold1) ).
fof(f1342,plain,
multiplication(sF1,sF2) = addition(one,multiplication(sF1,sF2)),
inference(superposition,[],[f249,f1313]) ).
fof(f1313,plain,
multiplication(sF1,sF2) = addition(sF2,sF1),
inference(forward_demodulation,[],[f1312,f141]) ).
fof(f141,plain,
sF2 = addition(sF2,one),
inference(forward_demodulation,[],[f127,f40]) ).
fof(f127,plain,
sF2 = addition(one,sF2),
inference(superposition,[],[f88,f63]) ).
fof(f1312,plain,
addition(sF2,sF1) = multiplication(sF1,addition(sF2,one)),
inference(forward_demodulation,[],[f1311,f437]) ).
fof(f437,plain,
! [X6,X7,X5] : multiplication(X5,addition(X6,X7)) = multiplication(X5,addition(X7,X6)),
inference(forward_demodulation,[],[f403,f45]) ).
fof(f403,plain,
! [X6,X7,X5] : addition(multiplication(X5,X7),multiplication(X5,X6)) = multiplication(X5,addition(X6,X7)),
inference(superposition,[],[f45,f40]) ).
fof(f1311,plain,
addition(sF2,sF1) = multiplication(sF1,addition(one,sF2)),
inference(forward_demodulation,[],[f1310,f394]) ).
fof(f1310,plain,
addition(sF2,sF1) = addition(sF1,multiplication(sF1,sF2)),
inference(forward_demodulation,[],[f1286,f40]) ).
fof(f1286,plain,
addition(sF2,sF1) = addition(multiplication(sF1,sF2),sF1),
inference(superposition,[],[f97,f249]) ).
fof(f97,plain,
! [X23] : addition(one,addition(multiplication(sF1,sF2),X23)) = addition(sF2,X23),
inference(superposition,[],[f43,f63]) ).
fof(f249,plain,
! [X0] : addition(X0,sF1) = addition(one,addition(X0,sF1)),
inference(superposition,[],[f149,f40]) ).
fof(f149,plain,
! [X0] : addition(sF1,X0) = addition(one,addition(sF1,X0)),
inference(superposition,[],[f43,f126]) ).
fof(f1315,plain,
multiplication(sF1,sF2) = addition(sF2,multiplication(sK0,sF1)),
inference(backward_demodulation,[],[f261,f1313]) ).
fof(f261,plain,
addition(sF2,multiplication(sK0,sF1)) = addition(sF2,sF1),
inference(superposition,[],[f151,f73]) ).
fof(f151,plain,
! [X0] : addition(sF2,X0) = addition(sF2,addition(one,X0)),
inference(superposition,[],[f43,f141]) ).
fof(f1555,plain,
addition(sF2,sK0) = multiplication(addition(sF2,sK0),sF1),
inference(forward_demodulation,[],[f1554,f126]) ).
fof(f1554,plain,
addition(sF2,sK0) = multiplication(addition(sF2,sK0),addition(one,sF1)),
inference(forward_demodulation,[],[f1553,f88]) ).
fof(f1553,plain,
multiplication(addition(sF2,sK0),addition(one,sF1)) = addition(sF2,addition(sF2,sK0)),
inference(forward_demodulation,[],[f1545,f40]) ).
fof(f1545,plain,
multiplication(addition(sF2,sK0),addition(one,sF1)) = addition(addition(sF2,sK0),sF2),
inference(superposition,[],[f394,f1446]) ).
fof(f25168,plain,
( sF2 != multiplication(addition(sF2,sK0),sF1)
| sF2 = star(multiplication(sK0,sF1)) ),
inference(forward_demodulation,[],[f25142,f1406]) ).
fof(f25142,plain,
( sF2 = star(multiplication(sK0,sF1))
| sF2 != addition(sF2,multiplication(sK0,sF1)) ),
inference(superposition,[],[f18429,f22800]) ).
fof(f22800,plain,
! [X3] :
( sF2 = multiplication(star(X3),sF2)
| sF2 != addition(sF2,X3) ),
inference(forward_demodulation,[],[f22799,f88]) ).
fof(f22799,plain,
! [X3] :
( sF2 != addition(sF2,addition(sF2,X3))
| sF2 = multiplication(star(X3),sF2) ),
inference(forward_demodulation,[],[f22726,f40]) ).
fof(f22726,plain,
! [X3] :
( sF2 = multiplication(star(X3),sF2)
| sF2 != addition(addition(sF2,X3),sF2) ),
inference(resolution,[],[f20133,f42]) ).
fof(f42,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',order) ).
fof(f20133,plain,
! [X0] :
( ~ leq(addition(sF2,X0),sF2)
| sF2 = multiplication(star(X0),sF2) ),
inference(forward_demodulation,[],[f20051,f417]) ).
fof(f20051,plain,
! [X0] :
( sF2 = multiplication(star(X0),sF2)
| ~ leq(addition(multiplication(sF2,sF1),X0),sF2) ),
inference(resolution,[],[f13441,f2445]) ).
fof(f2445,plain,
! [X0,X1] :
( leq(multiplication(X0,sF2),X1)
| ~ leq(addition(multiplication(X1,sF1),X0),X1) ),
inference(superposition,[],[f48,f51]) ).
fof(f48,plain,
! [X2,X0,X1] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X2,X0),X1),X2)
=> leq(multiplication(X1,star(X0)),X2) ),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',star_induction2) ).
fof(f13441,plain,
! [X8,X9] :
( ~ leq(multiplication(X8,X9),X9)
| multiplication(star(X8),X9) = X9 ),
inference(forward_demodulation,[],[f13440,f38]) ).
fof(f13440,plain,
! [X8,X9] :
( multiplication(addition(one,multiplication(star(X8),X8)),X9) = X9
| ~ leq(multiplication(X8,X9),X9) ),
inference(forward_demodulation,[],[f13439,f2483]) ).
fof(f2483,plain,
! [X14,X12,X13] : multiplication(addition(one,multiplication(X12,X13)),X14) = addition(X14,multiplication(X12,multiplication(X13,X14))),
inference(superposition,[],[f1400,f44]) ).
fof(f44,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',multiplicative_associativity) ).
fof(f1400,plain,
! [X16,X17] : multiplication(addition(one,X17),X16) = addition(X16,multiplication(X17,X16)),
inference(superposition,[],[f46,f34]) ).
fof(f34,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',multiplicative_left_identity) ).
fof(f13439,plain,
! [X8,X9] :
( addition(X9,multiplication(star(X8),multiplication(X8,X9))) = X9
| ~ leq(multiplication(X8,X9),X9) ),
inference(forward_demodulation,[],[f13297,f40]) ).
fof(f13297,plain,
! [X8,X9] :
( ~ leq(multiplication(X8,X9),X9)
| addition(multiplication(star(X8),multiplication(X8,X9)),X9) = X9 ),
inference(superposition,[],[f3912,f35]) ).
fof(f3912,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| addition(multiplication(star(X0),X2),X1) = X1 ),
inference(resolution,[],[f49,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X2,X0,X1] :
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X2),X1),X2)
=> leq(multiplication(star(X0),X1),X2) ),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',star_induction1) ).
fof(f18429,plain,
star(multiplication(sK0,sF1)) = multiplication(star(multiplication(sK0,sF1)),sF2),
inference(trivial_inequality_removal,[],[f18426]) ).
fof(f18426,plain,
( star(multiplication(sK0,sF1)) != star(multiplication(sK0,sF1))
| star(multiplication(sK0,sF1)) = multiplication(star(multiplication(sK0,sF1)),sF2) ),
inference(superposition,[],[f16886,f456]) ).
fof(f456,plain,
star(multiplication(sK0,sF1)) = multiplication(star(multiplication(sK0,sF1)),sF1),
inference(superposition,[],[f411,f73]) ).
fof(f411,plain,
! [X16] : star(X16) = multiplication(star(X16),addition(one,X16)),
inference(backward_demodulation,[],[f204,f394]) ).
fof(f204,plain,
! [X16] : star(X16) = addition(star(X16),multiplication(star(X16),X16)),
inference(forward_demodulation,[],[f184,f40]) ).
fof(f184,plain,
! [X16] : star(X16) = addition(multiplication(star(X16),X16),star(X16)),
inference(superposition,[],[f117,f38]) ).
fof(f16886,plain,
! [X3] :
( multiplication(X3,sF1) != X3
| multiplication(X3,sF2) = X3 ),
inference(forward_demodulation,[],[f16885,f126]) ).
fof(f16885,plain,
! [X3] :
( multiplication(X3,addition(one,sF1)) != X3
| multiplication(X3,sF2) = X3 ),
inference(forward_demodulation,[],[f16884,f394]) ).
fof(f16884,plain,
! [X3] :
( addition(X3,multiplication(X3,sF1)) != X3
| multiplication(X3,sF2) = X3 ),
inference(forward_demodulation,[],[f16862,f40]) ).
fof(f16862,plain,
! [X3] :
( multiplication(X3,sF2) = X3
| addition(multiplication(X3,sF1),X3) != X3 ),
inference(resolution,[],[f14093,f42]) ).
fof(f14093,plain,
! [X4] :
( ~ leq(multiplication(X4,sF1),X4)
| multiplication(X4,sF2) = X4 ),
inference(backward_demodulation,[],[f13610,f13917]) ).
fof(f13917,plain,
sF2 = star(sF2),
inference(trivial_inequality_removal,[],[f13916]) ).
fof(f13916,plain,
( sF2 != sF2
| sF2 = star(sF2) ),
inference(forward_demodulation,[],[f13887,f35]) ).
fof(f13887,plain,
( sF2 = star(sF2)
| sF2 != addition(sF2,sF2) ),
inference(resolution,[],[f13878,f42]) ).
fof(f13878,plain,
( ~ leq(sF2,sF2)
| sF2 = star(sF2) ),
inference(forward_demodulation,[],[f13788,f1732]) ).
fof(f1732,plain,
star(sF2) = multiplication(sF2,star(sF2)),
inference(superposition,[],[f1587,f141]) ).
fof(f1587,plain,
! [X8] : star(X8) = multiplication(addition(X8,one),star(X8)),
inference(superposition,[],[f1443,f40]) ).
fof(f1443,plain,
! [X14] : star(X14) = multiplication(addition(one,X14),star(X14)),
inference(backward_demodulation,[],[f202,f1400]) ).
fof(f202,plain,
! [X14] : star(X14) = addition(star(X14),multiplication(X14,star(X14))),
inference(forward_demodulation,[],[f182,f40]) ).
fof(f182,plain,
! [X14] : star(X14) = addition(multiplication(X14,star(X14)),star(X14)),
inference(superposition,[],[f117,f37]) ).
fof(f13788,plain,
( ~ leq(sF2,sF2)
| sF2 = multiplication(sF2,star(sF2)) ),
inference(superposition,[],[f13046,f13772]) ).
fof(f13772,plain,
sF2 = multiplication(sF2,sF2),
inference(trivial_inequality_removal,[],[f13771]) ).
fof(f13771,plain,
( sF2 != sF2
| sF2 = multiplication(sF2,sF2) ),
inference(forward_demodulation,[],[f13747,f35]) ).
fof(f13747,plain,
( sF2 = multiplication(sF2,sF2)
| sF2 != addition(sF2,sF2) ),
inference(resolution,[],[f13654,f42]) ).
fof(f13654,plain,
( ~ leq(sF2,sF2)
| sF2 = multiplication(sF2,sF2) ),
inference(forward_demodulation,[],[f13605,f51]) ).
fof(f13605,plain,
( ~ leq(sF2,sF2)
| sF2 = multiplication(sF2,star(sF1)) ),
inference(superposition,[],[f13046,f417]) ).
fof(f13046,plain,
! [X8,X9] :
( ~ leq(multiplication(X8,X9),X8)
| multiplication(X8,star(X9)) = X8 ),
inference(forward_demodulation,[],[f13045,f37]) ).
fof(f13045,plain,
! [X8,X9] :
( multiplication(X8,addition(one,multiplication(X9,star(X9)))) = X8
| ~ leq(multiplication(X8,X9),X8) ),
inference(forward_demodulation,[],[f13044,f394]) ).
fof(f13044,plain,
! [X8,X9] :
( addition(X8,multiplication(X8,multiplication(X9,star(X9)))) = X8
| ~ leq(multiplication(X8,X9),X8) ),
inference(forward_demodulation,[],[f13043,f44]) ).
fof(f13043,plain,
! [X8,X9] :
( addition(X8,multiplication(multiplication(X8,X9),star(X9))) = X8
| ~ leq(multiplication(X8,X9),X8) ),
inference(forward_demodulation,[],[f12882,f40]) ).
fof(f12882,plain,
! [X8,X9] :
( ~ leq(multiplication(X8,X9),X8)
| addition(multiplication(multiplication(X8,X9),star(X9)),X8) = X8 ),
inference(superposition,[],[f2444,f35]) ).
fof(f2444,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| addition(multiplication(X2,star(X1)),X0) = X0 ),
inference(resolution,[],[f48,f41]) ).
fof(f13610,plain,
! [X4] :
( ~ leq(multiplication(X4,sF1),X4)
| multiplication(X4,star(sF2)) = X4 ),
inference(forward_demodulation,[],[f13609,f126]) ).
fof(f13609,plain,
! [X4] :
( ~ leq(multiplication(X4,addition(one,sF1)),X4)
| multiplication(X4,star(sF2)) = X4 ),
inference(forward_demodulation,[],[f13608,f394]) ).
fof(f13608,plain,
! [X4] :
( ~ leq(addition(X4,multiplication(X4,sF1)),X4)
| multiplication(X4,star(sF2)) = X4 ),
inference(forward_demodulation,[],[f13513,f40]) ).
fof(f13513,plain,
! [X4] :
( multiplication(X4,star(sF2)) = X4
| ~ leq(addition(multiplication(X4,sF1),X4),X4) ),
inference(resolution,[],[f13046,f2445]) ).
fof(f10692,plain,
star(multiplication(sK0,sF1)) = addition(one,multiplication(sK0,star(multiplication(sK0,sF1)))),
inference(superposition,[],[f224,f1582]) ).
fof(f1582,plain,
star(multiplication(sK0,sF1)) = multiplication(sF1,star(multiplication(sK0,sF1))),
inference(superposition,[],[f1443,f73]) ).
fof(f224,plain,
! [X2,X3] : star(multiplication(X2,X3)) = addition(one,multiplication(X2,multiplication(X3,star(multiplication(X2,X3))))),
inference(superposition,[],[f37,f44]) ).
fof(f21544,plain,
( sF2 != addition(one,multiplication(sK0,sF2))
| sF1 = sF2 ),
inference(forward_demodulation,[],[f21543,f13772]) ).
fof(f21543,plain,
( multiplication(sF2,sF2) != addition(one,multiplication(sK0,sF2))
| sF1 = sF2 ),
inference(forward_demodulation,[],[f21542,f1556]) ).
fof(f21542,plain,
( addition(one,multiplication(sK0,sF2)) != multiplication(addition(sF2,sK0),sF2)
| sF1 = sF2 ),
inference(forward_demodulation,[],[f21541,f13832]) ).
fof(f13832,plain,
! [X6] : multiplication(addition(one,X6),sF2) = multiplication(addition(sF2,X6),sF2),
inference(forward_demodulation,[],[f13781,f1400]) ).
fof(f13781,plain,
! [X6] : addition(sF2,multiplication(X6,sF2)) = multiplication(addition(sF2,X6),sF2),
inference(superposition,[],[f46,f13772]) ).
fof(f21541,plain,
( multiplication(addition(one,sK0),sF2) != addition(one,multiplication(sK0,sF2))
| sF1 = sF2 ),
inference(forward_demodulation,[],[f21540,f1400]) ).
fof(f21540,plain,
( addition(one,multiplication(sK0,sF2)) != addition(sF2,multiplication(sK0,sF2))
| sF1 = sF2 ),
inference(forward_demodulation,[],[f21490,f151]) ).
fof(f21490,plain,
( sF1 = sF2
| addition(one,multiplication(sK0,sF2)) != addition(sF2,addition(one,multiplication(sK0,sF2))) ),
inference(resolution,[],[f14102,f42]) ).
fof(f14102,plain,
( ~ leq(sF2,addition(one,multiplication(sK0,sF2)))
| sF1 = sF2 ),
inference(backward_demodulation,[],[f13716,f13917]) ).
fof(f13716,plain,
( sF1 = star(sF2)
| ~ leq(sF2,addition(one,multiplication(sK0,sF2))) ),
inference(resolution,[],[f13650,f2829]) ).
fof(f2829,plain,
! [X0] :
( leq(X0,sF1)
| ~ leq(X0,addition(one,multiplication(sK0,X0))) ),
inference(superposition,[],[f1928,f50]) ).
fof(f1928,plain,
! [X0,X1] :
( leq(X1,strong_iteration(X0))
| ~ leq(X1,addition(one,multiplication(X0,X1))) ),
inference(forward_demodulation,[],[f1922,f40]) ).
fof(f1922,plain,
! [X0,X1] :
( leq(X1,strong_iteration(X0))
| ~ leq(X1,addition(multiplication(X0,X1),one)) ),
inference(superposition,[],[f47,f33]) ).
fof(f47,plain,
! [X2,X0,X1] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',infty_coinduction) ).
fof(f13650,plain,
( ~ leq(sF2,sF1)
| sF1 = star(sF2) ),
inference(forward_demodulation,[],[f13584,f2181]) ).
fof(f2181,plain,
star(sF2) = multiplication(sF1,star(sF2)),
inference(superposition,[],[f1496,f1732]) ).
fof(f1496,plain,
! [X4] : multiplication(sF2,X4) = multiplication(sF1,multiplication(sF2,X4)),
inference(superposition,[],[f44,f1350]) ).
fof(f13584,plain,
( ~ leq(sF2,sF1)
| sF1 = multiplication(sF1,star(sF2)) ),
inference(superposition,[],[f13046,f1350]) ).
fof(f52,plain,
sF1 != sF2,
inference(definition_folding,[],[f30,f51,f50,f50]) ).
fof(f30,plain,
strong_iteration(sK0) != star(strong_iteration(sK0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
strong_iteration(sK0) != star(strong_iteration(sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f27]) ).
fof(f27,plain,
( ? [X0] : strong_iteration(X0) != star(strong_iteration(X0))
=> strong_iteration(sK0) != star(strong_iteration(sK0)) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0] : strong_iteration(X0) != star(strong_iteration(X0)),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] : strong_iteration(X0) = star(strong_iteration(X0)),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3] : strong_iteration(X3) = star(strong_iteration(X3)),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3] : strong_iteration(X3) = star(strong_iteration(X3)),
file('/export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653',goals) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE145+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 11:16:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.LkeoE6hZwo/Vampire---4.8_22653
% 0.14/0.37 % (22779)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (22785)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.22/0.42 % (22783)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.22/0.42 % (22784)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.22/0.42 % (22782)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.22/0.42 % (22786)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.22/0.43 % (22780)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.22/0.43 % (22781)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.22/0.43 % (22784)Refutation not found, incomplete strategy% (22784)------------------------------
% 0.22/0.43 % (22784)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (22784)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (22784)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43
% 0.22/0.43 % (22784)Memory used [KB]: 895
% 0.22/0.43 % (22784)Time elapsed: 0.003 s
% 0.22/0.43 % (22784)------------------------------
% 0.22/0.43 % (22784)------------------------------
% 0.22/0.49 % (22787)ott+4_40_av=off:bce=on:fsd=off:fde=unused:nm=4:nwc=1.1:sos=all:sp=frequency_375 on Vampire---4 for (375ds/0Mi)
% 0.22/0.49 % (22787)Refutation not found, incomplete strategy% (22787)------------------------------
% 0.22/0.49 % (22787)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.49 % (22787)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.49 % (22787)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.49
% 0.22/0.49 % (22787)Memory used [KB]: 895
% 0.22/0.49 % (22787)Time elapsed: 0.003 s
% 0.22/0.49 % (22787)------------------------------
% 0.22/0.49 % (22787)------------------------------
% 0.22/0.53 % (22788)lrs-11_16_av=off:bs=on:bsr=on:drc=off:fsd=off:fsr=off:nm=4:sp=scramble:tgt=ground:stl=62_367 on Vampire---4 for (367ds/0Mi)
% 4.63/1.08 % (22788)First to succeed.
% 4.63/1.08 % (22788)Refutation found. Thanks to Tanya!
% 4.63/1.08 % SZS status Theorem for Vampire---4
% 4.63/1.08 % SZS output start Proof for Vampire---4
% See solution above
% 4.63/1.08 % (22788)------------------------------
% 4.63/1.08 % (22788)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 4.63/1.08 % (22788)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 4.63/1.08 % (22788)Termination reason: Refutation
% 4.63/1.08
% 4.63/1.08 % (22788)Memory used [KB]: 17910
% 4.63/1.08 % (22788)Time elapsed: 0.555 s
% 4.63/1.08 % (22788)------------------------------
% 4.63/1.08 % (22788)------------------------------
% 4.63/1.08 % (22779)Success in time 0.717 s
% 4.63/1.08 % Vampire---4.8 exiting
%------------------------------------------------------------------------------